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It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating(More)
In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly nonconvex) and a convex (possibly nondifferentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis of(More)
This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the field of experts model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the(More)
We study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The proposed algorithm-named iPiano-combines forward-backward splitting with an inertial force and hence can be seen as an extension of the celebrated heavy-ball method proposed by Polyak already in(More)
For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at the expense of very high computation time, which clearly limits their practical relevance. In this work, we propose a(More)
We consider the analysis operator and synthesis dictionary learning problems based on the the 1 regularized sparse representation model. We reveal the internal relations between the 1-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of(More)
Inpainting based image compression approaches , especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of descriptive supporting points, which allow for an accurate reconstruction of the original image. It turns out in practice that(More)
—Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework to obtain simple but effective models for various image restoration problems. The proposed approach is based on the concept of nonlinear reaction diffusion, but we extend conventional nonlinear reaction(More)
Discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm,(More)
Image denoising is a fundamental operation in image processing and holds considerable practical importance for various real-world applications. Arguably several thousands of papers are dedicated to image denoising. In the past decade, sate-of-the-art denoising algorithm have been clearly dominated by non-local patch-based methods, which explicitly exploit(More)