Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise

Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new multiplicative noise removing models to the MHDM form. On the basis of previous work, we further present a tight and a refined version of the corresponding multiplicative MHDM. We discuss existence and uniqueness of solutions for the proposed models, and additionally, provide convergence properties. Moreover, we present a discrepancy principle stopping criterion which prevents recovering excess noise in the multiscale reconstruction. Through comprehensive numerical experiments and comparisons, we qualitatively and quantitatively evaluate the validity of all proposed models for denoising and deblurring images degraded by multiplicative noise. By construction, these multiplicative multiscale hierarchical decomposition methods have the added benefit of recovering many scales of an image, which can provide features of interest beyond image denoising

Astrophysically robust systematics removal using variational inference: application to the first month of Kepler data

Space-based transit search missions such as Kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage. However, before this scientific goldmine can be exploited fully, the data must be cleaned of instrumental artefacts. We present a new method to correct common-mode systematics in large ensembles of very high precision light curves. It is based on a Bayesian linear basis model and uses shrinkage priors for robustness, variational inference for speed, and a de-noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves. After demonstrating the performance of our method on a synthetic dataset, we apply it to the first month of Kepler data. We compare the results, which are publicly available, to the output of the Kepler pipeline's pre-search data conditioning, and show that the two generally give similar results, but the light curves corrected using our approach have lower scatter, on average, on both long and short timescales. We finish by discussing some limitations of our method and outlining some avenues for further development. The trend-corrected data produced by our approach are publicly available.Comment: 15 pages, 13 figures, accepted for publication in MNRA

Learning a Dilated Residual Network for SAR Image Despeckling

In this paper, to break the limit of the traditional linear models for synthetic aperture radar (SAR) image despeckling, we propose a novel deep learning approach by learning a non-linear end-to-end mapping between the noisy and clean SAR images with a dilated residual network (SAR-DRN). SAR-DRN is based on dilated convolutions, which can both enlarge the receptive field and maintain the filter size and layer depth with a lightweight structure. In addition, skip connections and residual learning strategy are added to the despeckling model to maintain the image details and reduce the vanishing gradient problem. Compared with the traditional despeckling methods, the proposed method shows superior performance over the state-of-the-art methods on both quantitative and visual assessments, especially for strong speckle noise.Comment: 18 pages, 13 figures, 7 table

Efficient parallelization on GPU of an image smoothing method based on a variational model

Medical imaging is fundamental for improvements in diagnostic accuracy. However, noise frequently corrupts the images acquired, and this can lead to erroneous diagnoses. Fortunately, image preprocessing algorithms can enhance corrupted images, particularly in noise smoothing and removal. In the medical field, time is always a very critical factor, and so there is a need for implementations which are fast and, if possible, in real time. This study presents and discusses an implementation of a highly efficient algorithm for image noise smoothing based on general purpose computing on graphics processing units techniques. The use of these techniques facilitates the quick and efficient smoothing of images corrupted by noise, even when performed on large-dimensional data sets. This is particularly relevant since GPU cards are becoming more affordable, powerful and common in medical environments

Nonlocal Myriad Filters for Cauchy Noise Removal

The contribution of this paper is two-fold. First, we introduce a generalized myriad filter, which is a method to compute the joint maximum likelihood estimator of the location and the scale parameter of the Cauchy distribution. Estimating only the location parameter is known as myriad filter. We propose an efficient algorithm to compute the generalized myriad filter and prove its convergence. Special cases of this algorithm result in the classical myriad filtering, respective an algorithm for estimating only the scale parameter. Based on an asymptotic analysis, we develop a second, even faster generalized myriad filtering technique. Second, we use our new approaches within a nonlocal, fully unsupervised method to denoise images corrupted by Cauchy noise. Special attention is paid to the determination of similar patches in noisy images. Numerical examples demonstrate the excellent performance of our algorithms which have moreover the advantage to be robust with respect to the parameter choice