Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

International audienceIn this paper, we are interested in color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling

Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization

Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine details and textures, and often suffers from undesirable staircase artifact. To reduce these effects, this letter presents an improved TV based image CS recovery algorithm by introducing a new nonlocal regularization constraint into CS optimization problem. The nonlocal regularization is built on the well known nonlocal means (NLM) filtering and takes advantage of self-similarity in images, which helps to suppress the staircase effect and restore the fine details. Furthermore, an efficient augmented Lagrangian based algorithm is developed to solve the above combined TV and nonlocal regularization constrained problem. Experimental results demonstrate that the proposed algorithm achieves significant performance improvements over the state-of-the-art TV based algorithm in both PSNR and visual perception.Comment: 4 Pages, 1 figures, 3 tables, to be published at IEEE Int. Symposium of Circuits and Systems (ISCAS) 201

Adaptive Image Decomposition Into Cartoon and Texture Parts Optimized by the Orthogonality Criterion

In this paper a new decomposition method is introduced that splits the image into geometric (or cartoon) and texture parts. Following a total variation based preprocesssing, the core of the proposed method is an anisotropic diffusion with an orthogonality based parameter estimation and stopping condition. The quality criterion is defined by the theoretical assumption that the cartoon and the texture components of an image should be orthogonal to each other. The presented method has been compared to other decomposition algorithms through visual and numerical evaluation to prove its superiority

Rician Noise Removal via a Learned Dictionary

This paper proposes a new effective model for denoising images with Rician noise. The sparse representations of images have been shown to be efficient approaches for image processing. Inspired by this, we learn a dictionary from the noisy image and then combine the MAP model with it for Rician noise removal. For solving the proposed model, the primal-dual algorithm is applied and its convergence is studied. The computational results show that the proposed method is promising in restoring images with Rician noise

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers

Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain Lipschitz condition on the denoisers. We then propose real spectral normalization, a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition. Finally, we present experimental results validating the theory.Comment: Published in the International Conference on Machine Learning, 201