Sparse Representations and Nonlinear Image Processing for Inverse Imaging Solution

This work applies sparse representations and nonlinear image processing to two inverse imaging problems. The first problem involves image restoration, where the aim is to reconstruct an unknown high-quality image from a low-quality observed image. Sparse representations of images have drawn a considerable amount of interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. The standard sparse representation, however, does not consider the intrinsic geometric structure present in the data, thereby leading to sub-optimal results. Using the concept that a signal is block sparse in a given basis ---i.e., the non-zero elements occur in clusters of varying sizes --- we present a novel and efficient algorithm for learning a sparse representation of natural images, called graph regularized block sparse dictionary (GRBSD) learning. We apply the proposed method towards two image restoration applications: 1) single-Image super-resolution, where we propose a local regression model that uses learned dictionaries from the GRBSD algorithm for super-resolving a low-resolution image without any external training images, and 2) image inpainting, where we use GRBSD algorithm to learn a multiscale dictionary to generate visually plausible pixels to fill missing regions in an image. Experimental results validate the performance of the GRBSD learning algorithm for single-image super-resolution and image inpainting applications. The second problem addressed in this work involves image enhancement for detection and segmentation of objects in images. We exploit the concept that even though data from various imaging modalities have high dimensionality, the data is sufficiently well described using low-dimensional geometrical structures. To facilitate the extraction of objects having such structure, we have developed general structure enhancement methods that can be used to detect and segment various curvilinear structures in images across different applications. We use the proposed method to detect and segment objects of different size and shape in three applications: 1) segmentation of lamina cribrosa microstructure in the eye from second-harmonic generation microscopy images, 2) detection and segmentation of primary cilia in confocal microscopy images, and 3) detection and segmentation of vehicles in wide-area aerial imagery. Quantitative and qualitative results show that the proposed methods provide improved detection and segmentation accuracy and computational efficiency compared to other recent algorithms.