This paper presents a procedure for reconstruction of spatially localized images from compressively sampled measurements making use of Bayesian priors. The contribution of this paper is twofold: firstly, we analytically derive the expected value of wavelet domain signal structures conditional to a suitably defined noisy estimate; secondly, we exploit such conditional expectation within a nonlinear estimation stage that is added to an iterative reconstruction algorithm at a very low computational cost. We present numerical results focusing on spatially localized images and assessing the accuracy of the resulting algorithm, which definitely outperforms state-of-theart competitors in very ill-posed conditions characterized by a low number of measurements. This contribution highlights the strong analogy between compressive sampling reconstruction and blind deconvolution, and paves the way to further work on joint design of image deconvolution/reconstruction from compressively sampled measurements.

Reconstruction of compressively sampled images using a nonlinear Bayesian prior / Colonnese, Stefania; Biagi, Mauro; Cusani, Roberto; Scarano, Gaetano. - (2017), pp. 1-5. (Intervento presentato al convegno 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) tenutosi a Curacao, Netherlands Antilles).

Reconstruction of compressively sampled images using a nonlinear Bayesian prior

stefania Colonnese
;
mauro Biagi;roberto Cusani;gaetano Scarano
2017

Abstract

This paper presents a procedure for reconstruction of spatially localized images from compressively sampled measurements making use of Bayesian priors. The contribution of this paper is twofold: firstly, we analytically derive the expected value of wavelet domain signal structures conditional to a suitably defined noisy estimate; secondly, we exploit such conditional expectation within a nonlinear estimation stage that is added to an iterative reconstruction algorithm at a very low computational cost. We present numerical results focusing on spatially localized images and assessing the accuracy of the resulting algorithm, which definitely outperforms state-of-theart competitors in very ill-posed conditions characterized by a low number of measurements. This contribution highlights the strong analogy between compressive sampling reconstruction and blind deconvolution, and paves the way to further work on joint design of image deconvolution/reconstruction from compressively sampled measurements.
2017
2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
Bayes methods; image reconstruction; reconstruction algorithms; estimation; noise measurement; iterative algorithms; wavelet transforms
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Reconstruction of compressively sampled images using a nonlinear Bayesian prior / Colonnese, Stefania; Biagi, Mauro; Cusani, Roberto; Scarano, Gaetano. - (2017), pp. 1-5. (Intervento presentato al convegno 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) tenutosi a Curacao, Netherlands Antilles).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1168387
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