Complex wavelet regularization for solving inverse problems in remote sensing

International audienceMany problems in remote sensing can be modeled as the minimization of the sum of a data term and a prior term. We propose to use a new complex wavelet based prior and an efficient scheme to solve these problems. We show some results on a problem of image reconstruction with noise, irregular sampling and blur. We also show a comparison between two widely used priors in image processing: sparsity and regularity priors

Complex wavelet regularization for solving inverse problems in remote sensing

International audienceMany problems in remote sensing can be modeled as the minimization of the sum of a data term and a prior term. We propose to use a new complex wavelet based prior and an efficient scheme to solve these problems. We show some results on a problem of image reconstruction with noise, irregular sampling and blur. We also show a comparison between two widely used priors in image processing: sparsity and regularity priors

Sparse Poisson Noisy Image Deblurring

International audienceDeblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. In this paper, we focus on confocal microscopy which is a very popular technique for 3D imaging of biological living specimens which gives images with a very good resolution (several hundreds of nanometers), even though degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations and we focus in this paper on techniques which promote the introduction of explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter which weights the trade-off between the data term and the regularizing term. Actually, only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise so it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter and we first propose an improvement of these estimators which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of Poisson noisy images deconvolution as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the anti log-likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problem using the recent Alternating Direction technique and we present results on synthetic and real data using well-known priors such as Total Variation and wavelet transforms. Among these wavelet transforms, we specially focus on the Dual-Tree Complex Wavelet transform and on the dictionary composed of Curvelets and undecimated wavelet transform

Complex wavelet regularization for 3D confocal microscopy deconvolution

Confocal microscopy is an increasingly popular technique for 3D imaging of biological specimens which gives images with a very good resolution (several tenths of micrometers), even though degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations, some of them being regularized on a Total Variation prior, which gives good results in image restoration but does not allow to retrieve the thin details (including the textures) of the specimens. We first propose here to use instead a wavelet prior based on the Dual-Tree Complex Wavelet transform to retrieve the thin details of the object. As the regularizing prior efficiency also depends on the choice of its regularizing parameter, we secondly propose a method to select the regularizing parameter following a discrepancy principle for Poisson noise. Finally, in order to implement the proposed deconvolution method, we introduce an algorithm based on the Alternating Direction technique which allows to avoid inherent stability problems of the Richardson-Lucy multiplicative algorithm which is widely used in 3D image restoration. We show some results on real and synthetic data, and compare these results to the ones obtained with the Total Variation and the Curvelets priors. We also give preliminary results on a modification of the wavelet transform allowing to deal with the anisotropic sampling of 3D confocal images