CS: NESTA, CS with Known Spectral Energy Density, CS based interior tomography, CS-UWB Comm system, a Summer School,.

Here is the new batch of Compressive Sensing related papers:

NESTA: a fast and accurate first-order method for sparse recovery by Stephen Becker, Jerome Bobin, and Emmanuel Candès. The abstract reads:

Accurate signal recovery or image reconstruction from indirect and possibly under-
sampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel first-order methods in convex optimization, most notably Nesterov's smoothing technique, this paper introduces a fast and accurate algorithm for solving common recovery problems in signal processing. In the spirit of Nesterov's work, one of the key ideas of this algorithm is a subtle averaging of sequences of iterates, which has been shown to improve the convergence properties of standard gradient-descent algorithms. This paper demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as 1) it is computationally efficient, 2) it is accurate and returns solutions with several correct digits, 3) it is flexible and amenable to many kinds of reconstruction problems, and 4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed state-of-the-art methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization, and convex programs seeking to minimize the l_1 norm of Wx under constraints, in which W is not diagonal.

I like the fact that they address point 4) which seems to be an issue with other methods (see this entry). I am looking forward to an implementation of this new scheme.

Compressive Sampling with Known Spectral Energy Density by Andriyan Suksmono. The abstract reads:

A method to improve L1 performance of the CS (Compressive Sampling) for signals with known spectral energy density is proposed. Instead of random sampling, the proposed method selects the location of samples to follow the distribution of the spectral energy. Samples collected from three different measurement methods; the uniform sampling, random sampling, and energy equipartition sampling, are used to reconstruct a given UWB (Ultra Wide Band) signal whose spectral energy density is known. Objective performance evaluation in term of PSNR (Peak Signal to Noise Ratio) indicates that the CS reconstruction of random sampling outperform the uniform sampling, while the energy equipartition sampling outperforms both of them. These results suggest that similar performance improvement can be achieved for CS-based devices, such as the compressive SFCW (Stepped Frequency Continuous Wave) radar and the compressive VLBI (Very Large Baseline Interferometry) imaging, allowing even higher acquisition speed or better reconstruction results.

From the good folks at Rice we have:

Compressed sensing based interior tomography by Hengyong Yu and Ge Wang. The abstract reads:

While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensing theory, herewe prove that if an object under reconstruction is essentially piecewise constant, a local ROI can be exactly and stably reconstructed via the total variation minimization. Because many objects in computed tomography (CT) applications can be approximately modeled as piecewise constant, our approach is practically useful and suggests a new research direction for interior tomography. To illustrate the merits of our finding, we develop an iterative interior reconstruction algorithm that minimizes the total variation of a reconstructed image and evaluate the performance in numerical simulation.

Compressive Sensing Based Ultra-wideband Communication System by Peng Zhang, Zhen Hu, Robert C. Qiu and Brian M. Sadler. The abstract reads:

UWB) communication. Our major contribution is to exploit the channel itself as part of compressed sensing, through waveformbased pre-coding at the transmitter. We also have demonstrated a UWB system baseband bandwidth (5 GHz) that would, if with the conventional sampling technology, take decades for the industry to reach. The concept has been demonstrated, through simulations, using real-world measurements. Realistic channel estimation is also considered.

the attendant conference paper is here: Compressive Sensing Based Ultra-wideband Communication System by Peng Zhang, Zhen Hu, Robert C. Qiu and Brian M. Sadler. The abstract reads:

Sampling is the bottleneck for ultra-wideband (UWB) communication. Our major contribution is to exploit the channel itself as part of compressive sampling, through
waveform-level pre-coding at the transmitter. We also have demonstrated a UWB system baseband bandwidth (5 GHz) that would, if with the conventional sampling technology, take decades for the industry to reach. The concept has been demonstrated, through simulations, using real-world measurements. Realistic channel estimation is also considered.

and a presentation on the subject is here: Peng Zhang, "Compressive Sensing Based UWB System," Presentation on Compressive Sensing.

I'll be adding this to the compressive sensing hardware page.

There is also a Summer School: Theoretical Foundations and Numerical Methods for Sparse Recovery at RICAM in Linz, Austria on Aug. 31 - Sept. 4. I'll add it to the compressive sensing calendar.

Of related interest we also have:

EM type algorithms for likelihood optimization with non-differentiable penalties by Stephane Chretien, Alfred O. Hero and Herve Perdry. The abstract reads:

The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth penalty functions. However, many relaxed versions of variable selection penalties are not smooth. The goal of this paper is to introduce a new class of Space Alternating Penalized Kullback Proximal extensions of the EM algorithm for nonsmooth likelihood inference. We show that the cluster points of the new method are stationary points even when on the boundary of the parameter set. Special attention has been paid to the construction of component-wise version of the method in order to ease the implementation for complicated models. Illustration for the problems of model selection for finite mixtures of regression and to sparse image reconstruction is presented.

and in arxiv: An alternating $\ell_1$ relaxation for compressed sensing by Stephane Chretien. I already talked about it before. The scilab and python codes are here

Image Credit: NASA/JPL/Space Science Institute, Saturn rings as seen by Cassini five days ago.