Compressed Sensing in Multi-Signal Environments.

Technological advances and the ability to build cheap high performance sensors make it possible to deploy tens or even hundreds of sensors to acquire information about a common phenomenon of interest. The increasing number of sensors allows us to acquire ever more detailed information about the underlying scene that was not possible before. This, however, directly translates to increasing amounts of data that needs to be acquired, transmitted, and processed. The amount of data can be overwhelming, especially in applications that involve high-resolution signals such as images or videos. Compressed sensing (CS) is a novel acquisition and reconstruction scheme that is particularly useful in scenarios when high resolution signals are difficult or expensive to encode. When applying CS in a multi-signal scenario, there are several aspects that need to be considered such as the sensing matrix, the joint signal model, and the reconstruction algorithm. The purpose of this dissertation is to provide a complete treatment of these aspects in various multi-signal environments. Specific applications include video, multi-view imaging, and structural health monitoring systems. For each application, we propose a novel joint signal model that accurately captures the joint signal structure, and we tailor the reconstruction algorithm to each signal model to successfully recover the signals of interest.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98007/1/jaeypark_1.pd

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure

Coded aperture compressive temporal imaging.

We use mechanical translation of a coded aperture for code division multiple access compression of video. We discuss the compressed video's temporal resolution and present experimental results for reconstructions of > 10 frames of temporal data per coded snapshot

An Adaptive Optimal Bandwidth Sensor for Video Imaging and Sparsifying Basis

Many compressive sensing architectures have shown promise towards reducingthe bandwidth for image acquisition significantly. In order to use these architectures for video acquisition we need a scheme that is able to effectively exploit temporal redundancies in a sequence. In this thesis we study a method to efficiently sample and reconstruct specific video sequences. The method is suitable for implementation using a single pixel detector along with a digital micromirror device (DMD) or other forms of spatial light modulators (SLMs). Conventional implementations of single pixel cameras are able to spatially compress the signal but the compressed measurements make it difficult to exploit temporal redundancies directly. Moreover a single pixel camera needs to make measurements in a sequential manner before the scene changes making it inefficient for video imaging. In this thesis we discuss a measurement scheme that exploits sparsity along the time axis for video imaging. After acquiring all measurements required for the first frame, measurements are only acquired from the areas which change in subsequent frames. We segment the first frame and detect magnitude and direction of change for each segment and acquire compressed measurements for the changing segments in the predicted direction. TV minimization is used to reconstruct the dynamic areas and PSNR variation is studied against different parameters of proposed scheme. We show the reconstruction results for a few test sequences commonly used for performance analysis and demonstrate the practical utility of the scheme. A comparison is made with existing algorithms to show the eeffectiveness of proposed method for specific video sequences. We also discuss use of customized transform to improve reconstruction of submililimeter wave single pixel imager. We use a sparseness inducing transformation onthe measurements and optimize the result using l1 minimization algorithms. We demonstrate improvement in result of several images acquired and reconstructed using this technique

Robust Algorithms for Low-Rank and Sparse Matrix Models

Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them. This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd