arXiv subjects

Jean-Christophe Pesquet

Publications and source records attributed to Jean-Christophe Pesquet.

77 records · Page 5Linked to original sources

arXiv2009

An Iterative Method for Parallel MRI SENSE-based Reconstruction in the Wavelet Domain

To reduce scanning time and/or improve spatial/temporal resolution in some MRI applications, parallel MRI (pMRI) acquisition techniques with multiple coils acquisition have emerged since the early 1990s as powerful 3D imaging methods that allow faster acquisition of reduced Field of View (FOV) images. In these techniques, the full FOV image has to be reconstructed from the resulting acquired undersampled k-space data. To this end, several reconstruction techniques have been proposed such as the widely-used SENSE method. However, the reconstructed image generally presents artifacts when perturbations occur in both the measured data and the estimated coil sensitivity maps. In this paper, we aim at achieving good reconstructed image quality when using low magnetic field and high reduction factor. Under these severe experimental conditions, neither the SENSE method nor the Tikhonov regularization in the image domain give convincing results. To this aim, we present a novel method for SENSE-based reconstruction which proceeds with regularization in the complex wavelet domain. To further enhance the reconstructed image quality, local convex constraints are added in the regularization process. In vivo experiments carried out on Gradient-Echo (GRE) anatomical and Echo-Planar Imaging (EPI) functional MRI data at 1.5 Tesla indicate that the proposed algorithm provides reconstructed images with reduced artifacts for high reduction factor.

math.OC↗

arXiv2009

Optimization of Synthesis Oversampled Complex Filter Banks

An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.

cs.IT↗

arXiv2009

A SURE Approach for Digital Signal/Image Deconvolution Problems

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein's unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Stein's risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method w.r.t. conventional wavelet-based restoration methods.

stat.ME↗

arXiv2009

A Proximal Decomposition Method for Solving Convex Variational Inverse Problems

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of nonsmooth functions and establish its convergence. The algorithm fully decomposes the problem in that it involves each function individually via its own proximity operator. A significant improvement over the methods currently in use in the area of inverse problems is that it is not limited to two nonsmooth functions. Numerical applications to signal and image processing problems are demonstrated.

math.OC↗

arXiv2007

A nonlinear Stein based estimator for multichannel image denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein's principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

physics.data-an↗