Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Single-image super-resolution using sparsity constraints and non-local similarities at multiple resolution scales

Traditional super-resolution methods produce a clean high-resolution image from several observed degraded low-resolution images following an acquisition or degradation model. Such a model describes how each output pixel is related to one or more input pixels and it is called data fidelity term in the regularization framework. Additionally, prior knowledge such as piecewise smoothness can be incorporated to improve the image restoration result. The impact of an observed pixel on the restored pixels is thus local according to the degradation model and the prior knowledge. Therefore, the traditional methods only exploit the spatial redundancy in a local neighborhood and are therefore referred to as local methods. Recently, non-local methods, which make use of similarities between image patches across the whole image, have gained popularity in image restoration in general. In super-resolution literature they are often referred to as exemplar-based methods. In this paper, we exploit the similarity of patches within the same scale (which is related to the class of non-local methods) and across different resolution scales of the same image (which is also related to the fractal-based methods). For patch fusion, we employ a kernel regression algorithm, which yields a blurry and noisy version of the desired high-resolution image. For the final reconstruction step, we develop a novel restoration algorithm. The joint deconvolution/denoising algorithm is based on the split Bregman iterations and, as prior knowledge, the algorithm exploits the sparsity of the image in the shearlet-transformed domain. Initial results indicate an improvement over both classical local and state-of-the art non-local super-resolution methods

Обработка изображений с помощью Shearlets

В статье дано определение и основные возможности для приложений Shearlets. Рассматривается проблема удаления шума с изображения с по- мощью вейвлетов и Shearlets. Проводится сравнение полученных резуль- татов

Optimal sparsity allows reliable system-aware restoration of fluorescence microscopy images

Incluye: artículo, material suplementario, videos y software.Fluorescence microscopy is one of the most indispensable and informative driving forces for biological research, but the extent of observable biological phenomena is essentially determined by the content and quality of the acquired images. To address the different noise sources that can degrade these images, we introduce an algorithm for multiscale image restoration through optimally sparse representation (MIRO). MIRO is a deterministic framework that models the acquisition process and uses pixelwise noise correction to improve image quality. Our study demonstrates that this approach yields a remarkable restoration of the fluorescence signal for a wide range of microscopy systems, regardless of the detector used (e.g., electron-multiplying charge-coupled device, scientific complementary metal-oxide semiconductor, or photomultiplier tube). MIRO improves current imaging capabilities, enabling fast, low-light optical microscopy, accurate image analysis, and robust machine intelligence when integrated with deep neural networks. This expands the range of biological knowledge that can be obtained from fluorescence microscopy.We acknowledge the support of the National Institutes of Health grants R35GM124846 (to S.J.) and R01AA028527 (to C.X.), the National Science Foundation grants BIO2145235 and EFMA1830941 (to S.J.), and Marvin H. and Nita S. Floyd Research Fund (to S.J.). This research project was supported, in part, by the Emory University Integrated Cellular Imaging Microscopy Core and by PHS Grant UL1TR000454 from the Clinical and Translational Science Award Program, National Institutes of Health, and National Center for Advancing Translational Sciences.S

On the optimization of the satellite imaging chain

In this paper, we focus on the global optimization of the satellite imaging chain. The theoretical analysis of the satellite imaging chain optimization is a difficult problem that needs lot of approximations. In order to consider the complex real satellite imaging chain, we propose to address this problem numerically and we present, based on numerical experiments, techniques to optimize the quality of the reconstructed final image. We first focus on the common question of the position of the restoration step in the imaging chain, that is on-board before coding or on-ground after coding. Then, we present several methods to remove the coding artifacts inherent in wavelet based coder schemes. From these numerical results we propose a new satellite imaging chain and we show visual and rate-distortion results on a real satellite image