Wavelet-Based Reconstruction for Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) scanners produce raw measurements that are unfit to direct interpretation, unless an algorithmic step, called reconstruction, is introduced. Up to the last decade, this reconstruction was performed by algorithms of moderate complexity. This worked because substantial efforts were devoted to adjust the MRI hardware to suit the algorithmic component. More recently, new techniques have reversed this trend by putting more emphasis on the algorithms and alleviating the constraints on the hardware. Whereas many new methods suffer from a marked increase in computational complexity, this thesis focuses on the development of reconstruction algorithms that are faster and simpler than state-of-the-art solutions, while preserving their quality. First, we present the physical principles that underlie the acquisition of MRI data and motivate the classical linear model. Based on this continuous equation, we derive efficient implementations of a discrete model. Standard and state-of-the-art reconstruction algorithms are reviewed and presented in a general framework where reconstruction is regarded as an optimization problem that can naturally integrate regularization. Next, we propose novel simulation tools for the validation of reconstruction methods. Those tools model the sensitivity of the receiving coil, which allows for the simulation of parallel MRI experiments. To honor the continuous nature of the underlying physics, we suggest the use of analytical phantoms. Unlike rasterized simulations, our phantoms do not introduce aliasing artifacts. Instead, they allow us to study how rasterization itself impacts the quality of reconstruction. To achieve this goal, we were able to work out closed-form solutions for the Fourier transform of parametric regions that can realistically reproduce anatomical features. Our results show that the inverse-crime situation impairs significantly the assessment of the performance of reconstruction methods, particularly, the non-linear ones. Finally, we investigate the design of algorithms that achieve reconstruction with a sparsity constraint expressed in a wavelet domain. Based on the latest developments in large-scale convex optimization, we derive an acceleration strategy that can be tailored to the MRI setup and provide theoretical evidence of its benefit. We develop it into a practical method that combines the advantages of speed and quality. Applied on challenging reconstruction problems, with simulated and in-vivo data, we significantly reduce the reconstruction time over state-of-the-art techniques without compromising quality.

Data-driven Measurement Designs for Magnetic Resonance Imaging

Baran Gözcü

Despite being a powerful medical imaging technique which does not emit any ionizing radiation, magnetic resonance imaging (MRI) always had the major problem of long scanning times that can take up to an hour depending on the application. It also requires uncomfortable breath-holds due to the slow acquisition, sedation of children and repeated scans in the cases of degraded image quality due to body motion. Recent years have seen new image reconstruction techniques that need less amount of acquired data (i.e., accelerated scans) for reconstructing MRI images: parallel imaging and compressed sensing (CS). Although much work has been done on the reconstruction side, there has been relatively less work on experimental design, i.e., which parts of the Fourier domain to acquire during the scan, an essential factor that considerably affects the performance of image reconstructions. The state-of-the-art experimental designs use random subsampling either based on parametric models or heuristical adaptive models. The requirement of extensive parameter tuning and the random nature of the performance render these methods impractical and unreliable for clinical use. Can we systematically use the data acquired during past MRI scans for the design of accelerated scans with a reliable image quality? This problem is the focus of this thesis which proposes a data-driven scan design approach and training procedures which efficiently and effectively learn the structure inherent in the data, and accordingly, design the scans that directly acquire only the most relevant information during acquisition given an acceleration rate constraint. As a result, this boosts the performance of the existing state-of-the-art compressive sensing techniques on real-world datasets. Moreover, this approach provides strong theoretical guarantees by using tools from statistical learning theory. The intensive computational training procedures of our approach are made feasible by large-scale implementations on a parallel computing cluster. In return, this approach avoids any dependence on parametric or heuristic models and provides a reliably consistent image reconstruction performance for accelerated scans. Our approach is flexible and capable of giving deterministic scan designs specific to the anatomy, to the acceleration rate in use, to the reconstruction algorithm and the scan settings such as static/dynamic and parallel imaging. Apart from measurement designs for MRI, this thesis also considers the reconstruction problem. In particular, we focus on the inverse problems that involve a mixture of regularizers in the objective function, exploiting multiple structures at the same time. For these problems, we propose a reliable and systematic optimization framework and illustrate its effectiveness. Finally, in the last part of the thesis, we present a data-driven model and an optimization method for the design of nearly isometric, linear and dimensionality reducing embeddings.

EPFL2019

Low Complexity Scheduling and Coding for Wireless Networks

Siddhartha Brahma

The advent of wireless communication technologies has created a paradigm shift in the accessibility of communication. With it has come an increased demand for throughput, a trend that is likely to increase further in the future. A key aspect of these challenges is to develop low complexity algorithms and architectures that can take advantage of the nature of the wireless medium like broadcasting and physical layer cooperation. In this thesis, we consider several problems in the domain of low complexity coding, relaying and scheduling for wireless networks. We formulate the Pliable Index Coding problem that models a server trying to send one or more new messages over a noiseless broadcast channel to a set of clients that already have a subset of messages as side information. We show through theoretical bounds and algorithms, that it is possible to design short length codes, poly-logarithmic in the number of clients, to solve this problem. The length of the codes are exponentially better than those possible in a traditional index coding setup. Next, we consider several aspects of low complexity relaying in half-duplex diamond networks. In such networks, the source transmits information to the destination through

n

half-duplex intermediate relays arranged in a single layer. The half-duplex nature of the relays implies that they can either be in a listening or transmitting state at any point of time. To achieve high rates, there is an additional complexity of optimizing the schedule (i.e. the relative time fractions) of the relaying states, which can be

2^n

in number. Using approximate capacity expressions derived from the quantize-map-forward scheme for physical layer cooperation, we show that for networks with

n\leq 6

relays, the optimal schedule has atmost

n+1

active states. This is an exponential improvement over the possible

2^n

active states in a schedule. We also show that it is possible to achieve at least half the capacity of such networks (approximately) by employing simple routing strategies that use only two relays and two scheduling states. These results imply that the complexity of relaying in half-duplex diamond networks can be significantly reduced by using fewer scheduling states or fewer relays without adversely affecting throughput. Both these results assume centralized processing of the channel state information of all the relays. We take the first steps in analyzing the performance of relaying schemes where each relay switches between listening and transmitting states randomly and optimizes their relative fractions using only local channel state information. We show that even with such simple scheduling, we can achieve a significant fraction of the capacity of the network. Next, we look at the dual problem of selecting the subset of relays of a given size that has the highest capacity for a general layered full-duplex relay network. We formulate this as an optimization problem and derive efficient approximation algorithms to solve them. We end the thesis with the design and implementation of a practical relaying scheme called QUILT. In it the relay opportunistically decodes or quantizes its received signal and transmits the resulting sequence in cooperation with the source. To keep the complexity of the system low, we use LDPC codes at the source, interleaving at the relays and belief propagation decoding at the destination. We evaluate our system through testbed experiments over WiFi.

EPFL2015

Coordination and Sampling in Distributed Constraint Optimization

Brammert Ottens

The Distributed Constraint Optimization (DCOP) framework can be used to model a wide range of optimization problems that are inherently distributed. A distributed optimization problem can be viewed as a problem distributed over a set of agents, where agents are responsible for finding a solution for their part of the problem. In the DCOP framework, the decisions the agents need to take are modeled using decision variables, and both the local problems and the inter-dependencies are modeled using constraints. In this thesis, we attack two problems related to the DCOP framework. In the first part of this thesis, we look at coordination problems with complex, non- trivial preferences. In the DCOP literature, the notion of complex is used for problems where agents need to take multiple-decisions and thus own multiple decision variables. To express the fact that agents preferences are hard to obtain, we introduce the notion of a non-trivial local problem. The present DCOP literature has largely ignored the origin of preferences, i.e. algorithms assume that the constraints are known a-priori. In coordination problems with complex, non-trivial preferences this assumption no longer holds. In order to investigate the behavior of existing DCOP algorithms on such coordination problems, we first introduce a new DCOP model for such coordination problems, where we make an explicit distinction between the coordination part of the problem, and the local preferences of the agents. We then introduce two new benchmarks with complex, non-trivial local subproblems, and perform an evaluation of several complete and non-complete DCOP algorithms. Our results show that the O-DPOP algorithm, which elicits preferences from agents in a best-first order, outper- forms both other complete approaches as also local search approaches. We show that, despite the fact that a best first order cannot always be guaranteed when dealing with non-trivial local problems, O-DPOP still finds solutions that are either better, or on par with, local search algorithms. In the second part of this thesis, we introduce a new sampling based approach to solving DCOPs. Existing DCOP algorithms are either complete, but do not scale well, or scale well but are not guaranteed to find a solution. Our approach, inspired by the application of the UCB algorithm for the multi-armed bandit problem on trees, aims to provide method that scales well. Furthermore, given certain assumptions on the problem structure, our method is guaranteed to find good solutions. We introduce the Distributed UCT (DUCT) algorithm, that uses bounds similar to those used in the UCT algorithm, which is an adaptation of the UCB approach on trees. We introduce and evaluate four different variations of the DUCT algorithm, DUCT-A, DUCT-B, DUCT-C and DUCT-D, that differ in the bounds that they use. To evaluate our algorithms, we compare them with existing DCOP approaches on three different types of problems, both with and without hard constraints. Our results show that, compared with other DCOP algorithms, the DUCT-D variant consistently performs well on the problems used, with respect to both solution quality and runtime. Furthermore, it consistently sends less information than the state-of-the-art DCOP algorithms, and is thus shown to be a suitable and practical algorithm for solving DCOPs.

EPFL2012