A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

The cross-entropy method for blind multiuser detection

We consider the problem of blind multiuser detection. We adopt a Bayesian approach where unknown parameters are considered random and integrated out. Computing the maximum a posteriori estimate of the input data sequence requires solving a combinatorial optimization problem. We propose here to apply the Cross-Entropy method recently introduced by Rubinstein. The performance of cross-entropy is compared to Markov chain Monte Carlo. For similar Bit Error Rate performance, we demonstrate that Cross-Entropy outperforms a generic Markov chain Monte Carlo method in terms of operation time.