48 research outputs found

    Range resolution improvement in FM-based passive radars using deconvolution

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    FM-based passive bistatic radar (PBR) systems suffer from low range resolution because of the low baseband bandwidth of commercial FM broadcasts. In this paper, we propose a range resolution improvement method using deconvolution. The output of the PBR matched filter is processed using a deconvolution algorithm which assumes that targets are isolated, i.e., sparse in the range domain. The deconvolution algorithm is iterative and was implemented by performing successive orthogonal projections onto supporting hyperplanes of the epigraph set of a convex cost function. Simulation examples are presented. © 2016, Springer-Verlag London

    Image restoration and reconstruction using projections onto epigraph set of convex cost fuchtions

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    Cataloged from PDF version of article.This thesis focuses on image restoration and reconstruction problems. These inverse problems are solved using a convex optimization algorithm based on orthogonal Projections onto the Epigraph Set of a Convex Cost functions (PESC). In order to solve the convex minimization problem, the dimension of the problem is lifted by one and then using the epigraph concept the feasibility sets corresponding to the cost function are defined. Since the cost function is a convex function in R N , the corresponding epigraph set is also a convex set in R N+1. The convex optimization algorithm starts with an arbitrary initial estimate in R N+1 and at each step of the iterative algorithm, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The PESC algorithm provides globally optimal solutions for different functions such as total variation, `1-norm, `2-norm, and entropic cost functions. Denoising, deconvolution and compressive sensing are among the applications of PESC algorithm. The Projection onto Epigraph Set of Total Variation function (PES-TV) is used in 2-D applications and for 1-D applications Projection onto Epigraph Set of `1-norm cost function (PES-`1) is utilized. In PES-`1 algorithm, first the observation signal is decomposed using wavelet or pyramidal decomposition. Both wavelet denoising and denoising methods using the concept of sparsity are based on soft-thresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domain such as Fourier, DCT, and/or wavelet domain and transform domain coefficients of the noisy signal are soft-thresholded to reduce noise. Here, the relationship between the standard soft-thresholding based denoising methods and sparsity-based wavelet denoising methods is described. A deterministic soft-threshold estimation method using the epigraph set of `1-norm cost function is presented. It is demonstrated that the size of the `1-ball can be determined using linear algebra. The size of the `1-ball in turn determines the soft-threshold. The PESC, PES-TV and PES-`1 algorithms, are described in detail in this thesis. Extensive simulation results are presented. PESC based inverse restoration and reconstruction algorithm is compared to the state of the art methods in the literature.Tofighi, MohammadM.S

    Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

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    In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the epigraph set of Total Variation (TV) function. This set does not need a prescribed upper bound on the total variation of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both of these two closed and convex sets can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin

    Projections onto the epigraph set of the filtered variation function based deconvolution algorithm

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    A new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in RN, then the corresponding epigraph set is also a convex set in the lifted set in RN+1. At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in RN+1, first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image. © 2016 IEEE

    Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

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    In this paper, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the Epigraph Set of Total Variation (ESTV) function. This set does not need a prescribed upper bound on the Total Variation (TV) of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both the TV of the image and the blurring filter are regularized using the ESTV set. Both the phase information set and the ESTV are closed and convex sets. Therefore they can be used as a part of any blind deconvolution algorithm. Simulation examples are presented. © 2015 IEEE

    Proximity Operators of Discrete Information Divergences

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    Information divergences allow one to assess how close two distributions are from each other. Among the large panel of available measures, a special attention has been paid to convex φ\varphi-divergences, such as Kullback-Leibler, Jeffreys-Kullback, Hellinger, Chi-Square, Renyi, and Iα_{\alpha} divergences. While φ\varphi-divergences have been extensively studied in convex analysis, their use in optimization problems often remains challenging. In this regard, one of the main shortcomings of existing methods is that the minimization of φ\varphi-divergences is usually performed with respect to one of their arguments, possibly within alternating optimization techniques. In this paper, we overcome this limitation by deriving new closed-form expressions for the proximity operator of such two-variable functions. This makes it possible to employ standard proximal methods for efficiently solving a wide range of convex optimization problems involving φ\varphi-divergences. In addition, we show that these proximity operators are useful to compute the epigraphical projection of several functions of practical interest. The proposed proximal tools are numerically validated in the context of optimal query execution within database management systems, where the problem of selectivity estimation plays a central role. Experiments are carried out on small to large scale scenarios

    Range resolution improvement in passive bistatic radars using nested FM channels and least squares approach

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    One of the main disadvantages of using commercial broadcasts in a Passive Bistatic Radar (PBR) system is the range resolution. Using multiple broadcast channels to improve the radar performance is offered as a solution to this problem. However, it suffers from detection performance due to the side-lobes that matched filter creates for using multiple channels. In this article, we introduce a deconvolution algorithm to suppress the side-lobes. The two-dimensional matched filter output of a PBR is further analyzed as a deconvolution problem. The deconvolution algorithm is based on making successive projections onto the hyperplanes representing the time delay of a target. Resulting iterative deconvolution algorithm is globally convergent because all constraint sets are closed and convex. Simulation results in an FM based PBR system are presented. © 2015 SPIE

    Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

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    This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This version has updated reference
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