IEEE Trans Image Process - Compressive sensing by learning a Gaussian mixture model from measurements.

Tópicos

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Resumo

Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.

Resumo Limpo

compress sens signal drawn gaussian mixtur model gmm admit closedform minimum mean squar error reconstruct incomplet linear measur accur gmm signal model usual avail priori difficult obtain train signal match statist signal sens propos solv problem learn signal model situ base direct compress measur signal without resort signal train model key featur method signal sens treat random variabl integr likelihood deriv maximum margin likelihood estim mmle maxim likelihood gmm under signal given linear compress measur extend mmle gmm domin lowrank covari matric gain comput speedup report extens experiment result imag inpaint compress sens highspe video compress hyperspectr imag latter two base real compress camera result demonstr propos method outperform stateoftheart method signific margin

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