Monday, February 21, 2011

This is not a hardware-only or solver-only problem ...

There is a gap of five years between these two shots [1] [2]:

Let me say something stupid based on nothing else than a hunch. If both images need TV-regularization to be reconstructed and that similar regularizations are used to rid one of multiplicative noise [3][4][5], then maybe, just maybe, these experiments suffer from multiplicative noise ?

Since both of them use a DMD chip, I can see several sources for that type of noise. My foray in MEMS , yielded a few facts. Among these facts was that the switching of the mirrors on the TI DMD [6] being electromechanical in nature (this is the point of MEMS) is likely to have some amount of stabilization issues. This is an issue that is unimportant to the human eye and the reason why the DMD is so successful for digital projectors, however, while tiny it contributes directly to affecting the coefficients of the measurement matrix.

Unless one does a better job of quantifying multiplicative noise on Donoho-Tanner phase transition we are bound to have the same photos as above in five years. Do we want that ? Of course not. Aren't we scared that this noise is being so bad that it will make any CS solution worthless: No surely not, it is not because the folks in the solver business are vaillantly coming up with suboptimal results stemming from the physics of the image acquisition that we cannot do anything. We want to design systems that can devise what this noise is as the image is being acquired. 

[1] Michael Wakin, Jason Laska, Marco Duarte, Dror Baron, Shriram Sarvotham, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk, An Architecture for Compressive Imaging (Proc. International Conference on Image Processing -- ICIP 2006, Atlanta, GA, Oct. 2006)
[2] Active illumination single-pixel camera based on compressive sensing, Filipe Magalhães, Francisco M. Araújo, Miguel V. Correia, Mehrdad Abolbashari, and Faramarz Farahi
[3] Multiplicative Noise Cleaning via a Variational Method Involving Curvelet Coefficients by Sylvain Durand, Jalal Fadili, and Mila Nikolova
[4] Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients by Sylvain DurandJalal Fadili,  Mila Nikolova
[5] Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization, José M. Bioucas-Dias, and Mário A. T. Figueiredo.
[6] Digital Light Processing TM for High-Brightness, High-Resolution Applications, Larry J. Hornbeck

1 comment:

Anonymous said...

Regarding the work presented by F. Magalhães et al., the projector used does not use DMD technology but LCD instead...

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