Dual constrained TV-based regularization

International audienceAlgorithms based on the minimization of the Total Variation are prevalent in computer vision. They are used in a variety of applications such as image denoising, compressive sensing and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa-Osher's projection algorithms for TV minimization in a flexible graph data representation by generalizing the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of a fast parallel proximal algorithm, which performs better than the classical TV approach for denoising, and is also applicable to inverse problems such as image deblurring

Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

International audienceThis paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms

Hyperspectral pan-sharpening: a variational convex constrained formulation to impose parallel level lines, solved with ADMM

In this paper, we address the issue of hyperspectral pan-sharpening, which consists in fusing a (low spatial resolution) hyperspectral image HX and a (high spatial resolution) panchromatic image P to obtain a high spatial resolution hyperspectral image. The problem is addressed under a variational convex constrained formulation. The objective favors high resolution spectral bands with level lines parallel to those of the panchromatic image. This term is balanced with a total variation term as regularizer. Fit-to-P data and fit-to-HX data constraints are effectively considered as mathematical constraints, which depend on the statistics of the data noise measurements. The developed Alternating Direction Method of Multipliers (ADMM) optimization scheme enables us to solve this problem efficiently despite the non differentiabilities and the huge number of unknowns.Comment: 4 pages, detailed version of proceedings of conference IEEE WHISPERS 201

Reconstruction of compressed spectral imaging based on global structure and spectral correlation

In this paper, a convolution sparse coding method based on global structure characteristics and spectral correlation is proposed for the reconstruction of compressive spectral images. The proposed method uses the convolution kernel to operate the global image, which can better preserve image structure information in the spatial dimension. To take full exploration of the constraints between spectra, the coefficients corresponding to the convolution kernel are constrained by the norm to improve spectral accuracy. And, to solve the problem that convolutional sparse coding is insensitive to low frequency, the global total-variation (TV) constraint is added to estimate the low-frequency components. It not only ensures the effective estimation of the low-frequency but also transforms the convolutional sparse coding into a de-noising process, which makes the reconstructing process simpler. Simulations show that compared with the current mainstream optimization methods (DeSCI and Gap-TV), the proposed method improves the reconstruction quality by up to 7 dB in PSNR and 10% in SSIM, and has a great improvement in the details of the reconstructed image