CS: Fourier-transform Ghost Imaging, Message Passing Algorithms for Compressed Sensing

This is new, Nuit Blanche has now a PageRank of 6 but according to Wikipedia, PageRank does not mean anything anymore. Oh well, I hope you liked yesterday's first installment of "These Technologies Do Not Exist" ?

In the meantime, one can only imagine how much of an improvement some of these technologies might bring by looking at some of the current results obtained by David Brady and Scott McCain at Duke and Applied Quantum Technologies respectively.

Thanks to Alex Conrad, I now have a Google Wave account. I have no invitation to give though, a situation which surely could be mapped into another Seinfeld moment but I can't think of one for the moment.

Today, we have three new papers from Arxiv:

Fourier-transform Ghost Imaging for pure phase object based on Compressive Sampling algorithm by Hui Wang, Shensheng Han. The abstract reads:

A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is discussed based on the Compressive Sampling (CS) theory. Though developed mostly in real space, CS algorithm could also be used for the Fourier spectrum reconstruction of pure phase object by setting a proper sensing matrix. This could find its application in diffraction imaging of X-ray, neutron and electron with higher efficiency and resolution. Simulation and experiment results are also presented to prove the feasibility.

and a continuation of a previous paper on approximate message passing reconstruction algorithm which seems to be fast and seems to also go farther than the regular IST solver:

Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction by David Donoho, Arian Maleki, Andrea Montanari. The abstract reads:

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP, for approximate message passing. This is the first of two conference papers describing the derivation of these algorithms, connection with the related literature, extensions of the original framework, and new empirical evidence.
In particular, the present paper outlines the derivation of AMP from standard sum-product belief propagation, and its extension in several directions. We also discuss relations with formal calculations based on statistical mechanics methods.

Message Passing Algorithms for Compressed Sensing: II. Analysis and Validation by David Donoho, Arian Maleki, Andrea Montanari. The abstract reads:

In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP, for approximate message passing. This is the second of two conference papers describing the derivation of these algorithms, connection with related literature, extensions of original framework, and new empirical evidence.
This paper describes the state evolution formalism for analyzing these algorithms, and some of the conclusions that can be drawn from this formalism. We carried out extensive numerical simulations to confirm these predictions. We present here a few representative results.