A Multichannel Spatial Compressed Sensing Approach for Direction of Arrival Estimation

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-15995-4_57ESPRC Leadership Fellowship EP/G007144/1EPSRC Platform Grant EP/045235/1EU FET-Open Project FP7-ICT-225913\"SMALL

On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix A in R^{m x n} and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: * A proof that linf/l1 sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson-Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. * A new lower bound for the number of linear measurements required to solve l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude. * A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of measurements required to solve deterministic norm estimation, i.e., to recover |x|_2 +/- eps|x|_1. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of l1/l1 sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems

Defining the essence of innovation how important terms in promoting of transformation processes in Ukraine

Feature hierarchies are essential to many visual object recognition systems and are well motivated by observations in biological systems. The present paper proposes an algorithm to incrementally compute feature hierarchies. The features are represented as estimated densities, using a variant of local soft histograms. The kernel functions used for this estimation in conjunction with their unitary extension establish a tight frame and results from framelet theory apply. Traversing the feature hierarchy requires resampling of the spatial and the feature bins. For the resampling, we derive a multi-resolution scheme for quadratic spline kernels and we derive an optimization algorithm for the upsampling. We complement the theoretic results by some illustrative experiments, consideration of convergence rate and computational efficiency.DIPLECSGARNICSELLII

Selection of Wavelet Subbands Using Genetic Algorithm for Face Recognition

Abstract. In this paper, a novel representation called the subband face is proposed for face recognition. The subband face is generated from selected subbands obtained using wavelet decomposition of the original face image. It is surmised that certain subbands contain information that is more significant for discriminating faces than other subbands. The problem of subband selection is cast as a combinatorial optimization problem and genetic algorithm (GA) is used to find the optimum subband combination by maximizing Fisher ratio of the training features. The performance of the GA selected subband face is evaluated using three face databases and compared with other wavelet-based representations.

General Adaptive Neighborhood Image Restoration, Enhancement and Segmentation

12 pagesInternational audienceThis paper aims to outline the General Adaptive Neighborhood Image Processing (GANIP) approach [1–3], which has been recently introduced. An intensity image is represented with a set of local neighborhoods defined for each point of the image to be studied. These so-called General Adaptive Neighborhoods (GANs) are simultaneously adaptive with the spatial structures, the analyzing scales and the physical settings of the image to be addressed and/or the human visual system. After a brief theoretical introductory survey, the GANIP approach will be successfully applied on real application examples in image restoration, enhancement and segmentation

Wavelets techniques for pointwise anti-Holderian irregularity

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem