19 research outputs found
A New Approach to Sparse Image Representation Using MMV and K-SVD
This paper addresses the problem of image representation based on a sparse decomposition over a learned dictionary. We propose an improved matching pursuit algorithm for Multiple Measurement Vectors (MMV) and an adaptive algorithm for dictionary learning based on multi-Singular Value Decomposition (SVD), and combine them for image representation. Compared with the traditional K-SVD and orthogonal matching pursuit MMV (OMPMMV) methods, the proposed method runs faster and achieves a higher overall reconstruction accuracy
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 -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
Recommended from our members
Target tracking based network Active Queue Management
Active Queue Management (AQM) methods attempt to predict and control network router queue levels and provide feedback regarding network congestion to data sources through packet marking/ dropping. AQM methods have not employed statistical signal processing principles largely due to the requirement of low complexity. In this paper, we apply optimal filtering and target tracking methods to the design of AQM. In particular, we develop Kalman Filter based AQM which results in router queues with reduced queue level variance. To account for networks with more bursty traffic, we use Interacting Multiple Models (IMM) which similarly result in reduced queue variance in simulations with both long-term and bursty short-term traffic. In comparisons with other AQM methods, these low complexity target tracking-based AQM methods give a more constant queue length without any loss in source throughput
Recommended from our members
Fast basis selection methods
In this paper three methods of basis selection are considered: basic matching pursuit (BMP), order recursive matching pursuit (ORMP) and modified matching pursuit (MMP). These algorithms are briefly described and particular attention is paid, in the formulation of these algorithms, to the computation required. Fast versions of the algorithms are developed. The algorithms are evaluated in terms of their ability to produce a sparse solution and also in terms of their computational complexity and the storage necessary to implement them. Complexity-wise, BMP and MMP are shown to be comparable while ORMP is the most complex. In terms of their ability to select basis vectors, ORMP was the best followed by MMP and then BMP
Robust MEG Source Localization of Event Related Potentials: Identifying Relevant Sources by Non-Gaussianity
Independent Component Analysis (ICA) is a frequently used preprocessing step in source localization of MEG and EEG data. By decomposing the measured data into maximally independent components (ICs), estimates of the time course and the topographies of neural sources are obtained. In this paper, we show that when using estimated source topographies for localization, correlations between neural sources introduce an error into the obtained source locations. This error can be avoided by reprojecting ICs onto the observation space, but requires the identification of relevant ICs. For Event Related Potentials (ERPs), we identify relevant ICs by estimating their non-Gaussianity. The efficacy of the approach is tested on auditory evoked potentials (AEPs) recorded by MEG. It is shown that ten trials are sufficient for reconstructing all important characteristics of the AEP, and source localization of the reconstructed ERP yields the same focus of activity as the average of 250 trials