A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Model selection by MCMC computation
Signal Processing - Special section on Markov Chain Monte Carlo (MCMC) methods for signal processing
Bayesian wavelet denoising: Besov priors and non-Gaussian noises
Signal Processing - Special section on Markov Chain Monte Carlo (MCMC) methods for signal processing
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Compressed sensing and Bayesian experimental design
Proceedings of the 25th international conference on Machine learning
Bayesian Inference for Sparse Generalized Linear Models
ECML '07 Proceedings of the 18th European conference on Machine Learning
Fast bayesian compressive sensing using Laplace priors
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Hierarchical Bayesian sparse image reconstruction with application to MRFM
IEEE Transactions on Image Processing
Efficient computational methods for wavelet domain signalrestoration problems
IEEE Transactions on Signal Processing
A Bayesian approach for simultaneous segmentation andclassification of count data
IEEE Transactions on Signal Processing
Monte Carlo Methods for Adaptive Sparse Approximations of Time-Series
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Random Models for Sparse Signals Expansion on Unions of Bases With Application to Audio Signals
IEEE Transactions on Signal Processing - Part I
Recursive consistent estimation with bounded noise
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Visibility of wavelet quantization noise
IEEE Transactions on Image Processing
Comparison of different methods of classification in subband coding of images
IEEE Transactions on Image Processing
New image compression techniques using multiwavelets and multiwavelet packets
IEEE Transactions on Image Processing
Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Image analysis using a dual-tree M-band wavelet transform
IEEE Transactions on Image Processing
Fusion of Hidden Markov Random Field Models and Its Bayesian Estimation
IEEE Transactions on Image Processing
Bayesian compressive sensing for cluster structured sparse signals
Signal Processing
| Hi-index | 35.68 |
In many signal processing problems, it is fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyperparameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyperparameters is derived. Hybrid Markov chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyperparameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyperparameters. Application to practical problems of image denoising in the presence of uniform noise illustrates the impact of the resulting Bayesian estimation on the recovered signal quality.