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Inverse problems in signal processing: Functional optimization, parameter estimation and machine learning
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.ORCID iD: 0000-0003-3054-7210
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 [en]
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: urn:nbn:se:kth:diva-256079ISBN: 978-91-7873-213-5 (print)OAI: oai:DiVA.org:kth-256079DiVA, id: diva2:1343946
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
List of papers
1. Cell detection by functional inverse diffusion and non-negative group sparsity – Part I: Modeling and Inverse Problems
Open this publication in new window or tab >>Cell detection by functional inverse diffusion and non-negative group sparsity – Part I: Modeling and Inverse Problems
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
Keywords
Inverse problems, Biomedical imaging, Convex optimization, Source localization, Biological modeling
National Category
Signal Processing Medical Image Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-233824 (URN)10.1109/TSP.2018.2868258 (DOI)000444842400007 ()2-s2.0-85052785365 (Scopus ID)
Funder
Swedish Research Council, 2015-04026
Note

QC 20180918

Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2019-08-20Bibliographically approved
2. Cell detection by functional inverse diffusion and non-negative group sparsity – Part II: Proximal optimization and Performance evaluation
Open this publication in new window or tab >>Cell detection by functional inverse diffusion and non-negative group sparsity – Part II: Proximal optimization and Performance evaluation
2018 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5422-5437Article 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 second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics.

Place, publisher, year, edition, pages
IEEE, 2018
Keywords
Proximal operator, Non-negative group sparsity, Functional optimization, Biomedical imaging, Source localization
National Category
Signal Processing Medical Image Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-233827 (URN)10.1109/TSP.2018.2868256 (DOI)000444842400008 ()2-s2.0-85052808396 (Scopus ID)
Funder
Swedish Research Council, 2015-04026
Note

QC 20180918

Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2019-08-20Bibliographically approved
3. Clock synchronization over networks - Identifiability of the sawtooth model
Open this publication in new window or tab >>Clock synchronization over networks - Identifiability of the sawtooth model
Show others...
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we analyze the two-node joint clocksynchronization and ranging problem. We focus on the case of nodes that employ time-to-digital converters to determine the range between them precisely. This specific design leads to a sawtooth model for the captured signal, which has not been studied in detail before from an estimation theory standpoint. In the study of this model, we recover the basic conclusion of a well-known article by Freris, Graham, and Kumar in clock synchronization. Additionally, we discover a surprising identifiability result on the sawtooth signal model: noise improves the theoretical condition of the estimation of the phase and offset parameters. To complete our study, we provide performance references for joint clock synchronization and ranging. In particular, we present the Cramér-Rao lower bounds that correspond to a linearization of our model, as well as a simulation study on the practical performance of basic estimation strategies under realistic parameters. With these performance references, we enable further research in estimation strategies using the sawtooth model and pave the path towards industrial use.

Keywords
Clock synchronization, ranging, identifiability, sawtooth model, sensor networks, round-trip time (RTT)
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Control Engineering Signal Processing Telecommunications
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-256072 (URN)
Note

QC 20190820

Under review at the IEEE Transactions on Control Systems Technology.

Available from: 2019-08-19 Created: 2019-08-19 Last updated: 2019-08-20Bibliographically approved
4. Inferences from quantized data - Likelihood logconcavity
Open this publication in new window or tab >>Inferences from quantized data - Likelihood logconcavity
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we present to the signal processing community the most general likelihood logconcavity statement for quantized data to date, together with its proof, which has never been published. In particular, we show how Prékopa’s theorem can be used to show that the likelihood for quantized linear models is jointly logconcave with respect to both its location and scale parameter in a broad range of cases. In order to show this result and explain the limitations of the proof technique, we study sets generated by combinations of points with positive semi-definite matrices whose sum is the identity.

Keywords
quantization, grouping, likelihood, logconcavity
National Category
Probability Theory and Statistics Signal Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-256078 (URN)
Note

QC 20190820

Available from: 2019-08-19 Created: 2019-08-19 Last updated: 2019-08-20Bibliographically approved
5. Cell detection on image-based immunoassays
Open this publication in new window or tab >>Cell detection on image-based immunoassays
2018 (English)In: 2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018), IEEE, 2018, p. 431-435Conference paper, Published paper (Refereed)
Abstract [en]

Cell detection and counting in the image-based ELISPOT and Fluorospot immunoassays is considered a bottleneck.The task has remained hard to automatize, and biomedical researchers often have to rely on results that are not accurate.Previously proposed solutions are heuristic, and data-based solutions are subject to a lack of objective ground truth data. In this paper, we analyze a partial differential equations model for ELISPOT, Fluorospot, and assays of similar design. This leads us to a mathematical observation model forthe images generated by these assays. We use this model to motivate a methodology for cell detection. Finally, we provide a real-data example that suggests that this cell detection methodology and a human expert perform comparably.

Place, publisher, year, edition, pages
IEEE, 2018
Keywords
Inverse problems, Optimization, Source localization, Immunoassays
National Category
Signal Processing Medical Image Processing
Research subject
Technology and Health; Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-223933 (URN)10.1109/ISBI.2018.8363609 (DOI)000455045600098 ()2-s2.0-85048099869 (Scopus ID)978-1-5386-3636-7 (ISBN)978-1-5386-3637-4 (ISBN)978-1-5386-3635-0 (ISBN)
Conference
2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018), Washington, DC, USA, April 4-7, 2018
Funder
Swedish Research Council, 2015-04026
Note

QC 20180611

Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2019-08-20Bibliographically approved
6. Convolutional group-sparse coding and source localization
Open this publication in new window or tab >>Convolutional group-sparse coding and source localization
2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we present a new interpretation of non-negatively constrained convolutional coding problems as blind deconvolution problems with spatially variant point spread function. In this light, we propose an optimization framework that generalizes our previous work on non-negative group sparsity for convolutional models. We then link these concepts to source localization problems that arise in scientific imaging, and provide a visual example on an image derived from data captured by the Hubble telescope.

Place, publisher, year, edition, pages
IEEE, 2018
Series
IEEE International Conference on Acoustics, Speech and Signal Processing, E-ISSN 2379-190X
Keywords
Sparse representation, Source localization, Non-negative group sparsity
National Category
Signal Processing
Research subject
Electrical Engineering; Computer Science
Identifiers
urn:nbn:se:kth:diva-224253 (URN)10.1109/ICASSP.2018.8462235 (DOI)000446384602188 ()2-s2.0-85054240957 (Scopus ID)978-1-5386-4659-5 (ISBN)978-1-5386-4658-8 (ISBN)978-1-5386-4657-1 (ISBN)
Conference
2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 15-20 April 2018, Calgary, AB, Canada
Funder
Swedish Research Council, 2015-04026The Royal Swedish Academy of Sciences
Note

QC 20180917

Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2019-08-20Bibliographically approved
7. SpotNet – Learned iterations for cell detection in image-based immunoassays
Open this publication in new window or tab >>SpotNet – Learned iterations for cell detection in image-based immunoassays
2019 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Accurate cell detection and counting in the image-based ELISpot and FluoroSpot immunoassays is a challenging task. Recently proposed methodology matches human accuracy by leveraging knowledge of the underlying physical process of these assays and using proximal optimization methods to solve an inverse problem. Nonetheless, thousands of computationally expensive iterations are often needed to reach a near-optimal solution. In this paper, we exploit the structure of the iterations to design a parameterized computation graph, SpotNet, that learns the patterns embedded within several training images and their respective cell information. Further, we compare SpotNet to a convolutional neural network layout customized for cell detection. We show empirical evidence that, while both designs obtain a detection performance on synthetic data far beyond that of a human expert, SpotNet is easier to train and obtains better estimates of particle secretion for each cell.

Keywords
Source localization, Immunoassays, Convolutional sparse coding, Artificial neural networks
National Category
Signal Processing Medical Image Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-250464 (URN)
Conference
2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019)
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)
Note

QC 20190430

Available from: 2019-04-30 Created: 2019-04-30 Last updated: 2019-08-20Bibliographically approved

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