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Imaging systems play an important role in many diverse applications. Requirements for these applications, however, can lead to complex or sub-optimal designs. Traditionally, imaging systems are designed to yield a visually pleasing representation, or "pretty picture", of the scene or object. Often this is because a human operator is viewing the acquired image to perform a specific task. With digital computers increasingly being used for automation, a large number of algorithms have been designed to accept as input a pretty picture. This isomorphic representation however is neither necessary nor optimal for tasks such as data compression, transmission, pattern recognition or classification. This disconnect between optical measurement and post processing for the final system outcome has motivated an interest in computational imaging (CI). In a CI system the optical sub-system and post-processing sub-system is jointly designed to optimize system performance for a specific task. In these hybrid imagers, the measured image may no longer be a pretty picture but rather an intermediate non-traditional measurement. In this work, applications of non-traditional measurements are considered for computational imaging. Two systems for an image reconstruction task are studied and one system for a detection task is investigated. First, a CI system to extend the field of view is analyzed and an experimental prototype demonstrated. This prototype validates the simulation study and is designed to yield a 3x field of view improvement relative to a conventional imager. Second, a CI system to acquire time-varying natural scenes, i.e. video, is developed. A candidate system using 8x8x16 spatiotemporal blocks yields about 292x compression compared to a conventional imager. Candidate electro-optical architectures, including charge-domain processing, to implement this approach are also discussed. Lastly, a CI system with x-ray pencil beam illumination is investigated for a detection task where system performance is quantified using an information-theoretic metric.

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

Three problems in compressive sensing, namely, recovery of sparse signals from noise-free measurements, recovery of sparse signals from noisy measurements, and recovery of so called block-sparse signals from noisy measurements, are investigated. In Chapter 2, the reconstruction of sparse signals from noise-free measurements is investigated and three algorithms are developed. The first and second algorithms minimize the approximate L0 and Lp pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasi-Newton algorithm. An efficient line search based on Banach's fixed-point theorem is developed and applied in the second algorithm. The third algorithm minimizes the approximate Lp pseudonorm in the null space by using a sequential conjugate-gradient (CG) algorithm. Simulation results are presented which demonstrate that the proposed algorithms yield improved signal reconstruction performance relative to that of the iterative reweighted (IR), smoothed L0 (SL0), and L1-minimization based algorithms. They also require a reduced amount of computations relative to the IR and L1-minimization based algorithms. The Lp-minimization based algorithms require less computation than the SL0 algorithm. In Chapter 3, the reconstruction of sparse signals and images from noisy measurements is investigated. First, two algorithms for the reconstruction of signals are developed by minimizing an Lp-pseudonorm regularized squared error as the objective function using the sequential optimization procedure developed in Chapter 2. The first algorithm minimizes the objective function by taking steps along descent directions that are computed in the null space of the measurement matrix and its complement space. The second algorithm minimizes the objective function in the time domain by using a CG algorithm. Second, the well known total variation (TV) norm has been extended to a nonconvex version called the TVp pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVp-pseudonorm regularized squared error using a sequential Fletcher-Reeves' CG algorithm. Simulation results are presented which demonstrate that the first two algorithms yield improved signal reconstruction performance relative to the IR, SL0, and L1-minimization based algorithms and require a reduced amount of computation relative to the IR and L1-minimization based algorithms. The TVp-minimization based algorithm yields improved image reconstruction performance and a reduced amount of computation relative to Romberg's algorithm. In Chapter 4, the reconstruction of so-called block-sparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p pseudonorm, and an algorithm based on the minimization of an L2/p-pseudonorm regularized squared error is developed. The minimization is carried out using a sequential Fletcher-Reeves' CG algorithm and the line search described in Chapter 2. A reweighting technique for the reduction of amount of computation and a method to use prior information about the locations of nonzero blocks for the improvement in signal reconstruction performance are also proposed. Simulation results are presented which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to the L2/1-minimization based, block orthogonal matching pursuit, IR, and L1-minimization based algorithms. / Graduate

Automatic target recognition (ATR) is the ability for a computer to discriminate between different objects in a scene. ATR is often performed on point cloud data from a sensor known as a Ladar. Increasing the resolution of this point cloud in order to get a more clear view of the object in a scene would be of significant interest in an ATR application. A technique to increase the resolution of a scene is known as super resolution. This technique requires many low resolution images that can be combined together. In recent years, however, it has become possible to perform super resolution on a single image. This thesis sought to apply Gabor Wavelets and Compressive Sensing to single image super resolution of digital images of natural scenes. The technique applied to images was then extended to allow the super resolution of a point cloud.

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ITC/USA 2011 Conference Proceedings / The Forty-Seventh Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2011 / Bally's Las Vegas, Las Vegas, Nevada / In this paper we study a new streaming Compressive Sensing (CS) technique that aims to replace high speed Analog to Digital Converters (ADC) for certain classes of signals and reduce the artifacts that arise from block processing when conventional CS is applied to continuous signals. We compare the performance of both streaming and block processing methods on several types of signals and quantify the signal reconstruction quality when packet loss is applied to the transmitted sampled data.

The field of compressive sensing deals with the recovery of a sparse signal from a small set of measurements or linear projections of the signal. In this thesis, we introduce a stochastic framework that allows a collection of correlated sparse signals to be recovered by exploiting both intra and inter signal correlation. Our approach differs from others by not assuming that the collection of sparse signals have a common support or a common component; in some cases, this assumption does not hold true. Imagine a simplified cognitive radio problem, where users can send a single tone (sine-wave) in a finite number of frequencies; it is desired to find the used frequencies over a large area (creation of a radio map). This is a sparse problem; however, as we move spatially, the occuppied frequencies change, thus voiding the assumption of a common support/component. Our solution to multi sparse signal recovery addresses this problem, where signals that are close geographically are highly correlated and their support gradually changes as the distance between signals grow. Our approach consists of the creation of a probabilistic model that accounts for inter and intra signal correlation and then using belief propagation to calculate the posterior distribution of the signals and perform recovery.