64 IS16 Abstracts IP1 Nonconformist Image Processing with the Graph Thomas Strohmer Laplacian Operator Universityof California,Davis Departmentof Mathematics The key building blocks of modern image processing are [email protected] two-fold: a measure of affinity between pixels; and an op- erator that turns these affinities into filters that can ac- complishavarietyofusefultasks. Examplesoftheaffinity IP4 measurearemany,includingbilateral, NLM,etc. Andthe Semantic Scene Parsing by Entropy Pursuit standard operator usedtoconstruct thefiltersis the(nor- malized) weighted average of the affinities. But if we con- The grand challenge of computer vision is to build a ma- sider thepixels in an image as nodes in a weighted graph, chinewhichproducesarichsemanticdescriptionofanun- the Laplacian operator on this graph gives us a strikingly derlyingscene based on image data. Mathematical frame- versatiletoolforbuildingaverygeneralclassoffilterswith works are advanced from time to time, but none clearly a much larger range of applications. A little-appreciated points the way to closing the performance gap with nat- property of the (continuous) Laplacian operator is that it ural vision. Entropy pursuit is a sequential Bayesian ap- measures the nonconformity of a function to its surround- proach to object detection and localization. The role of ings. Thisremarkablepropertyanditsdiscreteapproxima- the prior model is to apply contextual constraints in or- tionsenable(1)progressiveimagedecompositionfromfine der to determine, and coherently integrate, the evidence to coarse scale, yielding a principled framework for image acquiredat eachstep. Theevidenceisprovidedbyalarge smoothing, sharpening and local tone manipulation; and familyofpowerfulbutexpensivehigh-levelclassifiers(e.g., (2)aclearframework forbuildingimage-adaptedpriorsto CNNs). Theorderofexecutionisdeterminedonline,andis solvemoregeneralinverseproblemssuchasdeblurring. We drivenbyremovingas muchuncertaintyaspossible about have used this framework to develop many components of theoverallsceneinterpretationgiventheevidencetodate. a practical imaging pipeline for mobile and other applica- Thegoal istomatch,orevenexceed, theperformance ob- tions. tainedwithalltheclassifiersbyimplementingonlyasmall fraction. Peyman Milanfar Google Donald Geman [email protected] Johns HopkinsUniversity [email protected] IP2 High Resolution Tactile Sensing for Robotics, IP5 Metrology, and Medicine Recent Advances in Seismic Technology: From Imaging to Inversion Theinteractionoflightandmatteratasurfaceiscomplex. A GelSight sensor overrides the native optics and isolates Theprimarygoalofseismicimagingistotransformseismic 3D shape. A clear elastomer slab with a reflective mem- time reflection data recorded at the earths surface into a brane is pressed against the surface. An embedded cam- reflectivity or impedance image of the subsurface in order era views the membrane; computer vision extracts shape. to locate hydrocarbon reserves. Historically this has been Whileconceivedasarobottouchsensor,GelSightsmicron- accomplished in seismic processing through imaging algo- scaleresolutionhasspawnedcommercialapplicationsin3D rithms that are based on the adjoint of acoustic forward surfacemetrology(profilometry). Inrobotics,itshighreso- Born or Kirchhoff scattering. More recently, however, ad- lution,combinedwithitsabilitytocaptureshape,texture, vancesinalgorithmdevelopmenthaveledtotheinitialuse shear,andslip,providesuniquetactilecapabilities. Weare of nonlinear inversion as an alternative to standard imag- also exploring medical measurements, ranging from blood ingalgorithms. InthistalkIwill brieflyreviewthehistor- pressure to tissue pathology. ical development of seismic imaging, and then discuss the status of nonlinear inversion in the seismic industry, in- Edward Adelson cluding the use of Full-Waveform Inversion for impedance MIT modelestimation,andmorerecenttomographicextensions [email protected] that attempt to promote inversion technology into a full- bandwidth model-recovery solution. The various concepts Ipresentwillbeillustratedwithseismicimagingandinver- IP3 sion examples from a number of geologic settings around Image Processing, Internet-of-Things, and In- theworld. verse Problems: Blind Deconvolution Meets Blind Demixing UweAlbertin Chevron Energy Technology Company Assume we need to correctly blindly deconvolve and sep- [email protected] arate (demix) multiple signals at the same time from one single received signal. This challenging problem appears in numerous applications, and is also expected to arise in IP6 the future Internet-of-Things. We will prove that under Event-Based Silicon Retina Technology reasonable assumptions, it is indeed possible to solve this ill-posed inverseproblemandrecovermultipletransmitted This talk will be about the development of asynchronous functions fi and the associated impulse responses gi ro- silicon retina vision sensors that offer a spike-event out- bustly and efficiently from just one single received signal put like biological retinas. These neuromorphic sensors via semidefinite programming. We will tip our toes into offer advantages for real-world vision problems in terms the mathematical techniques behind our theory and dis- of latency, dynamic range, temporal resolution, and post- cuss efficient numerical algorithms as well as applications. processing cost. These event-based sensors offer oppor- IS16 Abstracts 65 tunities for theoretical and practical developments of new [email protected] classes ofalgorithmsaimed atmanydynamicvision appli- cations. The presentation will include a demonstration of a recent-vintage sensor. URL:http://sensors.ini.uzh.ch CP1 Algorithm to Build A Parametrized Model for the Tobi Delbruck Antenna Aperture Illumination for Radio Astro- University of Zurich and ETH Zurich nomical Imaging Application [email protected] Theimagingperformanceofmodernarrayradiotelescopes islimited bytheinstantaneousknowledgeofthetime,fre- SP1 quencyandpolarizationpropertiesoftheantennaaperture illuminationpattern(AIP).Whileimagingalgorithmsexist SIAG/Imaging Science Early Career Prize Lecture that can correct for these effects, they requirean accurate - Revisiting Classical Problems of Image Process- instantaneous model for the antenna AIP.We describe al- ing: Looking for New Ways to Address Longstand- gorithm for a low-order parametrized model for the AIP ing Problems and demonstrate that it captures the dominant time, fre- quencyandpolarizationdependenceofthetrueAIP.Mod- Digital images are generated by using physical acquisition ern interferometric radio telescopes consist of 100s of in- devices, such as digital cameras, but also by simulating dependent antennas with wide-band receivers (bandwidth light propagation through environmental models. In both 8GHz or more) which are together capable of imaging the cases, physical or computational limitations in the image sky at imaging dynamic range well exceeding a part in a formation process introduce artifacts such as image blur million. At such high sensitivities the antenna far-field or noise. Thus, developing image processing techniques pattern varies with time, frequency, polarization. Cor- becomes indispensable tohelp overcome these barriers. In recting for all these variables of the AIP during imag- this talk, I present several image processing applications ing has so far been considered a hard problem, limiting in which a change of perspective leads to new insight and theimaging performance of modern radio telescopes. The simpler, yet powerful, algorithms. Examples are: intrinsic methoddescribedhereisanimportantstepforwardinsolv- cameraPSFestimation,burstandvideodeblurring,Monte ing this major problem facing all current and future radio Carlo renderingdenoising. telescopes for deep-imaging observations. We use a com- putationally efficient ray-tracing code to predict the AIP Mauricio Delbracio parametrized for the physicaland electromagnetic charac- DukeUniversity teristicsoftheantenna. Weshowthatourmethodisopti- Electrical & Computer Engineering malinbuildingan AIPmodelthat minimizesthedegrees- [email protected] of-freedom and demonstrate that without such accurate models, modern radio telescopes cannot achieve their ad- vertised imaging performance. SP2 Sanjay Bhatnagar SIAG/Imaging Science Best Paper Prize Lecture - National Radio Astronomy Observatory,Socorro, New Scale Invariant Geometry for Nonrigid Shapes Mexico [email protected] Animals of the same species frequently exhibit local vari- ations in scale. Taking this into account we would like to Preshanth Jagannathan, Walter Brisken developmodelsandcomputationaltoolsthatanswerques- National Radio Astronomy Observatory tionsas: Howshouldwemeasurethediscrepancybetween [email protected], [email protected] a small dog with large ears and a large one with small ears? Are there geometric structures common to both an elephant and a giraffe? What is the morphometric simi- CP1 larity between a blue whale and a dolphin? There have Wide-field full-Stokes Radio Interferometric Imag- been two schools of thoughts that quantified similarities ing: The role of the antenna response function between surfaces which are insensitive to deformations in size. Namely, scale invariant local descriptors, and global All modern radio interferometry now use wide bandwidth normalization methods. Here, we propose a new tool for receivescapableofenablinghighsensitivityimaging. How- shape exploration. We introduce a scale invariant met- ever such receivers and high sensitivities brings with it a ric for surfaces that allows us to analyze nonrigid shapes, number of instrumental and atmospheric effects that in- generate locally invariant features, producescale invariant hibithighfidelity,highdynamicrangecontinuumimaging. geodesics, embed one surface into anotherdespite changes The dominant instrumental direction dependent effect is in local and global size, and assist in the computational that of the antenna far field voltage pattern. Apart from studyofintrinsicsymmetries wherethesizeof afeatureis timeandfrequencydependence,theantennaapertureillu- insignificant. mination pattern (AIP– Fourier transform of thefar-field voltage pattern) also introduces significant instrumental Yonathan Aflalo polarizationindirectionsawayfromthecenterinthefield- Technion University of-view. Tocorrect for theerrors dueto all theseeffects, I johnafl[email protected] presentageneralized imaging algorithm that enablesdeep wide-bandimagingoftheradioskyinallStokes. Theradio Ron Kimmel sky is inherently linearly polarized at only a few percent Technion, Haifa, Israel level. The full-polarization antenna response to the signal [email protected] in any one direction is given by theJones matrix. The di- agonal termsof theJones matrix encodetheantennagain Dan Raviv for thetwoincoming purepolarization products(linear or MIT circular), while the off diagonal terms contains magnitude 66 IS16 Abstracts of theleakage of onepolarization intootherduetoinstru- SBRAS Novosibirsk, Russia; (b) UniCIRP, Bergen, mental imperfections. In practice these off-diagonal terms Norway aremuchstrongerthanthesignalmakingprecisemeasure- [email protected] ment of sky impossible. The existing A-Projection algo- rithm accounts for only the diagonal terms. In this talk I Vladimir Tcheverda will demonstrate the limitations that arise from ignoring Inst. of Petroleum Geology and Geophysics SB RAS the off diagonal terms and theneed for thegeneralized A- Russia Projection algorithm. I will then describe the Full-Jones [email protected] A-Projection algorithm, and show that it will be required forallcurrentandfuturetelescopestoachievetheiradver- tised high fidelity,high dynamicrange imaging capability. CP1 CompressiveMid-InfraredSpectroscopicTomogra- Preshanth Jagannathan phy: Label Free and Chemically Specific 3D Imag- National Radio Astronomy Observatory ing. [email protected] We develop a mid-infrared optical imaging modality that Sanjay Bhatnagar combines scattering microscopy and imaging spectroscopy National Radio Astronomy Observatory,Socorro, New todeterminespatialmorphologyandchemicalcomposition Mexico inthreespatialdimensionsfrominterferometricdata. The [email protected] forwardimagingmodelincorporatestheconstraintthatthe sample comprises few chemical species with known spec- Urvashi Rau tra. Images are formed using an iterative reconstruction National Radio Astronomy Observatory algorithm with sparsity-drivenregularization. Simulations [email protected] illustrate imaging of layered media and sub-wavelength point scatterers in the presence of noise. Russ Taylor LukePfister University of Cape Town Universityof Illinois at UrbanaChampaign University of Western Cape lpfi[email protected] [email protected] Yoram Bresler CP1 Departmentof Electrical and Computer Engineering and the Effect of Micro-CT Scans Resolution and Scale on Coordinated Science Laboratory, Universityof Illinois the Prediction of Transport Properties of Digital [email protected] Rocks Westudiedtheeffectsofimageresolutionontheprediction P.Scott Carney of transportproperties ofdigital rocksamples. Having3D Universityof Illinois at UrbanaChampaign micro-CT scans of Benthein sandstone acquired with dif- [email protected] ferentresolutionsweestimatedstatisticalpropertiesofseg- mentedimagesandperformedstatisticalimagereconstruc- tion. Afterthattransportpropertiesandtopologicalstruc- CP1 ture of the original digital rocks and those reconstructed Sparse View Compton Scatter Tomography with on the base of truncated Gaussian simulation were com- Energy Resolved Data puted showing that transport properties stabilizes when resolution goes below 3 micrometers. The useof energy selective detectors for Compton Scatter Tomographyholdsthehopeofenhancingtheperformance Vadim Lisitsa especially for problems with limited- view in presence of Institute of Petropeum Geology & Geophysics of SBRAS highlyattenuatingmaterials. Wepresentabroken-rayfor- Russia ward model mappingmass densityand photoelectrical co- [email protected] efficients into observed scattered photons, an iterative re- constructionmethodforimageformationandinitialresults Nadezhda Arefeva for recovering spatial maps of these physical properties to Novosibirsk State University characterizematerialinbaggagescreeningapplicationwith Russia limited view, energy-resolved data. [email protected] Hamideh Rezaee PhD Candidate, Electrical and Computer Engineering Yaroslav Bazaikin Department,Tufts University Inst. of Mathematics of SB RAS [email protected] Russia [email protected] Brian Tracey, Eric Miller TuftsUniversity Tatyana Khachkova [email protected], [email protected] Inst. of Petroleum Geology and Geophysics SB RAS Russia [email protected] CP2 Matrix Decompositions Using Sub-Gaussian Ran- Dmitriy Kolyukhin dom Matrices (a) Trofimuk Instituteof Petroleum Geology and Geophysics Matrix decompositions, and especially SVD, are very im- IS16 Abstracts 67 portanttoolsindataanalysis. Whenbigdataisprocessed, [email protected] thecomputationofmatrixdecompositionsbecomesexpen- sive and impractical. In recent years, several algorithms, LotharReichel which approximate matrix decomposition, have been de- KentState University veloped. These algorithms are based on metric conserva- [email protected] tion features for linear spaces of random projections. We present a randomized method based on sparse matrix dis- tributionthatachievesafastapproximationwithbounded CP2 error for low rank matrix decomposition. Parallel Douglas Rachford Algorithm for Restor- Yariv Aizenbud ing Images with Values in Symmetric Hadamard Department of Applied Mathematics, School of Manifolds Mathematical Sciences, Tel Aviv University. [email protected] The talk addresses a generalization of the Douglas- Rachfordalgorithm tosymmetricHadamardmanifolds. It can be used to minimize an anisotropic TV functional for Amir Averbuch images having values on these manifolds. We derive an School of Computer Sciences parallelDRalgorithm,thatcanbeevaluatedfast. Conver- Tel AvivUniversity. genceofthealgorithmtoafixedpointisproofedforspaces [email protected] withconstantcurvature. Severalnumericalexamplesshow its beneficial performance when compared with the cyclic CP2 proximal point algorithm or half-quadratic minimization. Iterated Tikhonov with General Penalty Term Johannes Persch, RonnyBergmann, Gabriele Steidl In many applications, such as astronomy and medicine, Universityof Kaiserslautern arises the problem of image deblurring, this inverse prob- [email protected], lem is ill-conditioned and the inevitable presence of noise [email protected],[email protected] make a very difficult task obtaining a good reconstruction kl.de ofthetrueimage. Thediscreteformulationofthisproblem comes as a linear system CP2 Ax=b, A New Variable Metric Line-Search Proximal- whereAisaverylargeandseverelyillconditionedmatrix Gradient Method for Image Reconstruction and b is corrupted by noise. In order to compute a fair approximationoftheoriginalimagetheproblemhastobe We present a variable metric line–search based proximal– regularized. One of the most used regularization method gradient method for the minimization of the sum of a is Tikhonov regularization smooth, possibly nonconvex function plus a convex, pos- xα =argmin(cid:2)Ax−b(cid:2)2+α(cid:2)Lx(cid:2)2, α>0. sibly nonsmooth term. The strong convergence of the x method can be proved if the objective function satisfies theKurdyka–L(cid:4)ojasiewicz property at each point of its do- The formulation above is called general from, since it in- main. Numerical experience on some nonconvex image cludes also the presence of a regularization operator L reconstruction problems shows the proposed approach is which weights the penalty term. This operator enhance competitive with other state-of-the-art methods. some features of the solution while penalizing others. In the case L = I, in order to improve the quality of the re- construction, a refinement techniquehas been introduced. SimoneRebegoldi At each step the reconstruction error is approximated us- Universityof Modena and Reggio Emilia ing the Tikhonov minimization on the error equation and [email protected] isusedasacorrectionterm,sothisalgorithmisdenotedas IteratedTikhonov. However,tothebestofourknowledge, Silvia Bonettini the general theory about this iterative method has been Dipartimentodi Matematica e Informatica developed only in the standard form, i.e., when L=I. In Universit{`a} di Ferrara this talk we want to cover the theory behind the general [email protected] iteratedTikhonov,whenoneconsidertheiteration related to Tikhonov minimization in general form. We will form Ignace Loris the method, describe its characteristics and, in particular, FNRSChercheurQualifi´e (ULB, Brussels) weprovethattheproposediteration convergesandthatis Mathematics a regularization method. Moreover we will introduce the [email protected] non-stationaryiterationswhichwillshowtobemorerobust in respect to thechoice of theregularization parameter α. Federica Porta Finally, we will show the effectiveness of this method on Dipartimentodi Matematica e Informatica image deblurring test data. Universit{`a} di Ferrara Alessandro Buccini [email protected] Universit`a dell’Insubria [email protected] Marco Prato Dipartimentodi Scienze Fisiche, Informatiche e Marco Donatelli Matematiche University of Insubria Universit{`a} di Modena e Reggio Emilia 68 IS16 Abstracts [email protected] Recoverywith Applications to Mri Reconstruction A powerful new class of MRI reconstruction techniques CP2 require solving a large-scale structured low-rank ma- trix recovery problem. We present a novel, fast algo- Modulus Iterative Methods for Nonnegative Con- rithm for this class of problem that adapts an iteratively strained Least Squares Problems Arising from Im- reweightedleastsquaresapproachtoincorporatemulti-fold age Restoration Toeplitz/Hankelstructures. Theiteratescanbesolvedeffi- cientlyintheoriginalproblemdomainwithfewFFTs. We For the solution of large sparse nonnegative constrained demonstrate the algorithm on undersampled MRI recon- least squares (NNLS) problems with Tikhonov regulariza- struction, which shows significant improvement over stan- tionarisingfromimagerestoration,anewiterativemethod dard compressed sensing techniques. is proposed which usestheCGLS method for theinnerit- erations and the modulus iterative method for the outer Gregory Ongie iterations to solve the linear complementarity problem Universityof Iowa resulted from the Karush-Kuhn-Tucker condition of the Departmentof Mathematics NNLS problem. Theoretical convergence analysis includ- [email protected] ingtheoptimalchoiceoftheparametermatrixispresented for the proposed method. In addition, the method can be Mathews Jacob further enhanced by incorporating the active set strategy, Electrical and Computer Engineering which contains two stages where thefirst stage consists of Universityof Iowa modulusiterationstoidentifytheactiveset,whilethesec- [email protected] ond stage solves the reduced unconstrained least squares problems only on the inactive variables. Numerical exper- iments show the efficiency of the proposed methods com- CP3 paredtoprojectiongradient-typemethodswithlessmatrix Enhanced Sparse Low-Rank Matrix Estimation vector multiplications and CPU time. We propose to estimate sparse low-rank matrices by min- Ning Zheng imizing a convex objective function consisting of a data- SOKENDAI(The Graduate Universityfor Advanced fidelitytermandtwonon-convexregularizers. Theregular- Studies) izersinducesparsityofthesingularvaluesandtheelements [email protected] ofthematrix,moreeffectivelythanthenuclearandthe(cid:3)1 norm, respectively. We derive conditions on theregulariz- Ken Hayami erstoensurestrictconvexityoftheobjectivefunction. An National Instituteof Informatics ADMMbasedalgorithmisderivedandisappliedtoimage [email protected] denoising. Junfeng Yin AnkitParekh Department of Mathematics, Tongji University,Shanghai Departmentof Mathematics, School of Engineering [email protected] NewYork University [email protected] CP3 IvanSelesnick Departmentof Electrical and Comp. Engg Image Deblurring With An Imprecise Blur Kernel NYUSchool of Engineering Using a Group-Based Low-Rank Image Prior [email protected] Wepresentaregularizationmodelfortheimagedeblurring problem with an imprecise blur kernel degraded by ran- CP3 dom errors. Inthemodel, therestored imageand blurare Image Regularization with Structure Tensors - characterized by a group-based low-rank prior enforcing Edge Detection, Filtering, Denoising simultaneously the nonlocal self-similarity, local sparsity, andmean-preservingproperties. Analternatingminimiza- Edge detection, filtering, and denoising are fundamental tion algorithm is developed to solve the proposed model. topics in digital image and video processing area. Edge Experimental results demonstrate the effectiveness of our preserving regularization and diffusion based methods al- model and theefficiency of ournumerical scheme. though extensively studied and widely used for image restoration,stillhavelimitationsinadaptingtolocalstruc- Tian-Hui Ma, Ting-Zhu Huang, Xi-LeZhao tures. We consider a class of filters based on multiscale School of Mathematical Sciences structure tensor based features. The spatially varying University of Electronic Scienceand Technology of China exponent model we develop leads to a novel restoration [email protected], [email protected], methodwhich retainsandenhancesedgestructuresacross [email protected] scales without generating artifacts. Promising extensions to handle jpeg decompression, edge detection, and multi- Yifei Lou, Yifei Lou channelimageryareconsidered. Relatedprojectpagecon- Department of Mathematical Sciences tainsmoredetails: http://cell.missouri.edu/pages/MTTV. University of Texas at Dallas [email protected], [email protected] SuryaPrasath Universityof Missouri-Columbia [email protected] CP3 AFastAlgorithmforStructuredLow-RankMatrix Dmitry A.Vorotnikov IS16 Abstracts 69 Universidade deCoimbra [email protected] [email protected] CP4 Rengarajan Pelapur, ShaniJose University of Missouri-Columbia, USA Sparse Approximation of Images by Adaptive [email protected], [email protected] Thinning Anisotropic triangulations provide efficient methods for Kannappan Palaniappan sparse image representations. We propose a locally adap- University of Missouri-Columbia tive algorithm for sparse image approximation, adaptive [email protected] thinning, which relies on linear splines on anisotropic tri- angulations. Wediscuss both theoretical and practical as- Guna Seetharaman pects concerning image approximation by adaptive thin- Navy Research Lab, USA ning. This includes asymptotically optimal N-term ap- [email protected] proximations on relevant classes of target functions, such as horizon functions across α H¨older smooth boundaries andregularfunctionsofWα,p regularity,for α>2/p−1. CP3 Armin Iske Signal Classification Using Sparse Representation Universityof Hamburg on Enhanced Training Dictionary Departmentof Mathematics [email protected] We propose a method to classify high-dimensional signals basedonhowsparselyatestsignalcanberepresentedover Laurent Demaret adictionarycontainingselectedtrainingsamplesandbasis Instituteof Biomathematics and Biometry vectorsoftheapproximatedtangentplanesatthosetrain- Helmholtz ZentrumMu¨nchen, Germany ingsamples,whicharecomputedusinglocalPCA.Ourex- [email protected] periments on various datasets including the standard face databasesdemonstratethatthismethodcanachievehigher classification accuracy than other sparse representation- CP4 basedmethodswhentheclassmanifoldsarenonlinearand Joint Deconvolution and Blind Source Separation sparsely-sampled. of Hyperspectral Data Using Sparsity Thehyperspectralrestorationisverychallengingwhentak- Naoki Saito ing into account not only the spectral mixing, but also Department of Mathematics blurring effects. We propose a new Blind Source Separa- University of California, Davis tion method which addresses this problem by alternating [email protected] twominimizers, onesolvingahyperspectraldeconvolution problem using sparsity, and leading to a generalization of Chelsea Weaver the FORWARD algorithm, and the second estimating the University of California, Davis mixing matrix by a least square inversion. A range of ex- [email protected] amples illustrates theresults. Ming Jiang CP3 CEA-Saclay [email protected] Low-Rank Approximation Pursuit for Matrix and Tensor Completion Jean-LucStarck, J´erome Bobin CEA Saclay weintroduceanefficientgreedyalgorithm formatrixcom- [email protected], [email protected] pletion, which is literally a generalization of orthogonal rank-one matrix pursuit method (OR1MP) in the sense that multiple s candidates are identified per iteration by CP4 low-rank matrix approximation. Owing to the selection Sparse Source Reconstruction for Nanomagnetic of multiple s candidates, our approach is finished with Relaxometry much smaller number of iterations when compared to the OR1MP. Inaddition, we extendtheOR1MP algorithm to Source reconstruction for nanomagnetic relaxometry re- deal with tensor completion. quiressolving themagnetic inverse problem. By discretiz- ing the field of view, we can compute a lead field matrix thatrelates thecontribution of each pixeltothesignal re- An-Bao Xu ceivedbythedetectors. Wethenapproximateaminimum Hunan University [email protected] l0-norm solution by iterating over the minimization prob- lem: min||xi||1 s.t. ||Ax−b||2 ≤(cid:4) Dongxiu Xie x wi School of science Ourapproachforverificationandvalidationofouralgorith- Beijing Information Science and Technology University mic implementation in phantom studies will be presented. [email protected] Tin-Yau Tam Sara Loupot, Wolfgang Stefan, Reza Medankan,Kelsey AuburnUniversity Mathieu, David Fuentes,John Hazle 70 IS16 Abstracts University of Texas MD Anderson Cancer Center Model with Directional Forward Differences [email protected], [email protected], [email protected], [email protected], Focusedionbeamtomographyprovideshighresolutionvol- [email protected], [email protected] umetric images on a micro scale. However, due to the physical acquisition process the resulting images are often corrupted by a so-called curtaining effect. In this talk, a CP4 new convex variational model for removing such effects is Convolutional Laplacian Sparse Coding proposed. More precisely, an infimal convolution model is applied tosplit thecorrupted3D image intotheclean im- We propose to extend the the standard convolutional age and two types of corruptions, namely a striped and a sparse representation by combining it with a non-local laminar part. graph Laplacian term. This additional term is chosen to address some of the deficiencies of the (cid:3)1 norm in regular- Jan Henrik Fitschen izing these representations, and is shown to have an ad- Universityof Kaiserslautern vantageinbothdictionarylearningandanexampleimage fi[email protected] reconstruction problem. Jianwei Ma Xiyang Luo Departmentof Mathematics University of California, Los Angeles Harbin Instituteof Technology [email protected] [email protected] Brendt Wohlberg Sebastian Schuff Los Alamos National Laboratory Universityof Kaiserslautern Theoretical Division schuff@mv.uni-kl.de [email protected] CP5 CP4 NonLocal via Local–NonLinear via Linear: A New Gap Safe Rules for Speeding-Up Sparse Regular- Part-Coding Distance Field via Screened Poisson ization Equation Highdimensionalregression/inverseproblemsmightben- efit from sparsity promoting regularizations. Screening We propose a repeated use of Screened Poisson PDE to rulesleveragethesparsityofthesolutionbyignoringsome compute a part coding field for perceptual tasks such as variables in the optimization, hence speeding up solvers. shape decomposition. Despite efficient local and linear When the procedure is proven not to discard features computations, thefield exhibitshighly nonlinear andnon- wrongly, the rules are said to be ”safe”. We derive new local behavior. Our scheme is applicable to shapes in ar- saferulesforgeneralizedlinearmodelsregularizedwithL1 bitrary dimensions, even to those implied by fragmented or L1/L2 norms. The rules are based on duality gap com- partial contours. The local behavior is independent of the putationsallowingtosafelydiscardmorevariables,inpar- image context in which theshape resides. ticular for low regularization parameters. Our GAP Safe rulecancopewithanyiterativesolverandweillustrateits Murat Genctav, Asli Genctav, Sibel Tari performanceonLasso,multi-taskLasso,binaryandmulti- Middle East Technical University nomial logistic regression, demonstrating significant speed [email protected], [email protected], ups on all tested datasets with respect to previous safe [email protected] rules. This is a joint work with E. Ndiaye, O. Fercoq and A. Gramfort CP5 Eugene Ndiaye Boundary Formulationof Finite Differences: Anal- Telecom-ParisTech, CNRS LTCI ysis and Applications Universit´e Paris-Saclay [email protected] Estimationofnumericalderivativesontheboundaryvalues remainsanunresolveddilemmainmanyinverseproblems. Olivier Fercoq Many formulations such as cyclic or Neumann conditions Telecom-ParisTech, CNRS LTCI violate the derivative continuity and cause discrepancies. Universit´e Paris-Saclay,75013, Paris, France This presentation provides a numerical solution to calcu- [email protected] latederivativeson theboundarieswith highorderpolyno- mialaccuracyinaunifiedconvolutionmatrix. Thenumer- Alexandre Gramfort icalstabilityofthismatrixisanalyzedviathedistribution Telecom-ParisTech, CNRS LTCI oftheeigenvaluesandperturbationanalysisandcompared Universit´e Paris-Saclay tothe existing formulations in theliterature. [email protected] Mahdi S.Hosseini, Konstantinos N. Plataniotis Joseph Salmon Universityof Toronto Telecom-ParisTech, CNRS LTCI [email protected], [email protected] [email protected] CP5 CP5 Solving Variational Problems and Partial Differen- Removal of Curtaining Effects by a Variational tial Equations That Map Between Manifolds Via IS16 Abstracts 71 the Closest Point Method metryonatilemapsallregionsofonecolortotheregions of another color. In this work, we propose a novel ap- Maps from a manifold M to a manifold N appear in im- proach to extract the unit cells and fundamental domains age processing, medical imaging, and many other areas. oftileswithvariouscolorsymmetries,bothconsideringand Thistalkintroducesanumericalframeworkforvariational ignoring color permutations. We use multiple ideas from problems and PDEs that map between manifolds. The variational and PDE based image processing methods. problem of solving a constrained PDE between M and N is reduced into two simpler problems: solving a PDE on VeneraAdanova M and projecting onto N. Numerical examples of denois- Middle East Technical University ing texture maps, diffusing random maps, and enhancing [email protected] colour images are presented. SibelTari Nathan D.King ComputerEngineering Department Department of Mathematics Middle East Technical University,Turkey Simon Fraser University [email protected] [email protected] Steven Ruuth CP6 Mathematics NewTechniquesforInversionofFull-WaveformIn- Simon Fraser University duced Polarization Data [email protected] Induced polarization (IP) is a geophysical method that measures electrical polarization of the subsurface. Stan- CP5 dardmethodsforinversionofIPdatausesimplifiedmodels Regularization Strategy for Inverse Problem for that neglect much of the information collected in modern 1+1 Dimensional Wave Equation surveys, limiting imaging resolution. We are developing high performance multigrid based methods for modelling Aninverseboundaryvalueproblem fora1+1dimensional full IP decay curves from large sources along with a cor- wave equation with wave speed c(x) is considered. We responding inversion algorithm that combines voxel-based give a regularisation strategy for inverting the map A : Tikhonovregularized inversion with aparametric-level set c (cid:4)→ Λ, where Λ is the hyperbolic Neumann-to-Dirichlet approach. map corresponding to the wave speed c. We consider the casewhenwearegivenaperturbationoftheNeumann-to- Patrick T. Belliveau Dirichlet map Λ˜ =Λ+E,and reconstruct anapproximate Universityof British Columbia wave speed c˜. Our regularization strategy is based on a [email protected] newformulatocomputecfromΛ. Moreoverwehavedone numericalimplementationandexecuteditwithasimulated Eldad Haber data. Departmentof Mathematics TheUniversity of British Columbia Jussi P. Korpela [email protected] University of Helsinki Department of Mathematics and Statistics jussi.korpela@helsinki.fi CP6 Bidirectional Texture Function Bernoulli-Mixture Compound Texture Model CP5 Exploiting Sparsity in PDEs with Discontinuous This paper introduces a method for modeling texturesus- Solutions ing a parametric BTF compound Markov random field model. Thepurposeofourapproachistoreproduce,com- Exploiting sparsity playsa centralrole in many recent de- press,and enlargea givenmeasured textureimage so that velopments in imaging and other related fields. We use (cid:3)1 ideally both natural and synthetictexturewill be visually regularization techniquesto promote sparsity in the edges indiscernible. ThemodelcanalsobeappliedtoBTFmate- of PDEs with discontinuous solutions. This has led us to rialediting. ThecontrolfieldisgeneratedbytheBernoulli thedevelopmentofnumericalalgorithms thatdonothave mixture model and the local textures are modeled using the restrictive stability conditions on time stepping that the3DCAR. normally occur. With these methods we increase the ac- curacy of methods that do not account for sparsity in the Michal Haindl solution. Instituteof Information Theory and Automation of the CAS Theresa A. Scarnati [email protected] Arizona StateUniversity School of Mathematical & Statistical Sciences [email protected] CP6 Information Theoretic Approach for Accelerated MagneticResonanceThermometryinthePresence CP6 of Uncertainties Extracting Plane Symmetry Group Information from Tiles with Color Permutations Amodel-basedinformationtheoreticapproachispresented toperform thetask of Magnetic Resonance (MR) thermal Repeatingabasemotifcreatesatilewithdifferentsymme- image reconstruction from a limited number of observed tries. A tile has color symmetry, if applying certain sym- samplesonk-space. Thekeyideaoftheproposedapproach 72 IS16 Abstracts is to optimally detect samples of k-space that are infor- sity algorithm in order to improve theconvergence rate of mation rich with respect to a model of the thermal data thesolution. Theexperimentalresultsondifferentdatasets acquisition. These highly informative k-space samples are verify thevalidity of theproposed model. thenusedtorefinethemathematicalmodelandefficiently reconstruct the image. PushpendraKumar Indian Instituteof Technology Roorkee Reza Madankan, Wolfgang Stefan, Christopher [email protected] MacLellan, Samuel Fahrenholtz, Drew Mitchell University of Texas MD Anderson Cancer Center Sanjeev Kumar, Balasubramanian Raman [email protected], [email protected], Indian Instituteof Technology Roorkee [email protected], [email protected], [email protected] [email protected], [email protected] CP7 R.J. Stafford Optical Flow on Evolving Sphere-Like Surfaces MD Anderson Cancer Center jstaff[email protected] Weconsideropticalflowonevolvingsurfaceswhichcanbe parametrisedfromthe2-sphere. Ourmainmotivationisto John Hazle estimate cell motion in time-lapse volumetric microscopy University of Texas MD Anderson Cancer Center images depicting fluorescently labelled cells of a live ze- [email protected] brafishembryo. Weexploitthefactthattherecordedcells floatonthesurfaceoftheembryoandallowfortheextrac- tion of an image sequence together with a sphere-like sur- David Fuenstes face. Wesolve the resulting variational problem by means MD Anderson Cancer Center ofaGalerkin method based onvectorspherical harmonics [email protected] and present numerical results. LukasF. Lang CP6 RICAM,Austrian Academyof Sciences BLA: A Weak Form Attenuation Compensation [email protected] Model for Ultrasonic Imagery OtmarScherzer Thequalityofmedicalsonographyishinderedbytheshad- Computational ScienceCenter owingorenhancementartifactsduetoacousticwaveprop- UniversityVienna agation and attenuation across tissue layers. We present [email protected] a Backscatter-Levelset-Attenuation (BLA) joint estima- tion model in the context of regional ultrasound attenua- tioncompensation andstructuralsegmentation. TheBLA CP7 model eliminates the need of solving PDEs over irregular domains,andisformulatedusinglevelsets. Weprovidenu- Classification of Hyperspectral Data Using the merical algorithms alongwith discretization schemes. The Besov Norm mainadvantageoftheBLAmethodisitsremarkablecom- putational efficiency. We demonstrate the results using Sparse representations have been extensively studied in simulated, phantom and in vivoultrasound images. image processing, however not much has been done with sparse-based classification problems. Inthisstudy,wedis- Jue Wang cuss the use of wavelets in hyperspectral imaging. The Union College analysis-based approach accounts for more aspects of the [email protected] datathanthecoordinate-wiseeuclideandistanceapproach. We estimate the local properties of the hyperspectral stack using the Besov norm for a given choice of wavelet. Yongjian Yu Thereby, allowing for multiscale and multidirectional fea- University of Virginia tures. [email protected] Richard N.Lartey Case Western ReserveUniversity CP7 Departmentof Mathematics,Applied Mathematics and A Fractional Order Variational Model for Optical Statistics Flow Estimation Based on Sparsity Algorithm [email protected] In this paper, a fractional order variational model is pro- WeihongGuo posed for estimating the optical flow. The proposed frac- Departmentof Mathematics, Case Western Reserve tionalordermodelisintroducedbygeneralizinganinteger University ordervariationalmodelformedwithaglobalmodelofHorn [email protected] and Schunck and the classical model of Nagel and Enkel- mann. In particular, the proposed model generalizes the existingvariationalmodelsfromintegertofractionalorder, Julia Dobrosotskaya andthereforeamoresuitableinestimatingtheopticalflow. Case Western ReserveUniversity However, it is difficult to solve this generalized model due [email protected] to the complex fractional order partial differential equa- tions. The Gru¨nwald-Letnikov derivative is used to dis- cretize the fractional order derivative. The corresponding CP7 sparselinearsystemofequationsissolvedbyusingaspar- New Uncertainty Principles for Image Feature Ex- IS16 Abstracts 73 traction oftheaffineparametersoftheregistration step,improving themodel’sreliability. Wediscusshowthisapproachcom- The motivation for this talk is window design for image parestosimilar methods,andpresentnumericalresultsto feature extraction by a filter bank. There is a conven- demonstrate its performance. tionalframework foranalyzinglocalization aspectsofwin- dow functions. Weclaim that theconventionalframework Jack A.Spencer, KeChen is flawed, and develop a new adequate theory. Our ap- Universityof Liverpool proachleadstonewuncertaintyprinciplesandnewoptimal [email protected], [email protected] window functions. Filter banks based on our new optimal window functions havea certain notion of sparsity. CP8 Ron Levie Error Estimates and Convergence Rates for Fil- School of Mathematical Sciences, tered Back Projection Tel AvivUniversity,Tel Aviv [email protected] The filtered back projection (FBP) formula allows us to reconstructbivariatefunctionsfrom givenRadonsamples. Nir Sochen However,theFBPformulaisnumericallyunstableandlow- Applied Mathematics Department passfiltersoffinitebandwidthareemployedtomakethere- Tel AvivUniversity constructionlesssensitivetonoise. Inthistalkweanalyse [email protected] the intrinsic reconstruction error incurred by the low-pass filter. We prove L2-error estimates on Sobolev spaces of fractional order along with asymptotic convergence rates, CP7 where thebandwidth goes to infinity. Hyperspectral Video Analysis Using Graph Clus- tering Methods Matthias Beckmann Universityof Hamburg Perhapsthemostchallengingimagingmodalitytoanalyze [email protected] in terms of thevast size of thedata are videos taken from hyperspectral cameras. We consider an example involv- Armin Iske ingstandoffdetectionofagasplumeinvolvingLongWave Universityof Hamburg Infrared spectral data with 128 bands. Rather than using Departmentof Mathematics PCAorasimilardimensionreductionmethodwetreatthis [email protected] as a ”big data” classification problem and simultaneously processallpixelsintheentirevideousingnovelnewgraph clusteringtechniques. Computationoftheentiresimilarity CP8 graph is prohibitive for such data so we use the Nystrom Density Compensation Factor Design for Non- extension to randomly sample the graph and compute a Uniform Fast Fourier Transforms modest number of eigenfunctions of the graph Laplacian. Averysmall partofthespectrumallows forspectralclus- Inapplicationssuchasmagneticresonanceimaging(MRI), tering of the data. However with a larger but still modest radar imaging, and radio astronomy, data may be col- number of eigenfunctions we can solve a graph-cut based lected as a sequence of non-uniform Fourier samples. One semisupervisedorunsupervisedmachinelearningproblem common approach used to reconstruct images from non- to sort the pixels into classes. We discuss challenges of uniform Fourier data involves regridding the non-uniform running such code on both desktopsand supercompers. Fourier data to uniform points, and then applying the FFT, a process often referred to as the non-uniform Gloria Meng FFT (NFFT). Intheregridding process, parameters often UCLA termed thedensity compensation factors (DCFs) are used [email protected] essentially as quadrature weights to construct the inverse Fourier transform. The DCFs are typically chosen using Ekaterina Merkurjev heuristic arguments, and, depending on the sampling pat- Department of Mathematics tern,may not lead to a convergent approximation. Inthis UCSD talkweillustratetheimportanceofchoosingDCFsappro- [email protected] priately. We develop an algorithm to design DCFs based on the given sampling scheme and demonstrate numerical Alice Koniges convergence. We further apply our algorithm to recover Lawrence Berekely Laboratory features (such as edges) of the underlying image, which is [email protected] especiallyusefulintargetidentificationortissueclassifica- tion. Andrea L. Bertozzi UCLA Department of Mathematics AnneGelb [email protected] Arizona StateUniversity [email protected] CP7 CP8 Image Segmentation with a Shape Prior The Factorization Method for Imaging Defects in We study variational models for segmentation incorporat- Anisotropic Materials ing ashapeprior, and ourmethod involvescomputingthe global minimiser of a functional with fixed fitting terms. In this presentation we consider the inverse acoustic or Wedefinethispriorimplicitlyinsuchawaythattheimage electromagnetic scattering problem of reconstructing pos- intensityinformationisincorporatedintotheminimisation sibly multiple defective penetrable regions in a known