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

DVB-S based passive polarimetric ISAR – methods and experimental validation

In this work, we focus on passive polarimetric ISAR for ship target imaging using DVB-S signals of opportunity. A first goal of the research is to investigate if, within the challenging passive environment, different scattering mechanisms, belonging to distinct parts of the imaged target, can be separated in the polarimetric domain. Furthermore, a second goal is at verifying if polarimetric diversity could enable the formation of ISAR products with enhanced quality with respect to the single channel case, particularly in terms of better reconstruction of the target shape. To this purpose, a dedicated trial has been conducted along the river Rhine in Germany by means of an experimental DVB-S based system developed at Fraunhofer FHR and considering a ferry as cooperative target. To avoid inaccuracies due to data-driven motion compensation procedures and to fairly interpret the polarimetric results, we processed the data by means of a known-motion back-projection algorithm obtaining ISAR images at each polarimetric channel. Then, different approaches in the polarimetric domain have been introduced. The first one is based on the well-known Pauli Decomposition. The others can be divided in two main groups: (i) techniques aimed at separating the different backscattering mechanisms, and (ii) image domain techniques to fuse the polarimetric information in a single ISAR image with enhanced quality. The different considered techniques have been applied to several data sets with distinct bistatic geometries. The obtained results clearly demonstrate the potentialities of polarimetric diversity that could be fruitfully exploited for classification purposes

Advanced Ground-Based Real and Synthetic Aperture Radar

Ground-based/terrestrial radar interferometry (GBRI) is a scientific topic of increasing interest in recent years. The GBRI is used in several field as remote sensing technique for monitoring natural environment (landslides, glacier, and mines) or infrastructures (bridges, towers). These sensors provide the displacement of targets by measuring the phase difference between sending and receiving radar signal. If the acquisition rate is enough the GBRI can provide the natural frequency, e.g. by calculating the Fourier transform of displacement. The research activity, presented in this work, concerns design and development of some advanced GBRI systems. These systems are related to the following issue: detection of displacement vector, Multiple Input Multiple Output (MIMO) and radars with 3D capability

A sparsity-driven approach for joint SAR imaging and phase error correction

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements it provides over existing techniques for model error compensation in SAR

SAR image reconstruction by expectation maximization based matching pursuit

Cataloged from PDF version of article.Synthetic Aperture Radar (SAR) provides high resolution images of terrain and target reflectivity. SAR systems are indispensable in many remote sensing applications. Phase errors due to uncompensated platform motion degrade resolution in reconstructed images. A multitude of autofocusing techniques has been proposed to estimate and correct phase errors in SAR images. Some autofocus techniques work as a post-processor on reconstructed images and some are integrated into the image reconstruction algorithms. Compressed Sensing (CS), as a relatively new theory, can be applied to sparse SAR image reconstruction especially in detection of strong targets. Autofocus can also be integrated into CS based SAR image reconstruction techniques. However, due to their high computational complexity, CS based techniques are not commonly used in practice. To improve efficiency of image reconstruction we propose a novel CS based SAR imaging technique which utilizes recently proposed Expectation Maximization based Matching Pursuit (EMMP) algorithm. EMMP algorithm is greedy and computationally less complex enabling fast SAR image reconstructions. The proposed EMMP based SAR image reconstruction technique also performs autofocus and image reconstruction simultaneously. Based on a variety of metrics, performance of the proposed EMMP based SAR image reconstruction technique is investigated. The obtained results show that the proposed technique provides high resolution images of sparse target scenes while performing highly accurate motion compensation. (C) 2014 Elsevier Inc. All rights reserved

Passive Synthetic Aperture Radar Imaging Using Commercial OFDM Communication Networks

Modern communication systems provide myriad opportunities for passive radar applications. OFDM is a popular waveform used widely in wireless communication networks today. Understanding the structure of these networks becomes critical in future passive radar systems design and concept development. This research develops collection and signal processing models to produce passive SAR ground images using OFDM communication networks. The OFDM-based WiMAX network is selected as a relevant example and is evaluated as a viable source for radar ground imaging. The monostatic and bistatic phase history models for OFDM are derived and validated with experimental single dimensional data. An airborne passive collection model is defined and signal processing approaches are proposed providing practical solutions to passive SAR imaging scenarios. Finally, experimental SAR images using general OFDM and WiMAX waveforms are shown to validate the overarching signal processing concept