Joan Duran

Self-similarity and Spectral Correlation Adaptive Algorithm for Color Demosaicking.

Most common cameras use a CCD sensor device measuring a single color per pixel. The other two color values of each pixel must be interpolated from the neighboring pixels in the so-called demosaicking process. State-of-the-art demosaicking algorithms take advantage of interchannel correlation locally selecting the best interpolation direction. These methods give impressive results except when local geometry cannot be inferred from neighboring pixels or channel correlation is low. In these cases, they create interpolation artifacts. We introduce a new algorithm involving nonlocal image self-similarity in order to reduce interpolation artifacts when local geometry is ambiguous. The proposed algorithm introduces a clear and intuitive manner of balancing how much channel-correlation must be taken advantage of. Comparison shows that the proposed algorithm gives state-of-the-art methods in several image bases.

A Nonlocal Variational Model for Pansharpening Image Fusion

Pansharpening refers to the fusion process of inferring a high-resolution multispectral image from a high-resolution panchromatic image and a low-resolution multispectral one. In this paper we propose a new variational method for pansharpening which incorporates a nonlocal regularization term and two fidelity terms, one describing the relation between the panchromatic image and the high-resolution spectral channels and the other one preserving the colors from the low-resolution modality. The nonlocal term is based on the image self-similarity principle applied to the panchromatic image. The existence and uniqueness of minimizer for the described functional is proved in a suitable space of weighted integrable functions. Although quite successful in terms of relative error, state-of-the-art pansharpening methods introduce relevant color artifacts. These spectral distortions can be significantly reduced by involving the image self-similarity. Extensive comparisons with state-of-the-art algorithms are performed.

Collaborative Total Variation: A General Framework for Vectorial TV Models

Even after two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly on moving from scalar to vector-valued functions. In this paper, we consider the gradient of a color image as a three-dimensional matrix or tensor with dimensions corresponding to the spatial extent, the intensity differences between neighboring pixels, and the spectral channels. The smoothness of this tensor is then measured by taking different norms along the different dimensions. Depending on the types of these norms, one obtains very different properties of the regularization, leading to novel models for color images. We call this class of regularizations collaborative total variation (CTV). On the theoretical side, we characterize the dual norm, the subdifferential, and the proximal mapping of the proposed regularizers. We further prove, with the help of the generalized concept of singular vectors, that an

Chambolle's Projection Algorithm for Total Variation Denoising

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A survey of pansharpening methods with a new band-decoupled variational model

Denoising is the problem of removing the inherent noise from an image. The standard noise model is additive white Gaussian noise, where the observed image f is related to the underlying true image u by the degradation model f = u + �, andis supposed to be at each pixel inde- pendently and identically distributed as a zero-mean Gaussian random variable. Since this is an ill-posed problem, Rudin, Osher and Fatemi introduced the total variation as a regularizing term. It has proved to be quite efficient for regularizing images without smoothing the bound- aries of the objects. This paper focuses on the simple description of the theory and on the implementation of Cham- bolles projection algorithm for minimizing the total variation of a grayscale image. Further- more, we adapt the algorithm to the vectorial total variation for color images. The implementa- tion is described in detail and its parameters are analyzed and varied to come up with a reliable implementation.

Implementation of Nonlocal Pansharpening Image Fusion

Abstract Most satellites decouple the acquisition of a panchromatic image at high spatial resolution from the acquisition of a multispectral image at lower spatial resolution. Pansharpening is a fusion technique used to increase the spatial resolution of the multispectral data while simultaneously preserving its spectral information. In this paper, we consider pansharpening as an optimization problem minimizing a cost function with a nonlocal regularization term. The energy functional which is to be minimized decouples for each band, thus permitting the application to misregistered spectral components. This requirement is achieved by dropping the, commonly used, assumption that relates the spectral and panchromatic modalities by a linear transformation. Instead, a new constraint that preserves the radiometric ratio between the panchromatic and each spectral component is introduced. An exhaustive performance comparison of the proposed fusion method with several classical and state-of-the-art pansharpening techniques illustrates its superiority in preserving spatial details, reducing color distortions, and avoiding the creation of aliasing artifacts.

A Demosaicking Algorithm with Adaptive Inter-Channel Correlation

This paper focuses on the implementation of the pansharpened image fusion technique proposed in the companion paper [A Nonlocal Variational Model for Pansharpening Image Fusion, SIAM Journal on Imaging Sciences, 2014, to appear]. Pansharpening refers to the process of inferring a high resolution multispectral image from a high resolution panchromatic image and low resolution multispectral one. Although quite successful in terms of relative error, state-of-the-art pansharpening methods still introduce relevant color artifacts. The variational pansharpening model proposed by Buades et al. incorporates a nonlocal regularization term that takes advantage of image self-similarity, leading to signicant reduction of the above-mentioned color artifacts.

On the Implementation of Collaborative TV Regularization: Application to Cartoon+Texture Decomposition

Most common cameras use a CCD sensor device measuring a single color per pixel. Demosaicking is the interpolation process by which one can infer a full color image from such a matrix of values, thus interpolating the two missing components per pixel. Most demosaicking methods take advantage of inter-channel correlation locally selecting the best interpolation direction. The obtained results look convincing except when local geometry cannot be inferred from neighboring pixels or channel correlation is low. In these cases, these algorithms create interpolation artifacts such as zipper effect or color aliasing. This paper discusses the implementation details of the algorithm proposed in [J. Duran, A. Buades, “Self-Similarity and Spectral Correlation Adaptive Algorithm for Color Demosaicking”, IEEE Transactions on Image Processing, 23(9), pp. 4031–4040, 2014]. The proposed method involves nonlocal image self-similarity in order to reduce interpolation artifacts when local geometry is ambiguous. It further introduces a clear and intuitive manner of balancing how much channel-correlation must be taken advantage of. Source Code An ANSI C source code implementation of the described algorithms is accessible at the IPOL web page of this article 1 , together with an on-line demo.

An algorithm for nonconvex functional minimization and applications to image restoration

This paper deals with the analysis, implementation, and comparison of several vector-valued total variation (TV) methods that extend the Rudin-Osher-Fatemi variational model to color images. By considering the discrete gradient of a multichannel image as a 3D structure with dimensions corresponding to the spatial extent, the differences to other pixels, and the color channels, we introduce in [J. Duran, M. Moeller, C. Sbert, and D. Cremers, “Collaborative Total Variation: A General Framework for Vectorial TV Models”, SIAM Journal on Imaging Sciences, 9(1), pp. 116–151, 2016] collaborative sparsity enforcing norms for penalizing the resulting tensor. We call this class of regularizations collaborative total variation (CTV). We first analyze the denoising properties of each collaborative norm for suppressing color artifacts while preserving image features and aligning edges. We then describe the primal-dual hybrid gradient method for solving the minimization problem in detail. The resulting CTV–L2 variational model can successfully be applied to many image processing tasks. On the one hand, an extensive performance comparison of several collaborative norms for color image denoising is provided. On the other hand, we analyze the ability of different CTV methods for decomposing a multichannel image into a cartoon and a textural part. Finally, we also include a short discussion on alternative minimization methods and compare their computational efficiency. Source Code ANSI C source code to produce the same results as the demo is accessible at the IPOL web part of this article1.

Nonlocal Regularizing Constraints in Variational Optical Flow.

In this paper, we propose a new dual algorithm for the minimization of discrete nonconvex functionals, called half-linear regularization. Our approach alternates the calculation of a explicit weight with the minimization of a convex functional with respect to the solution. This minimization corresponds to the weighted total variation which is solved via the well-known Chambolles algorithm. Finally, we present experimental results by applying it to some image restoration problems as denoising and deconvolution.