Binary Compressed Imaging

Aurelien Bourquard just sent me the following:

I just wanted to let you know about a recent paper related to 1-bit compressive sensing, entitled "Binary Compressed Imaging", that will appear in March in IEEE Transactions on Image Processing. This journal paper focuses on the case of 1-bit-type measurements and addresses their potential use in an optical acquisition setting. Maybe it will be helpful for other colleagues in the field.

Thanks Aurelien! Aurelien tells me that the implementation featured in this paper should be released soon. Stay tuned.

Binary Compressed Imaging by Aurelien Bourquard, and Michael Unser. The abstract reads:

Abstract—Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition, at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in the one-bit setting. In this paper, our goal is to design a framework for binary compressed sensing that is adapted to images. Accordingly, we propose an acquisition and reconstruction approach that complies with the high dimensionality of image data and that provides reconstructions of satisfactory visual quality. Our forward model describes data acquisition and follows physical principles. It entails a series of random convolutions performed optically followed by sampling and binary thresholding. The binary samples that are obtained can be either measured or ignored according to predefined functions. Based on these measurements, we then express our reconstruction problem as the minimization of a compound convex cost that enforces the consistency of the solution with the available binary data under total-variation regularization. Finally, we derive an efficient reconstruction algorithm relying on convex-optimization principles. We conduct several experiments on standard images and demonstrate the practical interest of our approach.

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