541 research outputs found

    Info-Greedy sequential adaptive compressed sensing

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    We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of kk-sparse signals by connecting compressed sensing and blackbox complexity of sequential query algorithms, and present Info-Greedy algorithms for Gaussian and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse Info-Greedy measurements. Numerical examples demonstrate the good performance of the proposed algorithms using simulated and real data: Info-Greedy Sensing shows significant improvement over random projection for signals with sparse and low-rank covariance matrices, and adaptivity brings robustness when there is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear in IEEE Journal Selected Topics on Signal Processin

    Sequential Sensing with Model Mismatch

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    We characterize the performance of sequential information guided sensing, Info-Greedy Sensing, when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the directions of eigenvectors of the covariance matrix in a decreasing order of eigenvalues. We establish a set of performance bounds when a mismatched covariance matrix is used, in terms of the gap of signal posterior entropy, as well as the additional amount of power required to achieve the same signal recovery precision. Based on this, we further study how to choose an initialization for Info-Greedy Sensing using the sample covariance matrix, or using an efficient covariance sketching scheme.Comment: Submitted to IEEE for publicatio

    Adaptive Non-uniform Compressive Sampling for Time-varying Signals

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    In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among coefficients more intelligently. To this aim, a Bayesian inference method is proposed that does not require any prior knowledge of importance levels of coefficients or sparsity of the signal. Our numerical simulations show that ANCS is able to achieve the desired non-uniform recovery of the signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce the number of required measurements significantly.Comment: 6 pages, 8 figures, Conference on Information Sciences and Systems (CISS 2017) Baltimore, Marylan

    Sparse Representation of Astronomical Images

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    Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on http://www.nonlinear-approx.info/examples/node1.htm
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