A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise

Abstract

This paper proposes a general weighted l(2)-l(0) norms energy minimization model to remove mixed noise such as Gaussian-Gaussian mixture, impulse noise, and Gaussian-impulse noise from the images. The approach is built upon maximum likelihood estimation framework and sparse representations over a trained dictionary. Rather than optimizing the likelihood functional derived from a mixture distribution, we present a new weighting data fidelity function, which has the same minimizer as the original likelihood functional but is much easier to optimize. The weighting function in the model can be determined by the algorithm itself, and it plays a role of noise detection in terms of the different estimated noise parameters. By incorporating the sparse regularization of small image patches, the proposed method can efficiently remove a variety of mixed or single noise while preserving the image textures well. In addition, a modified K-SVD algorithm is designed to address the weighted rank-one approximation. The experimental results demonstrate its better performance compared with some existing methods.

Mixed Noise Removal by Weighted Encoding With Sparse Nonlocal Regularization

“…In our algorithm, a set of orthogonal PCA dictionaries are pre-learned from some high quality images, and one local PCA dictionary is adaptively selected to process a given image patch. In a recent work [36], a weighted dictionary learning model is developed for mixed noise removal. Though both our method and Liu et al's method introduce weights in the data fidelity term, they have clear differences.…”

“…The mixture of AWGN and IN, however, is also commonly encountered in practice due to the multiple sources of noise. A variety of mixed noise removal methods have been proposed in past decades [22]- [36].…”

“…A few methods have been developed to remove the mixed IN and AWGN noise [22]- [36]. The median-based signal-dependent rank ordered mean (SDROM) filter [24] can be used for IN removal as well as mixed noise removal.…”

“…Meanwhile, this new variable is used as a regularizer by assuming that the percentage of pixels damaged by IN is small. Recently, Liu et al [36] proposed a weighted dictionary learning model for mixed noise removal. This method integrates sparse coding and dictionary learning, image reconstruction, noise clustering and parameters estimation into a four-step framework, and each step solves a minimization problem.…”

An adaptive dynamically weighted median filter for impulse noise removal

“…Deng and An [31] and Sadri et al [32] used wavelet. Wang et al [33] and Liu et al [34] used dictionary learning-based impulse noise removal techniques. Dictionary learning-based techniques are very complex and result in changing properties of input image as they replace patches of input image with patches stored in predefined dictionary.…”