Bayesian approach to best basis selection

Pesquet, Jean-Christophe; Krim, Hamid; Leporini, D.; Hamman, Elizabeth

doi:10.1109/icassp.1996.548005

Cited by 45 publications

(45 citation statements)

References 5 publications

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“…Though GGD is more sophisticated with distribution shape parameter β, several factors support validity of simple GD modeling given the class labels as hidden variables. Empirical results from estimation have shown that the mixture model is simple yet effective [28], [5]. Modeling wavelet coefficients with hidden classes of "'large"' and "'small"' variance state are basic data models in Wavelet-based Hidden Markov Model (HMT) [13].…”

Section: Multiscale Discriminant Saliencymentioning

confidence: 99%

Multiscale Discriminant Saliency for Visual Attention

Ngo

Ang

Qiu

et al. 2013

Lecture Notes in Computer Science

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Abstract. The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between center and surround classes. Discriminant power of features for the classification is measured as mutual information between features and two classes distribution. The estimated discrepancy of two feature classes very much depends on considered scale levels; then, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden markov tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, saliency value for each dyadic square at each scale level is computed with discriminant power principle and the MAP. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multiscale discriminant saliency method (MDIS) against the well-know information-based saliency method AIM on its Bruce Database wity eye-tracking data. Simulation results are presented and analyzed to verify the validity of MDIS as well as point out its disadvantages for further research direction. Visual Attention -Computational ApproachVisual attention is a psychological phenomenon in which human visual systems are optimized for capturing scenic information. Robustness and efficiency of biological devices, the eyes and their control systems, visual paths in the brain have amazed scientists and engineers for centuries. From Neisser [26] to Marr [25], researchers have put intesive effort in discovering attention principles and engineering artificial systems with equivalent capability. For last two decades, this research field is dominated by visual saliency principles which proposes an existence of a saliency map for attention guidance. The idea is further promoted in Feature Integration Theory (FIT) [34] which elaborates computational principles of saliency map generation with center-surround operators and basic image features such as intensity, orientation and colors. Then, Itti et al. [21] implemented and released the first complete computer algorithms of FIT theory 5 . Feature Integration Theory are widely accepted as principles behind visual attention partly due to its utilization of basic image features. Moreover, this hypothesis is supported by several evidences from psychological experiments. However, it only defines theoretical aspects of visual attention with saliency maps, but does not investigate how such principles would be implemented algorithmically. [20], or saliency at each location depends on statistical modeling of the local feature distribution [32]. Though many approaches are mentioned in long and rich literature of visual saliency, only a few are built on a solid theory or linked to other well-establis...

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Section: Multiscale Discriminant Saliencymentioning

confidence: 99%

Multiscale Discriminant Saliency for Visual Attention

Ngo

Ang

Qiu

et al. 2013

Lecture Notes in Computer Science

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“…It is in fact a limiting case of the two Gaussians mixture model of equation (6). We can easily prove the following:…”

Section: Joint Source Separation and Denoisingmentioning

confidence: 90%

“…In wavelet based denoising, connections between hard/soft wavelet thresholding and Bayesian estimation have been established in [11,6,10], especially for the gpG and the BernoulliGaussian (BG) prior model. The BG model is given by:…”

Section: Joint Source Separation and Denoisingmentioning

confidence: 99%

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Hidden Markov Models for Wavelet Image Separation and Denoising

Ichir

Mohammad-Djafari

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.

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In this paper, we consider the problem of blind source separation of 2D images under a Bayesian formulation (Bayes-BSS). We transport the problem to the wavelet domain to be able to define appropriate prior distributions for the wavelet coefficients of the unobservable sources: an Independent Gaussians Mixture (IGM) model, a Hidden Markov Tree (HMT) model and Contextual Hidden Markov Field (CHMF) model.Indeed, we consider a limiting case of the aforementioned prior models to propose a simple procedure for joint source separation and denoising. This procedure shows to be efficient, especially for highly noise observations. Simulation examples and comparisons with standard classical methods are presented to show the performances of the proposed approach.

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“…Some examples are best basis search in dyadic wavelet packet trees and dyadic local cosine trees [3], matching pursuit [14] and its variants, and basis pursuit [2]. The applications of such algorithms include compression [18], extraction of time-frequency features [4], [6], [20] and geometric features [10], noise removal [11], [12], [16], [17], and others. The ultimate objective of these efforts is to adaptively compute a parsimonious representation at a low computational cost.…”

Section: Introductionmentioning

confidence: 99%