Dimensionality Reduction of Hyperspectral Imagery Using Random Projections

Hyperspectral imagery is often associated with high storage and transmission costs. Dimensionality reduction aims to reduce the time and space complexity of hyperspectral imagery by projecting data into a low-dimensional space such that all the important information in the data is preserved. Dimensionality-reduction methods based on transforms are widely used and give a data-dependent representation that is unfortunately costly to compute. Recently, there has been a growing interest in data-independent representations for dimensionality reduction; of particular prominence are random projections which are attractive due to their computational efficiency and simplicity of implementation. This dissertation concentrates on exploring the realm of computationally fast and efficient random projections by considering projections based on a random Hadamard matrix. These Hadamard-based projections are offered as an alternative to more widely used random projections based on dense Gaussian matrices. Such Hadamard matrices are then coupled with a fast singular value decomposition in order to implement a two-stage dimensionality reduction that marries the computational benefits of the data-independent random projection to the structure-capturing capability of the data-dependent singular value transform. Finally, random projections are applied in conjunction with nonnegative least squares to provide a computationally lightweight methodology for the well-known spectral-unmixing problem. Overall, it is seen that random projections offer a computationally efficient framework for dimensionality reduction that permits hyperspectral-analysis tasks such as unmixing and classification to be conducted in a lower-dimensional space without sacrificing analysis performance while reducing computational costs significantly

Single-pixel imaging 12 years on: a review

Modern cameras typically use an array of millions of detector pixels to capture images. By contrast, single-pixel cameras use a sequence of mask patterns to filter the scene along with the corresponding measurements of the transmitted intensity which is recorded using a single-pixel detector. This review considers the development of single-pixel cameras from the seminal work of Duarte et al. up to the present state of the art. We cover the variety of hardware configurations, design of mask patterns and the associated reconstruction algorithms, many of which relate to the field of compressed sensing and, more recently, machine learning. Overall, single-pixel cameras lend themselves to imaging at non-visible wavelengths and with precise timing or depth resolution. We discuss the suitability of single-pixel cameras for different application areas, including infrared imaging and 3D situation awareness for autonomous vehicles

Model-Based Acquisition for Compressive Sensing & Imaging

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

Detection and classification in the compressed domain for multispectral images

Various applications would benefit from rapid inference on multispectral images at the point of sensing. However, the acquisition of a full-resolution multispectral image requires advanced spectrometers and prohibitive sensing time. Also, performing the high-level vision tasks such as classification and segmentation on the multispectral data consumes more computation power than on the common RGB images. Compressed sensing (CS) circumvents this sensing process usually using a random sensing matrix to acquire fewer measurements and reconstructs the multispectral image based on a sparsity assumption. The further high-level analysis of images is performed on the reconstructed high-dimensional images. And a random sensing matrix may not be physically realizable or the best fit for extracting information pertaining to a high-level vision task. A realizable low-cost data acquisition scheme and a fast processing system that makes inference based on the acquired signal are desired for multispectral images. In this thesis, we present a systematic way to jointly optimize the sensing scheme subject to optical realizability constraints, and make inference of the multispectral image in the compressed domain. In the first part of the thesis, we state some open questions in compressed inference. We review the theory on inference in the compressed domain. We formulate the problem for compressed inference and state metrics to evaluate the inference performance. We then review some existing realizable optical compressed sensing imaging systems designed for multispectral images and derive the forward model of data acquisition. The feasibility of performing detection, classification and segmentation in the compressed domain directly is then discussed for the multispectral images. Using tools from detection and estimation theory, we derive the optimal decision rule to perform compressed detection, classification and segmentation in a simple data setting. Also, the feasibility of adjusting the optical acquisition schemes jointly with the neural network is discussed. The architecture of neural networks that can achieve the performance of the optimal decision rule is proposed and the existence of optimal weights is discussed. Next, we use a synthetic dataset to compare the performance of the proposed neural network and the optimal decision rule. Several synthetic multispectral image datasets and a clinical tumor biopsy dataset are used to verify the improvement of the obtained sensing scheme and compare the performance of the neural network with that of a known optimal decision rule