In compressive imaging the measurement quantization and its impact on the overall system performance is an important problem. This work considers several challenges that derive from quantization of compressive measurements. We investigate the design of scalar quantizer (SQ), vector quantizer (VQ), and tree-structured vector quantizer (TSVQ) for information-optimal compressive imaging. The performance of these quantizer designs is quantified for a variety of compression rates and measurement signal-to-noise-ratio (SNR) using simulation studies. Our simulation results show that in the low SNR regime a low bit-depth (3 bit per measurement) SQ is sufficient to minimize the degradation due to measurement quantization. However, in mid-to-high SNR regime, quantizer design requires higher bit-depth to preserve the information in the measurements. Simulation results also confirm the superior performance of VQ over SQ. As expected, TSVQ provides a good tradeoff between complexity and performance, bounded by VQ and SQ designs on either side of performance/complexity limits. In compressive image the size of final measurement data (i.e. in bits) is also an important system design metric. In this work, we also optimize the compressive imaging system using this design metric, and investigate how to optimally allocate the number of measurement and bits per measurement, i.e. the rate allocation problem. This problem is solved using both an empirical data driven approach and a model-based approach. As a function of compression rate (bits per pixel), our simulation results show that compressive imaging can outperform traditional (non-compressive) imaging followed by image compression (JPEG 2000) in low-to-mid SNR regime. However, in high SNR regime traditional imaging (with image compression) offers a higher image fidelity compare to compressive imaging for a given data rate. Compressive imaging using blockwise measurements is partly limited due to its inability to perform global rate allocation. We also develop an optimal minimum mean-square error (MMSE) reconstruction algorithm for quantized compressed measurements. The algorithm employs Monte-Carlo Markov Chain (MCMC) sampling technique to estimate the posterior mean. Simulation results show significant improvement over approximate MMSE algorithms.

We present a scalable information-optimal compressive imager optimized for the target classification task, discriminating between two target classes. Compressive projections are optimized using the Cauchy-Schwarz Mutual Information (CSMI) metric, which provides an upper-bound to the probability of error of target classification. The optimized measurements provide significant performance improvement relative to random and PCA secant projections. We validate the simulation performance of information-optimal compressive measurements with experimental data.

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.

Compressive sensing (CS) is a novel imaging technology based on the inherent redundancy of natural scenes. The minimum number of required measurements which defines the maximum image compression rate is lower-bounded by the sparsity of the image but is dependent on the type of acquisition patterns employed. Increased measurements by the Rice single pixel camera (SPC) slows down the acquisition process, which may cause the image recovery to be more susceptible to background noise and thus limit CS's application in imaging, detection, or classifying moving targets. In this study, two methods (hybrid-subspace sparse sampling (HSS) for imaging and secant projection on a manifold for classification are applied to solving this problem. For the HSS method, new image pattern are designed via robust principle component analysis (rPCA) on prior knowledge from a library of images to sense a common structure. After measuring coarse scale commonalities, the residual image becomes sparser, and then fewer measurements are needed. For the secant projection case, patterns that can preserve the pairwise distance between data points based on manifold learning are designed via semi-definite programming. These secant patterns turn out to be better in object classification over those learned from PCA. Both methods considerably decrease the number of required measurements for each task when compared with the purely random patterns of a more universal CS imaging system.

No description available.

Use of imaging systems for performing various situational awareness tasks in militaryand commercial settings has a long history. There is increasing recognition,however, that a much better job can be done by developing non-traditional opticalsystems that exploit the task-specific system aspects within the imager itself. Insome cases, a direct consequence of this approach can be real-time data compressionalong with increased measurement fidelity of the task-specific features. In others,compression can potentially allow us to perform high-level tasks such as direct trackingusing the compressed measurements without reconstructing the scene of interest.In this dissertation we present novel advancements in feature-specific (FS) imagersfor large field-of-view surveillence, and estimation of temporal object-scene changesutilizing the compressive imaging paradigm. We develop these two ideas in parallel.In the first case we show a feature-specific (FS) imager that optically multiplexesmultiple, encoded sub-fields of view onto a common focal plane. Sub-field encodingenables target tracking by creating a unique connection between target characteristicsin superposition space and the target's true position in real space. This isaccomplished without reconstructing a conventional image of the large field of view.System performance is evaluated in terms of two criteria: average decoding time andprobability of decoding error. We study these performance criteria as a functionof resolution in the encoding scheme and signal-to-noise ratio. We also includesimulation and experimental results demonstrating our novel tracking method. Inthe second case we present a FS imager for estimating temporal changes in the objectscene over time by quantifying these changes through a sequence of differenceimages. The difference images are estimated by taking compressive measurementsof the scene. Our goals are twofold. First, to design the optimal sensing matrixfor taking compressive measurements. In scenarios where such sensing matrices arenot tractable, we consider plausible candidate sensing matrices that either use theavailable <italic>a priori</italic> information or are non-adaptive. Second, we develop closed-form and iterative techniques for estimating the difference images. We present results to show the efficacy of these techniques and discuss the advantages of each.

This thesis exploits so called “Optical Eigenmodes” (OEi) in the focal plane of an optical system. The concept of OEi is introduced and the OEi operator approach is outlined, for which quadratic measures of the light field are expressed as real eigenvalues of an Hermitian operator. As an example, the latter is employed to locally minimise the width of a focal spot. The limitations of implementing these spots with state of the art spatial beam shaping technique are explored and a selected spot with a by 40 % decreased core width is used to confocally scan an in focus pair of holes, delivering a two-point resolution enhanced by a factor of 1.3. As a second application, OEi are utilised for fullfield imaging. Therefore they are projected onto an object and for each mode a complex coupling coefficient describing the light-sample interaction is determined. The superposition of the OEi weighted with these coefficients delivers an image of the object. Compared to a point-by-point scan of the sample with the same number of probes, i.e. scanning points, the OEi image features higher spatial resolution and localisation of object features, rendering OEi imaging a compressive imaging modality. With respect to a raster scan a compression by a factor four is achieved. Compared to ghost imaging as another fullfield imaging method, 2-3 orders of magnitude less probes are required to obtain similar images. The application of OEi for imaging in transmission as well as for fluorescence and (surface enhanced) Raman spectroscopy is demonstrated. Finally, the applicability of the OEi concept for the coherent control of nanostructures is shown. For this, OEi are generated with respect to elements on a nanostructure, such as nanoantennas or nanopads. The OEi can be superimposed in order to generate an illumination of choice, for example to address one or multiple nanoelements with a defined intensity. It is shown that, compared to addressing such elements just with a focussed beam, the OEi concept reduces illumination crosstalk in addressing individual nanoelements by up to 70 %. Furthermore, a fullfield aberration correction is inherent to experimentally determined OEi, hence enabling addressing of nanoelements through turbid media.

Les systèmes d'imagerie connaissent un développement soutenu et deviennent de plus en plus largement répandus. Les systèmes d'imagerie mettent en oeuvre des principes physiques variés dont l'élaboration continue de progresser (imagerie par résonance magnétique, thermographie, imagerie multi et hyperspectrale, etc). Au delà de leur constitution physique variée, les images produites ont en commun de constituer un support d'information. Dans ce contexte, nous proposons une contribution à des approches informationnelles en imagerie. Celle-ci est guidée par une transposition du paradigme informationnel de Shannon en imagerie développée selon deux axes. Nous présentons une approche de traitements conjoints où la finalité informationnelle de l'acquisition des images est une donnée connue a priori et utilisée pour optimiser certains réglages de la chaîne d'imagerie. Différentes problématiques de traitements conjoints de l'information sont présentées (échelle d'observation - estimation conjointe, compression - estimation conjointe, et acquisition - compression conjointe). Nous étendons ensuite le champ des études en résonance stochastique en explorant de nouveaux couplages signal-bruit se prêtant à des effets de bruit utile, en imagerie cohérente et en imagerie par résonance magnétique. La résonance stochastique est également considérée, de par sa signification informationnelle spécifique (le bruit utile à l'information), comme un phénomène permettant de tester et d'approfondir l'appréciation des propriétés et potentialités de mesures entropiques ou informationnelles appliquées en imagerie. Elle est en particulier utilisée comme un banc de test pour confronter ces mesures informationnelles à des mesures psychovisuelles sur des images.

Photos captured in the shortwave infrared (SWIR) spectrum are interesting in military applications because they are independent of what time of day the pic- ture is captured because the sun, moon, stars and night glow illuminate the earth with short-wave infrared radiation constantly. A major problem with today’s SWIR cameras is that they are very expensive to produce and hence not broadly available either within the military or to civilians. Using a relatively new tech- nology called compressive sensing (CS), enables a new type of camera with only a single pixel sensor in the sensor (a SPC). This new type of camera only needs a fraction of measurements relative to the number of pixels to be reconstructed and reduces the cost of a short-wave infrared camera with a factor of 20. The camera uses a micromirror array (DMD) to select which mirrors (pixels) to be measured in the scene, thus creating an underdetermined linear equation system that can be solved using the techniques described in CS to reconstruct the im- age. Given the new technology, it is in the Swedish Defence Research Agency (FOI) interest to evaluate the potential of a single pixel camera. With a SPC ar- chitecture developed by FOI, the goal of this thesis was to develop methods for sampling, reconstructing images and evaluating their quality. This thesis shows that structured random matrices and fast transforms have to be used to enable high resolution images and speed up the process of reconstructing images signifi- cantly. The evaluation of the images could be done with standard measurements associated with camera evaluation and showed that the camera can reproduce high resolution images with relative high image quality in daylight.

Exploiting signal sparsity has recently received considerable attention in a variety of areas including signal and image processing, compressive sensing, machine learning and so on. Many of these applications involve optimization models that are regularized by certain sparsity-promoting metrics. Two most popular regularizers are based on the l1 norm that approximates sparsity of vectorized signals and the total variation (TV) norm that serves as a measure of gradient sparsity of an image. Nevertheless, the l1 and TV terms are merely two representative measures of sparsity. To explore the matter of sparsity further, in this thesis we investigate relaxations of the regularizers to nonconvex terms such as lp and TVp "norms" with 0 <= p < 1. The contributions of the thesis are two-fold. First, several methods to approach globally optimal solutions of related nonconvex problems for improved signal/image reconstruction quality have been proposed. Most algorithms studied in the thesis fall into the category of iterative reweighting schemes for which nonconvex problems are reduced to a series of convex sub-problems. In this regard, the second main contribution of this thesis has to do with complexity improvement of the l1/TV-regularized methodology for which accelerated algorithms are developed. Along with these investigations, new techniques are proposed to address practical implementation issues. These include the development of an lp-related solver that is easily parallelizable, and a matrix-based analysis that facilitates implementation for TV-related optimizations. Computer simulations are presented to demonstrate merits of the proposed models and algorithms as well as their applications for solving general linear inverse problems in the area of signal and image denoising, signal sparse representation, compressive sensing, and compressive imaging. / Graduate