Wednesday, August 18, 2010

CS: To reconstruct or not to reconstruct, that is the question.

Today's common theme is how do you exract information from a random projection before you get to do a reconstruction. Enjoy!

This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known spectral targets and spectral anomalies from few incoherent projections. The proposed approaches accommodate targets of different signal strengths contaminated by a colored Gaussian background, and perform target detection without reconstructing the spectral input from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets in a known spectral dictionary. The anomaly detector is designed to control the number of false discoveries below a desired level and can be adapted to uncertainties in the user’s knowledge of the spectral dictionary. Unlike approaches based on the principles of compressed sensing, the proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the Johnson–Lindenstrauss lemma. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.

The attendant slides are here.

In a similar direction, we have: Joint compressive video coding and analysis by M. Cossalter, G. Valenzise, Marco Tagliasacchi, S. Tubaro. The abstract reads:
Traditionally, video acquisition, coding and analysis have been designed and optimized as independent tasks. This has a negative impact in terms of consumed resources, as most of the raw information captured by conventional acquisition devices is discarded in the coding phase, while the analysis step only requires a few descriptors of salient video characteristics. Recent Compressive Sensing literature has partially broken this paradigm by proposing to integrate sensing and coding in a unified architecture composed by a light encoder and a more complex decoder, which exploits sparsity of the underlying signal for efficient recovery. However, a clear understanding of how to embed video analysis in this scheme is still missing. In this paper, we propose a joint compressive video coding and analysis scheme and, as a specific application example, we consider the problem of object tracking in video sequences. We show that, weaving together compressive sensing and the information computed by the analysis module, the bit-rate required to perform reconstruction and tracking of the foreground objects can be considerably reduced, with respect to a conventional disjoint approach that postpones the analysis after the video signal is recovered in the pixel domain. These findings suggest that considerable gains in performance can be potentially obtained in video analysis applications, provided that a joint analysis-aware design of acquisition, coding and signal recovery is carried out.

In July there was a talk in Luxemburg on that theme:

Extracting Information from Compressive Sensing Measures without Reconstruction

Prof. Simon Morgan

Los Alamos National Laboratory and New Mexico Consortium

Date: Friday, July 30th, 2010

Time: 2.15 p.m.

Venue: University of Luxembourg - Campus Kirchberg – 6, rue Richard Coudenhove-Kalergi, Luxembourg, building ‘F’ room F211.

The SnT, at the University of Luxembourg carries out interdisciplinary research and graduate education in secure, reliable, and trustworthy ICT systems and services. It is our pleasure to host this seminar by Prof. Simon Morgan

Björn Ottersten, Director SnT

Title: Extracting Information from Compressive Sensing Measures without Reconstruction

Abstract : Algorithms to reconstruct signals from compressive sensing measures combine information from measures with prior knowledge information about signal sparsity. These algorithms involve optimization and rely on new mathematical results about signal recovery from measures at better than the Nyquist sampling rate. We present applications involving a single pixel camera where geometric information can be extracted from compressive sensing measures without reconstruction of the signal or prior knowledge about sparsity.

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