08492 Abstracts Collection -- Structured Decompositions and Efficient Algorithms

From 30.11. to 05.12.2008, the Dagstuhl Seminar 08492 ``Structured Decompositions and Efficient Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Seismic Signal Denoising Based on Surelet Transform for Energy Exploration

Seismic signals are critical for subsurface energy exploration like oil, coal, and natural gas. Processing these signals while minimizing environmental impacts is crucial but lacking in several appropriate multi-scale geometric analysis (MGA) techniques. This study proposes using the Surelet transform, based on Stein’s unbiased risk estimate (SURE), for seismic denoising. The method combines SURE to find optimal thresholds and linear expansion for coefficient estimation. Experiments on two-dimensional (2D) and three-dimensional (3D) synthetic seismic data showed Surelet achieved higher peak signal-to-noise ratios (PSNR) and faster processing compared to wavelet, curvelet, and wave atom. For example, with 20% noise, Surelet improved PSNR by 6.11% and reduced time by 78.4% versus wave atom. The feasibility of the proposed technique for efficient seismic denoising was demonstrated, highlighting implications for enabling cleaner signals in energy exploration

Rekonstrukcija signala iz nepotpunih merenja sa primenom u ubrzanju algoritama za rekonstrukciju slike magnetne rezonance

In dissertation a problem of reconstruction of images from undersampled measurements is considered which has direct application in creation of magnetic resonance images. The topic of the research is proposition of new regularization based methods for image reconstruction which are based on statistical Markov random field models and theory of compressive sensing. With the proposed signal model which follows the statistics of images, a new regularization functions are defined and four methods for reconstruction of magnetic resonance images are derived.У докторској дисертацији разматран је проблем реконструкције сигнала слике из непотпуних мерења који има директну примену у креирању слика магнетне резнонаце. Предмет истраживања је везан за предлог нових регуларизационих метода реконструкције коришћењем статистичких модела Марковљевог случајног поља и теорије ретке репрезентације сигнала. На основу предложеног модела који на веродостојан начин репрезентује статистику сигнала слике предложене су регуларизационе функције и креирана четири алгоритма за реконструкцију слике магнетне резонанце.U doktorskoj disertaciji razmatran je problem rekonstrukcije signala slike iz nepotpunih merenja koji ima direktnu primenu u kreiranju slika magnetne reznonace. Predmet istraživanja je vezan za predlog novih regularizacionih metoda rekonstrukcije korišćenjem statističkih modela Markovljevog slučajnog polja i teorije retke reprezentacije signala. Na osnovu predloženog modela koji na verodostojan način reprezentuje statistiku signala slike predložene su regularizacione funkcije i kreirana četiri algoritma za rekonstrukciju slike magnetne rezonance

Novel algorithms in X-ray computed tomography imaging from under-sampled data

This thesis presents novel algorithms in X-ray computed tomography imaging using limited or sparse data: I. A non-uniform rational basis splines (NURBS) curve is used to represent the boundary of a target. Markov chain Monte Carlo (MCMC) strategy is applied for estimating the unknown curve from the projection data and an attenuation value of the target. In this case, the target is assumed to be homogeneous (it contains only one material). Instead of a single output, the solution of MCMC as a Bayesian framework is a posterior distribution. In addition, the results of the method are conveniently in CAD-compatible format. II. Adaptive methods for choosing regularization parameter are proposed. The first approach is called the controlled wavelet domain sparsity (CWDS). This is based on enforcing sparsity in the two-dimensional wavelet transform domain, and the second so-called the controlled shearlet domain sparsity (CSDS) in the three-dimensional shearlet transform domain. The proposed methods offer a strategy to automatically choosing regularization parameter where the end-users could avoid manually tuning the parameters. A known {\it a priori} sparsity level calculated from some available objects/samples is required. Both algorithms above have been successfully implemented for real measured X-ray data and the results using under-sampled data outperform the baseline method. The proposed methods incur heavy computation costs, however implementing parallelization strategy could save the computation time.Tiivistelmä Tässä väitöskirjassa esitetään uusia algoritmeja röntgenkuvaukseen perustuvaan tietokonetomografiaan käyttäen harvan ja rajoitetun kulman mittausdataa. Erityisesti työssä esitetään seuraavat lähestymistavat: I. Ensimmäinen lähestymistapa perustuu NURBS (engl., non-uniform rational basis splines) –mallin käyttöön. NURBS on matemaattinen malli, jota käytetään kuvattavan kohteen reunojen esittämiseen. Soveltamalla tätä yhdessä Markovin ketju Monte Carlo –strategian (MCMC) kanssa voidaan estimoida reunan käyrä, sekä kohteen vaimenemista kuvaava arvo. Tässä lähestymistavassa kohde oletetaan homogeeniseksi eli sen oletetaan sisältävän vain yhtä ainetta. Käyttäen MCMC-mentelmää saadaan estimoitaville parametreille tilastollinen a posteriori -jakauma. II. Toinen lähestymistapa perustuu adaptiiviseen regularisointiparametrin valitsemiseen. Tätä varten kehitettiin kaksi strategiaa. Ensimmäinen näistä perustuu harvuuden vahvistamiseen ja kontrolloimiseen kaksiulotteisessa aallokemuunoksessa. Toinen taas perustuu harvuuden kontrolloimiseen nk. komiulotteisessa shearlet-sivuttaissiirtymämuunnoksessa. Molemmat menetelmät mahdollistavat regularisointiparametrin automaattisen valitsemisen ilman että loppukäyttäjän tarvitsee itse siihen puuttua. Ennakkotieto kuvattavan objektin harvuuden tasosta kuitenkin vaaditaan. Tässä väitöskirjassa molempia lähestymistapoja testattiin käytännössä käyttäen oikeaa mitattua röntgendataa. Molemmissa lähestymistavoissa uudet algoritmit toimivat paremmin kuin perinteiset vertailumenetelmät. Uudet algoritmit ovat kuitenkin laskennallisesti erittäin raskaita. Tulevaisuudessa suurteholaskennan keinoilla niihin käytettyä laskenta-aikaa voitaneen kuitenkin pienentää

Computational Spectral Imaging: A Contemporary Overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks

Spatial priors for tomographic reconstructions from limited data

Tomografie is het reconstrueren van het inwendige van een object a.d.h.v externe metingen, b.v. beelden verkregen met X-stralen of microgolven. Deze thesis bekijkt de specifieke aspecten van microgolftomografie en magnetische resonantie beeldvorming (Magnetic Resonance Imaging – MRI); beide technieken zijn onschadelijk voor de mens. Terwijl het gebruik van MRI wijdverspreid is voor veel klinische toepassingen, is microgolftomografie nog niet in klinisch gebruik ondanks zijn potentiële voordelen. Door de lage kost en draagbaarheid van de toestellen is het een waardevolle aanvulling aan het assortiment