Rank Conditioned Rank Selection Filters for Signal Restoration

A class of nonlinear filters called rank conditioned rank selection (RCRS) filters is developed and analyzed in this paper. The RCRS filters are developed within the general framework of rank selection(RS) filters, which are filters constrained to output an order statistic from the observation set. Many previously proposed rank order based filters can be formulated as RS filters. The only difference between such filters is in the information used in deciding which order statistic to output. The information used by RCRS filters is the ranks of selected input samples, hence the name rank conditioned rank selection filters. The number of input sample ranks used is referred to as the order of the RCRS filter. The order can range from zero to the number of samples in the observation window, giving the filters valuable flexibility. Low-order filters can give good performance and are relatively simple to optimize and implement. If improved performance is demanded, the order can be increased but at the expense of filter simplicity. In this paper, many statistical and deterministic properties of the RCRS filters are presented. A procedure for optimizing over the class of RCRS filters is also presented. Finally, extensive computer simulation results that illustrate the performance of RCRS filters in comparison with other techniques in image restoration applications are presented

On the filtering effect of iterative regularization algorithms for linear least-squares problems

Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to provide the fastest methods for the reconstruction of the solution, involving choices of adaptive parameters and scaling matrices. However, in presence of an ill-conditioned model and real data, the need of a regularized solution instead of the least-squares one changed the point of view in favour of iterative algorithms able to combine a fast execution with a stable behaviour with respect to the restoration error. In this paper we want to analyze some classical and recent gradient approaches for the linear least-squares problem by looking at their way of filtering the singular values, showing in particular the effects of scaling matrices and non-negative constraints in recovering the correct filters of the solution

Video enhancement using adaptive spatio-temporal connective filter and piecewise mapping

This paper presents a novel video enhancement system based on an adaptive spatio-temporal connective (ASTC) noise filter and an adaptive piecewise mapping function (APMF). For ill-exposed videos or those with much noise, we first introduce a novel local image statistic to identify impulse noise pixels, and then incorporate it into the classical bilateral filter to form ASTC, aiming to reduce the mixture of the most two common types of noises - Gaussian and impulse noises in spatial and temporal directions. After noise removal, we enhance the video contrast with APMF based on the statistical information of frame segmentation results. The experiment results demonstrate that, for diverse low-quality videos corrupted by mixed noise, underexposure, overexposure, or any mixture of the above, the proposed system can automatically produce satisfactory results

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

The Bitonic Filter: Linear Filtering in an Edge-preserving Morphological Framework.

A new filter is presented which has better edge and detail preserving properties than a median, noise reduction capability similar to a Gaussian, and is applicable to many signal and noise types. It is built on a definition of signal as bitonic, i.e. containing only one local maxima or minima within the filter range. This definition is based on data ranking rather than value, hence the bitonic filter comprises a combination of non-linear morphological and linear operators. It has no data-level-sensitive parameters and can locally adapt to the signal and noise levels in an image, precisely preserving both smooth and discontinuous signals of any level when there is no noise, but also reducing noise in other areas without creating additional artefactual noise. Both the basis and the performance of the filter are examined in detail, and it is shown to be a significant improvement on the Gaussian and median. It is also compared over various noisy images to the image-guided filter, anisotropic diffusion, non-local means, the grain filter, and self-dual forms of levelling and rank filters. In terms of signal-to-noise, the bitonic filter outperforms all these except non-local means, and sometimes anisotropic diffusion. However it gives good visual results in all circumstances, with characteristics which make it appropriate particularly for signals or images with varying noise, or features at varying levels. The bitonic has very few parameters, does not require optimisation nor prior knowledge of noise levels, does not have any problems with stability, and is reasonably fast to implement. Despite its non-linearity, it hence represents a very practical operation with general applicability