We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.

Ştiinţifice din Învăţământul Superior) prin grantul TD/47, nr. 33385/29.06.04. Această lucrare tratează problema extrem de actuală a diseminării ilegale a materialelor audio, video şi imagini pe Internet. O soluţie propusă ar fi înglobarea în semnalul multimedia a unui alt semnal numit marcaj (watermark) fără ca schimbările să fie sesizabile (watermarking). Ideea ar fi ca acest marcaj să conţină detalii despre deţinătorul drepturilor de autor. Este tratată exclusiv problema marcării transparente a imaginilor. Se pune accent pe tipurile de atacuri la care poate fi supusă o imagine marcată şi modul de construire a marcajului în funcţie de acestea. Primul capitol tratează problema dualităţii marcării transparente, respectiv a steganografiei faţă de cea a compresiei. Daca primele două tehnici sunt folosite pentru a „ascunde ” informaţie într-un semnal digital (fie că este vorba de comunicaţie punct-la-punct pentru steganografie, fie multipunct pentru watermarking), în mod evident compresia încearcă să identifice părţile nesemnificative (din punct de vedere vizual sau auditiv) şi să le elimine. Astfel, trebuie căutat un echilibru între cele două tipuri de tehnici: data hiding în general (în acest caz watermarking) şi compresie. De aceea cei

We present a non-linear method for solving linear inverse problems by thresholding coefficients in the wavelet domain 1. Our method is based on the wavelet-vaguelette decomposition of Donoho (1992). Numerical results for a synthetic travel-time inversion problem show that the wavelet based method

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can

Bayesian methods provide an effective tool for shrinkage in wavelet models. An important issue in any Bayesian analysis is the elicitation of a prior distribution. Elicitation in the wavelet domain is considered by first describing the structure of a wavelet model, and examining several prior

-ding the watermark, namely, 1) embedding only in the low pass subband (low-low), 2) embedding only in the high pass subbands (low-high, high-low and high-high) and 3) embed-ding in all subbands are considered to model popular wavelet domain watermarking methods. The performance of morpho-logical Haar and higher

per-ceptual mask in the wavelet domain, taking into account the noise sensitivity, texture and the luminance content of all image subbands. In this paper, we describe new techniques proposed by the authors, based on the modifications of this perceptual mask, in order to increase robustness, while

We investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters outperform many other denoising algorithms based on wavelet thresholding. However, up to now, it has not been clear how to choose the signal model used to design

wavelet domain watermarking},

Wavelets are the building blocks of wavelet transforms the same way that the functions e^inx are the building blocks of the ordinary Fourier transform. But in contrast to sines and cosines, wavelets can be (or almost can be) supported on an arbitrarily small closed interval. This feature makes