CS: Spectral Estimation and Compressive Sensing GNU Radio release, BCS New Release, CS can make you rich

Martin Braun just sent this to the GNU Radio project E-mail List:

Hi List,

I am happy to say that we from the INT have managed to merge some of our research with GNU Radio development and have released some code on CGRAN. There are two new projects:

1) Spectral Estimation Toolbox

This project aims to enhance GNU Radio with 'proper' spectral estimation routines; so far it only includes Welch's method as a hierarchical block.

2) Compressive Sensing Toolbox

The other project adds some Compressive Sensing routines to GNU Radio. So far, only compression algorithms have been implemented as C++ blocks, which makes the whole project of limited practical use, but it can already be used to run fast simulations (much faster than some other, expensive, proprietary software commonly used in academics). An example on how to do compressed spectral estimation is also included.

WIP includes:

- Compression algorithms for the FPGA
- Smashed Filter Detector Bank

We are currently not planning to add any reconstruction algorithms (l1 or other), since they are currently not of much use for Cognitive Radios.

Of course, collaborators are welcome. In particular, any implementation of parametric spectral estimation would be a nice extension for the spectral estimation toolbox. Reconstruction algorithms would also be interesting to have, but are of no priority for us at the moment.

I am happy to answer any questions regarding these codes off-list. Have fun,

Martin

Thanks Martin !

In light of the work focused on using additional prior information in order to reduce the number of measurements such as in Model Based CS here is a paper on a similar line of study in Exploiting Structure in Compressive Sensing with a JPEG Basis by Lihan He and Lawrence Carin. The abstract reads:

Traditional compressive sensing (CS) assumes that the transform coefficients of the underlying signal are drawn i.i.d. from a sparseness prior. Most natural data are characterized by known structure in the transform coefficients, that may be exploited when performing CS inversion. Almost all previous examples of exploiting structure in CS inversion have been based on the assumption that the underlying signal is sparse in a wavelet basis. However, the JPEG standard for image compression is based on a block-DCT decomposition, and here we exploit structure in the associated transform coefficients when performing CS inversion. The analysis is performed in a Bayesian setting, and comparisons are performed with many of the CS algorithms in the literature. Performance of the block-DCT construction is also compared with related performance of a wavelet-based construction, for noise-free and noisy CS measurements. We also examine the value of inverting multiple CS measurements jointly in this setting.

In light of this work, the Bayesian Compressive Sensing code (from the same group) has seen some upgrade. From the project page:

• BCS: At the moment, the distribution includes the core BCS code and the spike examples for the adaptive CS and the multi-task CS. Read the README file in the main directory for more information.

  Download: bcs_ver0.1.zip (Last Updated: Aug. 03, 2008)
  (NB: A bug was fixed in MT_CS.m for the cases where signals are dramatic undersampled.)

• VB-BCS: The basic BCS implemented via a variational Bayesian approach. The package includes the core VB-BCS code, one example of a 1-dimensional signal and two examples of 2-dimensional images.

  Download: bcs_vb.zip (Last Updated: Mar. 03, 2009)
  

• TS-BCS for wavelet: The TS-BCS for wavelet implemented by an MCMC approach. The package includes the core TS-BCS code for wavelet coefficients, one example of a 1-dimensional signal and two examples of 2-dimensional images.

  Download: tswcs.zip (Last Updated: Mar. 03, 2009)
  

• TS-BCS for block-DCT: The TS-BCS for block-DCT implemented by an MCMC approach. The package includes the core TS-BCS code for block-DCT coefficients and two examples of 2-dimensional images.

  Download: tsdctcs.zip (Last Updated: Mar. 04, 2009)

I am hearing from Larry that the videos of the CS workshop should be on Youtube next week. While we are on the subject of graphs, Leo Grady wrote the Graph Analysis Toolbox:

The Graph Analysis Toolbox for MATLAB was written as a by-product of my PhD thesis. My intention was to allow for flexible representation and analysis of data associated with a graph, specifically slanted toward computer vision applications.

Talking about the workshop, as it happens, while this blog tries to make available most information on CS, sometimes, some information can slip through mostly because of the ever continuous stream of preprint/publications on the subject. I personally would not expect that stream to decrease anytime soon as underdetermined systems are plenty. If you recall the discussion with Gerry Skinner, a specialist in coded aperture (not compressive sensing), you probably were getting the idea that compressive could not be used for detecting faint signals in some type of background. Two presentations at the workshop take a stab at this problem:

• Robert Nowak's presentation at the CS workshop on Distilled Sensing. Rui Castro (a co-author with Robert Nowak and Jarvis Haupt) did a longer presentation on the subject in a presentation entitled: Distilled Sensing: Active sensing for sparse recovery (ppt is here). The abstract reads:

  A selective sampling methodology called \emph{Distilled Sensing} (DS) is proposed for recovering sparse signals in noise. DS exploits the fact that it is often easier to rule out locations that do not contain signal than it is to detect the locations of non-zero signal components. We formalize this observation and use it to devise a sequential selective sensing strategy that focuses sensing/measurement resources towards the signal subspace. This adaptivity in sensing results in rather surprising gains in sparse signal recovery compared to non-adaptive sensing. We show that exponentially weaker sparse signals can be recovered via DS compared with conventional non-adaptive sensing.
  

• Another presentation by Rebecca Willett looked at that problem as well.

In other news, John Wright wins 30,000 buckarus from his paper on Robust face recognition via sparse recognition.

Credit: Cave of Crystal, Mexico (via this blog)