Friday, January 28, 2011

CS: Op-ed, some videos, Compressive Sensing Using the Entropy Functional, A Message-Passing Receiver for BICM-OFDM

Every so often, I get an email asking me to link back to certain sites, here is the latest instance, NB is listed in the Rest of the Best category, whatever that means, here is what struck me: the definition:
Math blogs are a great way for professors, scientists, and researchers to convey the purpose of their work to a broader audience. Some bloggers offer an introduction to mathematical concepts and current research, while others post updates on their research and interests. The following 50 blogs are the cream of the crop: entertaining and informative posts that have something to offer for math geeks of all stripes.
All I know is that Nuit Blanche ain't:
  • about Math
  • about conveying my work most of the time.
  • there to offer an introduction to current research most of the time.
  • there to post updates on my interests.
It's a chronicle... and, from my point of view, a good way to broker important and honest discussions.

One of you just contacted me and wondered if this paper was an instance of compressive sensing. I'll have to read the paper first. In the meantime, we have several videos, two papers and two announcements for talks. Enjoy.

First, the videos. The last one isn't about CS but rather how to use a Kinect sensor to perform some SLAM computations, wow.

Compressive Estimation for Signal Integration in Rendering

Robustness of Compressed Sensing Parallel MRI in the Presence of Inaccurate Sensitivity Estimates

6D SLAM with RGB-D Data

The papers:
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregman's row action D-projection method for compressive sensing applications. Simulation examples are presented.
I wonder when a solver will be available.

We propose a factor-graph-based approach to joint channel-estimation-and-decoding (JCED) of bit- interleaved coded orthogonal frequency division multiplexing (BICM-OFDM). In contrast to existing designs, ours is capable of exploiting not only sparsity in sampled channel taps but also clustering among the large taps, behaviors which are known to manifest at larger communication bandwidths. In order to exploit these channel-tap structures, we adopt a two-state Gaussian mixture prior in conjunction with a Markov model on the hidden state. For loopy belief propagation, we exploit a "generalized approximate message passing" (GAMP) algorithm recently developed in the context of compressed sensing, and show that it can be successfully coupled with soft-input soft-output decoding, as well as hidden Markov inference, through the standard sum-product framework. For N subcarriers and M bits per subcarrier (and any channel length L \lt N), the resulting JCED-GAMP scheme has a computational complexity of only O(N log2 N+N 2^M). Numerical experiments show that our scheme yields BER performance within 1 dB of the known-channel bound and 4 dB better than decoupled channel-estimation-and-decoding via LASSO.

At UT, there is going to be talk from somebody in industry on his use of compressed sensing and related techniques:

Detection of Patterns in Networks
ECE Seminar Series

Friday, February 4, 2011
12:00 - 2:00 PM
ENS 637

Dr. Randy C. Paffenroth

Numerica Corporation

Discuss the development and application of a mathematical and computational framework for detecting and classifying weak, distributed patterns in sensor networks. The work being done at Numerica demonstrates the effectiveness of space-time inference on graphs, robust matrix completion and second order analysis in the detection and classification of distributed patterns that are not discernible at the level of individual nodes. Our focus is on cyber security scenarios where computer nodes (such as terminals, routers and servers) are sensors that provide measurements of packet rates, user activity, central processing unit usage, etc. When viewed independently, they cannot provide a definitive determination of the underlying pattern, but when fused with data from across the network – both spatially and temporally – the relevant patterns emerge. The clear underlying suggestion is that only detectors and classifiers that use a rigorous mathematical analysis of temporal measurements at many spatially distributed points in the network can identify network attacks. This research builds upon work in compressed sensing and robust matrix completion and is an excellent example of industry-academic collaboration.

whereas at University of Illinois, there will be:

GE/IE 590 Seminar-Large-Scale Optimization with Applications in Compressed Sensing
Speaker Professor Fatma Kilinc-Karzan
Date Feb 3, 2011
Time 4:00 pm
Location 101 Transportation Building
Cost Free
Sponsor ISE
Contact Holly Tipsword
Phone 217-333-2730
Views 4
In this talk, we will cover some of the recent developments in large-scale optimization motivated by the compressed sensing paradigm. Sparsity plays a key role in dealing with high-dimensional data sets. Exploiting this fact, compressed sensing suggests a new paradigm by directly acquiring and storing only a few linear measurements (possibly corrupted with noise) of high-dimensional signals, and then using efficient -recovery procedures for reconstruction. Successful applications of this theory range from MRI image processing to statistics and machine learning. This talk will have two main parts. In the first part, after presenting the necessary background from compressed sensing, we will show that prior results can be generalized to utilize a priori information given in the form of sign restrictions on the signal. We will investigate the underlying conditions allowing successful -recovery of sparse signals and show that these conditions although difficult to evaluate lead to sufficient conditions that can be efficiently verified via linear or semidefinite programming. We will analyze the properties of these conditions, and describe their limits of performance. In the second part, we will develop efficient first-order methods with both deterministic and stochastic oracles for solving large-scale well-structured convex optimization problems. As an application of this theory, we will show how large-scale problems originating from compressed sensing fall into this framework. We will conclude with numerical results demonstrating the effectiveness of our algorithms.

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