In this paper the concept of sparsity for complex-valued variables is introduced in the following three types: directly in complex domain and for two real-valued pairs phase/amplitude and real/imaginary parts of complex variables. The nonlocal block-matching technique is used for sparsity implementation and filter design for each type of sparsity. These filters are complex domain generalization...

This article presents a new image denoising algorithm that uses Gaussian Symmetric Markov random fields based on maximum posteriori estimation. First, an model is built, and the problem was converted to estimation problem. The prior probability of can be estimated using Gibbs distribution, which equivalent fields. Second, calculated expectation-maximization conjugate gradient method, where used...

Though existing state-of-the-art denoising algorithms, such as BM3D, LPG-PCA and DDF, obtain remarkable results, these methods are not good at preserving details at high noise levels, sometimes even introducing non-existent artifacts. To improve the performance of these denoising methods at high noise levels, a generic denoising framework is proposed in this paper, which is based on guided prin...

This paper presents a Laplacian-based image filtering method. Using a local noise estimator function in an energy functional minimizing scheme we show that Laplacian that has been known as an edge detection function can be used for noise removal applications. The algorithm can be implemented on a 3x3 window and easily tuned by number of iterations. Image denoising is simplified to the reduction...

In many imaging applications, there exists potential for corruption of the images by sources of structured noise that completely loses original pixel information. The reconstruction of the original image from its corrupted observation is known as image inpainting. This paper seeks to investigate image inpainting using a particular algorithm, the alternating direction method of multipliers (ADMM...

Motivated by recent advances in adaptive sparse representations and nonlocal image modeling, we propose a patch-based image interpolation algorithm under a set theoretic framework. Our algorithm alternates the projection onto two convex sets: one is given by the observation data and the other defined by a sparsity-based nonlocal prior similar to BM3D. In order to optimize the design of observat...

The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise smooth functions such as images. In this paper, we propose a novel wavelet frame based sparse recovery model called Support Driven Sparse Regularization (SDSR) for image deblurring, where t...