Sparse representation for the ISAR image reconstruction

In this paper, a sparse representation for the data form a multi-input multi-output based inverse synthetic aperture radar (ISAR) system is derived for two dimensions. The proposed sparse representation motivates the use a of a Convex Optimization directly that recovers the image without the loss information of the image with far less samples that that is required by Nyquist–Shannon sampling theorem, which increases the efficiency and decrease the cost of calculation in radar imaging

Compressed Sensing Applied to Weather Radar

We propose an innovative meteorological radar, which uses reduced number of spatiotemporal samples without compromising the accuracy of target information. Our approach extends recent research on compressed sensing (CS) for radar remote sensing of hard point scatterers to volumetric targets. The previously published CS-based radar techniques are not applicable for sampling weather since the precipitation echoes lack sparsity in both range-time and Doppler domains. We propose an alternative approach by adopting the latest advances in matrix completion algorithms to demonstrate the sparse sensing of weather echoes. We use Iowa X-band Polarimetric (XPOL) radar data to test and illustrate our algorithms.Comment: 4 pages, 5 figrue

Sparse Bases and Bayesian Inference of Electromagnetic Scattering

Many approaches in CEM rely on the decomposition of complex radiation and scattering behavior with a set of basis vectors. Accurate estimation of the quantities of interest can be synthesized through a weighted sum of these vectors. In addition to basis decompositions, sparse signal processing techniques developed in the CS community can be leveraged when only a small subset of the basis vectors are required to sufficiently represent the quantity of interest. We investigate several concepts in which novel bases are applied to common electromagnetic problems and leverage the sparsity property to improve performance and/or reduce computational burden. The first concept explores the use of multiple types of scattering primitives to reconstruct scattering patterns of electrically large targets. Using a combination of isotropic point scatterers and wedge diffraction primitives as our bases, a 40% reduction in reconstruction error can be achieved. Next, a sparse basis is used to improve DOA estimation. We implement the BSBL technique to determine the angle of arrival of multiple incident signals with only a single snapshot of data from an arbitrary arrangement of non-isotropic antennas. This is an improvement over the current state-of-the-art, where restrictions on the antenna type, configuration, and a priori knowledge of the number of signals are often assumed. Lastly, we investigate the feasibility of a basis set to reconstruct the scattering patterns of electrically small targets. The basis is derived from the TCM and can capture non-localized scattering behavior. Preliminary results indicate that this basis may be used in an interpolation and extrapolation scheme to generate scattering patterns over multiple frequencies

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