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Adaptive algorithm for sparse signal recovery
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620X
2019 (English)In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 87, p. 16p. 10-18Article in journal (Refereed) Published
Abstract [en]

The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 87, p. 16p. 10-18
Keywords [en]
sparsity, adaptive algorithm, sparse signal recovery, spike and slab priors
National Category
Probability Theory and Statistics Signal Processing Medical Image Processing
Research subject
Mathematical Statistics; Signal Processing
Identifiers
URN: urn:nbn:se:umu:diva-146386DOI: 10.1016/j.dsp.2019.01.002ISI: 000461266700002Scopus ID: 2-s2.0-85060542792OAI: oai:DiVA.org:umu-146386DiVA, id: diva2:1195952
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-534
Note

Originally included in thesis in manuscript form

Available from: 2018-04-07 Created: 2018-04-07 Last updated: 2019-04-04Bibliographically approved
In thesis
1. Statistical methods in medical image estimation and sparse signal recovery
Open this publication in new window or tab >>Statistical methods in medical image estimation and sparse signal recovery
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis presents work on methods for the estimation of computed tomography (CT) images from magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. The study also demonstrates sparse signal recovery method, which is an intermediate method for magnetic resonance image reconstruction. The thesis consists of four articles. The first three articles are concerned with developing statistical methods for the estimation of CT images from MR images. We formulated spatial and non-spatial models for CT image estimation from MR images, where the spatial models include hidden Markov model (HMM) and hidden Markov random field model (HMRF) while the non-spatial models incorporate Gaussian mixture model (GMM) and skewed-Gaussian mixture model (SGMM). The statistical models are estimated via a maximum likelihood approach using the EM-algorithm in GMM and SGMM, the EM gradient algorithm in HMRF and the Baum–Welch algorithm in HMM. We have also examined CT image estimation using GMM and supervised statistical learning methods. The performance of the models is evaluated using cross-validation on real data. Comparing CT image estimation performance of the models, we have observed that GMM combined with supervised statistical learning method has the best performance, especially on bone tissues. The fourth article deals with a sparse modeling in signal recovery. Using spike and slab priors on the signal, we formulated a sparse signal recovery problem and developed an adaptive algorithm for sparse signal recovery. The developed algorithm has better performance than the recent iterative convex refinement (ICR) algorithm. The methods introduced in this work are contributions to the lattice process and signal processing literature. The results are an input for the research on replacing CT images by synthetic or pseudo-CT images, and for an efficient way of recovering sparse signal.

Abstract [sv]

Denna avhandling presenterar arbete kring metoder för skattning av datortomografibilder (CT) från magnetiska resonanstomografibilder (MR) för ett antal diagnostiska och terapeutiska arbetsflöden. Studien demonstrerar även en metod för gles signalrekonstruktion, vilket är en mellanliggande metod för rekonstruktion av MR-bilder. Avhandlingen består av fyra artiklar. De tre första artiklarna handlar om att utveckla statistiska metoder för uppskattning av CT-bilder från MR-bilder. Här formuleras rumsliga och icke-rumsliga modeller för skattning av CT-bilder från MR-bilder, där de rumsliga modellerna inkluderar dolda Markov-modeller (HMM) och dolda Markov-slumpfältmodeller (HMRF), medan de icke-rumsliga modellerna består av Gaussiska mix-modeller (GMM) och skeva Gaussiska mixmodeller (SGMM). De statistiska modellerna skattas via en maximum-likelihoodansats, där EM-algoritmen används för GMM och SGMM, EM-gradientalgoritmen för HMRF samt Baum-Welch-algoritmen för HMM. Vi har även undersökt CTbildskattning med hjälp av GMM och övervakade statistiska inlärningsmetoder. Modellernas prestanda har utvärderats med hjälp av korsvalidering på faktiska data. Genom att jämföra prestandan hos modellernas CT-bildskattningar har vi observerat att GMM kombinerat med övervakad statistisk inlärning har den bästa prestandan, i synnerhet ifråga om benvävnad. Den fjärde artikeln behandlar en gles modellering inom signalrekonstruktion. Med hjälp av så kallade ”spike and slab priors” för signalen formulerade vi ett glest signalrekonstruktionsproblem och utvecklade en adaptiv algoritm för gles signalrekonstruktion. Den utvecklade algoritmen har bättre prestanda än den nyligen föreslagna iterativ konvex förfining (ICR)-algoritmen. De metoder som introducerats i detta arbete är bidrag till litteraturen inom så kallade ”lattice-processer” och signalbehandling. Resultaten levererar ett bidrag till forskningen kring ersättandet av CT-bilder med syntetiska eller pseudo-CTbilder, samt till effektiv gles signalrekonstruktion.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2018. p. 59
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 63
Keywords
Computed tomography, magnetic resonance imaging, Gaussian mixture model, skew-Gaussian mixture model, hidden Markov random field, hidden Markov model, supervised statistical learning, synthetic CT images, pseudo-CT images, spike and slab prior, adaptive algorithm
National Category
Probability Theory and Statistics Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:umu:diva-147751 (URN)978-91-7601-890-3 (ISBN)
Public defence
2018-06-08, MA121, MIT-building, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2018-05-18 Created: 2018-05-16 Last updated: 2018-06-09Bibliographically approved

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Bayisa, FekaduZhou, ZhiyongCronie, OttmarYu, Jun

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