Tuesday, February 28, 2012

Joint Trace/TV Minimization: A New Efficient Approach for Spectral Compressive Imaging

Hyperspectral imagery is really one of those technologies we do not have. By that I mean that at a price of $100,000, no tinkerer will ever gets their hands on one of these cameras and as I explained the Dorkbot crowd two weeks ago, if no tinkerer can get their hands on it, then serendipity is unlikely to happen. The technology currently addresses broad needs but what we really need for this technology to be mainstream is the accidental discovery. It sure won't come if it cost 100,000 buckarus. David Brady and others are working on using compressive sensing to drown that cost by one or two orders of magnitude. Some of these advances  will not just come from hardware alone. Hence, I was ecstatic when I received this email last week from Pierre Vandergheynst:

Hi Igor
I'd like to draw your attention on the following paper: http://infoscience.epfl.ch/record/174926that advocates joint trace (or nuclear) - TV norm minimization for hyper spectral images, with really nice performances (see the effect of reconstructing with only m = 0.03 * n on Fig 2).
My student Mohammad is wrapping up the matlab code to be distributed on the same page. The data used in the paper is also publicly available.
Best regards   
Thanks Pierre for the heads-up. Here is the paper: Joint Trace/TV Minimization: A New Efficient Approach for Spectral Compressive Imaging by Mohammad GolbabaeePierre Vandergheynst:. The abstract reads:

In this paper we propose a novel and efficient model for compressed sensing of hyperspectral images. A large-size hyperspectral image can be subsampled by retaining only 3% of its original size, yet robustly recovered using the new approach we present here. Our reconstruction approach is based on minimizing a convex functional which penalizes both the trace norm and the TV norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and piecewise smooth structure: the two important priors explaining the underlying correlation structure of such data. Through simulations we will show our approach significantly enhances the conventional compression rate-distortion tradeoffs. In particular, in the strong undersampling regimes our method outperforms the standard TV denoising image recovery scheme by more than 17dB in the reconstruction MSE.

I wonder how this technique can used for blind deconvolution. But then eventually one can but wonder how this is going to affect actual compression hardware on satellites [1,2]

References of interest:

  1. CNES Studies for On-Board Compression of High-Resolution Satellite Images
  2.  by Carole Thiebaut and Roberto Camarero
  3. On-board Optical Image Compression for Future High Resolution Remote Sensing Systems

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