We propose a new approach to enforce integrability using recent advances in non-local methods. Our formulation consists in a sparse gradient data-fitting term to handle outliers together with a gradient-domain non-local low-rank prior. This regularization has two main advantages: 1) the low-rank prior ensures similarity between non-local gradient patches, which helps recovering high-quality clean patches from severe outliers corruption and 2) the low-rank prior efficiently reduces dense noise as it has been shown in recent image restoration works. We propose an efficient solver for the resulting optimization formulation using alternate minimization. Experiments show that the new method leads to an important improvement compared with previous optimization methods and is able to efficiently handle both outliers and dense noise mixed together.

Current state-of-the-art denoising methods, such as non-local low-rank approaches, have shown to give impressive results. They are, however, mainly tuned to work with uniform Gaussian noise corruption and known variance, which is far from the real noise scenario. In fact, noise level estimation is already a challenging problem and denoising methods are quite sensitive to this parameter. Moreover, these methods are based on shrinkage models that are too simple to reflect reality, which results in over-smoothing of important structures, such as small-scale text and textures. We propose in this paper a new approach for more realistic image restoration based on the concept of low-rankness transfer. Given a training clean/noisy image pair, our method learns a mapping between the non-local noisy singular values and the optimal values for denoising to be transfered to a new noisy input. One single image is enough for training the model and can be adapted to the noisy input by taking a correlated image. Experiments conducted on synthetic and real camera noise show that the proposed method leads to an important improvement both visually and in terms of PSNR/SSIM.

We present a new framework for fast edge-aware processing of images and videos. The proposed smoothing method is based on an optimization formulation with a non-convex sparse regularization for a better smoothing behavior near strong edges. We develop mathematical tools based on first order approximation of proximal operators to accelerate the proposed method while maintaining high-quality smoothing. The first order approximation is used to estimate a solution of the proximal form in a half-quadratic solver, and also to derive a warm-start solution that can be calculated quickly when the image is loaded by the user. We extend the method to large-scale processing by estimating the smoothing operation with independent 1D convolution operations. This approach linearly scales to the size of the image and can fully take advantage of parallel processing. The method supports full color filtering and turns out to be temporally coherent for fast video processing. We demonstrate the performance of the proposed method on various applications including image smoothing, detail manipulation, HDR tone-mapping, fast edge simplification and video edge-aware processing.

Reconstructing a surface/image from corrupted gradient fields is a crucial step in many imaging applications where a gradient field is subject to both noise and unlocalized outliers, resulting typically in a non-integrable field. We present in this paper a new optimization method for robust surface reconstruction. The proposed formulation is based on a triple sparsity prior: a sparse prior on the residual gradient field and a double sparse prior on the surface gradients. We develop an efficient alternate minimization strategy to solve the proposed optimization problem. The method is able to recover a good quality surface from severely corrupted gradients thanks to its ability to handle both noise and outliers. We demonstrate the performance of the proposed method on synthetic and real data. Experiments show that the proposed solution outperforms some existing methods in the three possible cases: noise only, outliers only and mixed noise/outliers.

Non-blind deconvolution consists in recovering a sharp latent image from a blurred image with a known kernel. Deconvolved images usually contain unpleasant artifacts due to the ill-posedness of the problem even when the kernel is known. Making use of natural sparse priors has shown to reduce ringing artifacts but handling noise remains limited. On the other hand, non-local priors have shown to give the best results in image denoising. We propose in this paper to combine both local and non-local priors to handle noise. We show that the blur increases the self-similarity within an image and thus makes non-local priors a good choice for denoising blurred images. However, denoising introduces outliers which are not Gaussian and should be well modeled. Experiments show that our method produces a better image reconstruction both visually and empirically compared to methods some popular methods.