1,721,362 research outputs found
Statistical and transform domain approach to pattern recognition and processing of aerial imagery
No full textPh.D. dissertation, Dip. di Elettronica, Politecnico di Torin
Gaussian Mixtures Based IRLS for Sparse Recovery With Quadratic Convergence
Full text linkIn this paper, we propose a new class of iteratively re-weighted least squares (IRLS) for sparse recovery problems. The proposed methods are inspired by constrained maximum-likelihood estimation under a Gaussian scale mixture (GSM) distribution assumption. In the noise-free setting, we provide sufficient conditions ensuring the convergence of the sequences generated by these algorithms to the set of fixed points of the maps that rule their dynamics and derive conditions verifiable a posteriori for the convergence to a sparse solution. We further prove that these algorithms are quadratically fast in a neighborhood of a sparse solution. We show through numerical experiments that the proposed methods outperform classical IRLS for l_p-minimization with p\in(0,1] in terms of speed and of sparsity-undersampling tradeoff and are robust even in presence of noise. The simplicity and the theoretical guarantees provided in this paper make this class of algorithms an attractive solution for sparse recovery problem
Fast IRLS for sparse reconstruction based on gaussian mixtures
Full text linkThe theory of compressed sensing has demonstrated that sparse signals can be reconstructed from few linear measurements. In this work, we propose a new class of iteratively reweighted least squares (IRLS) for sparse recovery. The proposed methods use a two state Gaussian scale mixture as a proxy for the signal model and can be interpreted as an Expectation Maximization algorithm that attempts to perform the constrained maximization of the log-likelihood function. Under some conditions, standard in the compressed sensing theory, the sequences generated by these algorithms converge to the fixed points of the maps that rule their dynamics. A condition for exact sparse recovery, that is verifible a posteriori, is derived and the convergence is proved to be quadratically fast in a neighborhood of the desired solution. Numerical experiments show that these new reconstructions schemes outperform classical IRLS for lp -minimization with p\in(0, 1] in terms of rate of convergence and accurac
Fast and Lightweight Rate Control for Onboard Predictive Coding of Hyperspectral Images
Full text linkPredictor analysis for onboard lossy predictive compression of multispectral and hyperspectral images
No full textThe predictive lossy compression paradigm, which is emerging as an interesting alternative to conventional transform coding techniques, is studied. We first discuss this paradigm and outline the advantages and drawbacks with respect to transform coding. Next, we consider two low-complexity predictors and compare them under equal conditions on a large set of multispectral and hyperspectral images. Besides their rate-distortion performance, we attempt to gain some insight on the "quality" of the prediction residuals, comparing bit-rate and variance, and calculating the kurtosis. The results allow us to outline the directions for improvement of the algorithms, mainly in the treatment of noisy channels and the use of appropriate statistical models for the entropy-coding stag
Steerable Discrete Fourier Transform
Full text linkDirectional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform (DFT), called steerable DFT (SDFT). Since the DFT is used in numerous fields, it may be of interest in a wide range of applications. Moreover, we also show that the SDFT is highly related to other well-known transforms, such as the Fourier sine and cosine transforms and the Hilbert transforms
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