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Cell detection by functional inverse diffusion and non-negative group sparsity – Part I: Modeling and Inverse Problems
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.ORCID iD: 0000-0003-3054-7210
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.ORCID iD: 0000-0001-6630-243X
2018 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5407-5421Article in journal (Refereed) Published
Abstract [en]

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.

Place, publisher, year, edition, pages
IEEE, 2018. Vol. 66, no 20, p. 5407-5421
Keywords [en]
Inverse problems, Biomedical imaging, Convex optimization, Source localization, Biological modeling
National Category
Signal Processing Medical Image Processing
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-233824DOI: 10.1109/TSP.2018.2868258ISI: 000444842400007Scopus ID: 2-s2.0-85052785365OAI: oai:DiVA.org:kth-233824DiVA, id: diva2:1242882
Funder
Swedish Research Council, 2015-04026
Note

QC 20180918

Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2019-08-20Bibliographically approved
In thesis
1. Inverse problems in signal processing: Functional optimization, parameter estimation and machine learning
Open this publication in new window or tab >>Inverse problems in signal processing: Functional optimization, parameter estimation and machine learning
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Inverse problems arise in any scientific endeavor. Indeed, it is seldom the case that our senses or basic instruments, i.e., the data, provide the answer we seek. It is only by using our understanding of how the world has generated the data, i.e., a model, that we can hope to infer what the data imply. Solving an inverse problem is, simply put, using a model to retrieve the information we seek from the data.

In signal processing, systems are engineered to generate, process, or transmit signals, i.e., indexed data, in order to achieve some goal. The goal of a specific system could be to use an observed signal and its model to solve an inverse problem. However, the goal could also be to generate a signal so that it reveals a parameter to investigation by inverse problems. Inverse problems and signal processing overlap substantially, and rely on the same set of concepts and tools. This thesis lies at the intersection between them, and presents results in modeling, optimization, statistics, machine learning, biomedical imaging and automatic control.

The novel scientific content of this thesis is contained in its seven composing publications, which are reproduced in Part II. In five of these, which are mostly motivated by a biomedical imaging application, a set of related optimization and machine learning approaches to source localization under diffusion and convolutional coding models are presented. These are included in Publications A, B, E, F and G, which also include contributions to the modeling and simulation of a specific family of image-based immunoassays. Publication C presents the analysis of a system for clock synchronization between two nodes connected by a channel, which is a problem of utmost relevance in automatic control. The system exploits a specific node design to generate a signal that enables the estimation of the synchronization parameters. In the analysis, substantial contributions to the identifiability of sawtooth signal models under different conditions are made. Finally, Publication D brings to light and proves results that have been largely overlooked by the signal processing community and characterize the information that quantized linear models contain about their location and scale parameters.

Abstract [sv]

Inversa problem uppstår vid alla vetenskapliga undersökningar. Våra sinnen och mätinstrument -rådata -ger faktiskt sällan svaren vi letar efter. Vi behöver då utveckla vår förståelse av hur data genererats, d.v.s., använda en modell, för att kunna dra korrekta slutsatser. Att lösa inversa problem är,enkelt uttryckt, att använda modeller för att få fram den information man vill ha från tillgängliga data.

Signalbehandling handlar om utveckling av system som skapar, behandlar eller överför signaler (d.v.s., indexerade data) för att nå ett visst mål. Ett exempel på mål för en sådant system är att lösa ett inverst problem utifrån den analyserade signalen med hjälp av en modell. Signalbehandling kan dock även handla om att skapa en signal, så att denna avslöjar en parameter för utredning genom ett inverst problem. Inversa problem och signalbehandling är två fält som överlappar i stor utsträckning, och som använder sig av samma koncept och verktyg. Denna avhandling utforskar gränslandet mellan dessa två fält, och presenterar resultat inom modellering, optimering, statistik, maskininlärning, biomedicinsk avbildning och automatisk kontroll.

Det nya vetenskapliga innehållet i den här avhandlingen är baserat på de sju artiklar som återges här i Del II. I fem av dessa artiklar beskrivs ett antal relaterade metoder för optimering och maskininlärning för källokalisering medhjälp av diffusions- och konvolutionsmodellering, med tillämpningar framförallt inom biomedicinsk bildbehandling. Dessa inkluderas i Publikationer A, B,E, F och G, och behandlar också modellering och simulering av en familj av bildbaserade immunkemiska detektionsmetoder. Publikation C presenterar analys av ett system för klocksynkronisering mellan två noder förbundna med en kanal, vilket är ett problem med särskild relevans för automatisk kontroll. Systemet använder en specifik noddesign för att generera en signal som möjliggör skattning av synkroniseringsparametrarna. Analysen bidrar avsevärt till metodiken för att identifiera sågtandsmönstrande signalmodeller under olika förhållanden. Avslutningsvis presenteras i Publikation D resultat som tidigare i stora drag förbisetts inom signalbehandlingsfältet. Här karaktäriseras även den information som kvantiserade linjära modeller innehåller om deras läges- och skalparametrar.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2019. p. 131
Series
TRITA-EECS-AVL ; 2019:51
Keywords
inverse problems, signal processing, machine learning, biomedical imaging, optimization, proximal optimization, regularization, mathematical modeling, identifiability, likelihood, logconcavity, immunoassays, convolutional coding, functional analysis, abstract inference, learned iterations, unrolled algorithms
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Signal Processing Probability Theory and Statistics Medical Image Processing Telecommunications
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-256079 (URN)978-91-7873-213-5 (ISBN)
Public defence
2019-09-16, F3, Lindstedtsvägen 26, Stockholm, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20190820

Available from: 2019-08-20 Created: 2019-08-19 Last updated: 2019-08-20Bibliographically approved

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del Aguila Pla, PolJaldén, Joakim

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