Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Sparse image reconstruction on the sphere: analysis and synthesis

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l1 norm appearing in the regularisation problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353 GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.Comment: 11 pages, 6 Figure

Effective denoising and adaptive equalization of indoor optical wireless channel with artificial light using the discrete wavelet transform and artificial neural network

Indoor diffuse optical wireless (OW) communication systems performance is limited due to a number of effects; interference from natural and artificial light sources and multipath induced intersymbol interference (ISI). Artificial light interference (ALI) is a periodic signal with a spectrum profile extending up to the MHz range. It is the dominant source of performance degradation at low data rates, which can be removed using a high-pass filter (HPF). On the other hand, ISI is more severe at high data rates and an equalizing filter is incorporated at the receiver to compensate for the ISI. This paper provides the simulation results for a discrete wavelet transform (DWT)—artificial neural network (ANN)-based receiver architecture for on-and-off keying (OOK) non-return-to-zero (NRZ) scheme for a diffuse indoor OW link in the presence of ALI and ISI. ANN is adopted for classification acting as an efficient equalizer compared to the traditional equalizers. The ALI is effectively reduced by proper selection of the DWT coefficients resulting in improved receiver performance compared to the digital HPF. The simulated bit error rate (BER) performance of proposed DWT-ANN receiver structure for a diffuse indoor OW link operating at a data range of 10-200 Mbps is presented and discussed. The results are compared with performance of a diffuse link with an HPF-equalizer, ALI with/without filtering, and a line-of-sight (LOS) without filtering. We show that the DWT-ANN display a lower power requirement when compared to the receiver with an HPF-equalizer over a full range of delay spread in presence of ALI. However, as expected compared to the ideal LOS link the power penalty is higher reaching to 6 dB at 200 Mbps data rate