A Discriminative Approach for Wavelet Denoising

Abstract

This paper suggests a discriminative approach for wavelet denoising where a set of mapping functions (MFs) are applied to the transform coefficients in an attempt to produce a noise free image. As opposed to the descriptive approaches, modeling image or noise priors is not required here and the MFs are learned directly from an ensemble of example images using least-squares fitting. The suggested scheme generates a novel set of MFs that are essentially different from the traditional soft/hard thresholding in the over-complete case. These MFs are demonstrated to obtain comparable performance to the state-of-the-art denoising approaches. Additionally, this framework enables a seamless customization of the shrinkage operation to a new set of restoration problems that were not addressed previously with shrinkage techniques, such as deblurring, JPEG artifact removal, and various types of additive noise that are not necessarily Gaussian white noise.

A weighted discriminative approach for image denoising with overcomplete representations

“…In our approach, the overcomplete representation constitutes of K sub-bands generated by filtering the image with the respective basis kernels of each sub-band. It can be easily proved [2] that when the Wavelet transform consists of windowed basis functions (e.g. DCT) the two approaches are equivalent.…”

“…In the discriminative approach [2] the denoising stage (3) is preceded by the MFs learning stage. The MFs are approximated by a piece-wise linear model and jointly estimated using set of example images whose clean and noisy counterparts are given offline.…”

“…We performed computer simulations of the proposed approach and compared it with the un-weighted approach [2]. The tested images were taken from the collection of [5] and every denoising result was averaged over 10 noise realizations.…”

“…Commonly, the conventional techniques design the MFs using a "descriptive" approach based on the statistical prior of the transform domain. In this paper we consider the utilization of local sparsity information, available in the overcomplete domain, for the performance enhancement of a "discriminative" shrinkage restoration approach [2]. In the discriminative approach, the MFs are learned from example images, targeting the denoising performance directly, rather than a descriptive approach which focuses on determining the statistical prior.…”

“…According to [2], substituting the boundary vector q with a different vector p in the form of The substitution property is the key principle behind the approximation of the shrinkage MFs.…”