CS: Linkedin Discussions, a Correction and Two Papers

Two discussions on LinkedIn have been started and are looking for answers:

• spectrogram and random phase matrix
• Coherence based error bounds

The group now has 450 members.

I also found this interesting blog entry: What I Don’t Know About Compressive Sensing by Brian Chesney

In a recent entry (CS: CS SPDE, Cramér-Rao Bound In Noisy CS, Compressive Fourier Transform Spectroscopy, compressive terahertz imaging and a job at Exxon ). I featured a paper entitled: On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing by Rad Niazadeh, Massoud Babaie-Zadeh, Christian Jutten. where one could read in the abstract that

...In this correspondence, we will first explain the mistake in the mentioned lemma in [Akackaya et. al., 2008] and will then state a new correct form of it...

Mehmet Akackaya responded in the comment section the following:

Dear Igor,

While reading your blog, I came across the paper "On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing," which claimed there was a mistake in one of our earlier works. I have contacted the authors of the work and clarified their source of confusion.

Our proof IS correct as it was published. Just wanted to let the community know :)

Thanks for running this blog, so that we become aware of such misunderstandings early on.

Thanks
Mehmet

Thanks Mehmet for the heads-up. Let us now wait for a new version of On the Achievability of Cramér-Rao Bound In Noisy Compressed Sensing.


Finally, I found two papers on CS:

A review of the compressive sampling framework in the lights of spherical harmonics: applications to distributed spherical arrays by Bruno Masiero and Martin Pollow. The abstract reads:

Compressive Sampling proposes a new framework on how to effectively sample information (signals or any other physical phenomena) with a reduced number of sensors. The main idea behind this concept is that if the information to be sampled can be sparsely described in a space that is incoherent to the measurement space, then this information can be restored by minimization. In this paper we describe the Compressive Sampling framework and present one example of application, namely, to sample an outgoing acoustic field with a distributed spherical array composed of a reduced number of sensing microphones without suffering from aliasing errors.

Compressive Sensing based Lightweight Sampling for Large Robot Groups by Sameera Poduri , Garrett Marcotte , Gaurav S. Sukhatme. The abstract reads:

This paper presents a lightweight method for spatial sampling of environmental phenomenon using a large group of robots. Data is gathered using simple random walks, aggregated centrally, and the field is reconstructed using tools from compressive sensing. Key to our approach is a recent remarkable result that it is possible to reconstruct compressible fields using O(log n) (where n is the dimension of the field) nonadaptive measurements in a basis that is ‘incoherent ’ to the representation basis and, under certain conditions, random measurements are as ‘good ’ as any other measurements [1]. We show that random walk sampling with large groups of robots can effectively reconstruct natural fields that are typically compressible in the frequency domain. The method is described analytically and demonstrated in simulation with real and simulated data. We also study the tradeoff between number of robots required and length of the random walk.

Image Credit: NASA/JPL/Space Science Institute, N00155237.jpg was taken on June 05, 2010 and received on Earth June 07, 2010. The camera was pointing toward TITAN at approximately 279,287 kilometers away, and the image was taken using the CL1 and CB3 filters.