Reconstruction Approaches For 1-Bit Compressed Sensing and Sparse Interpolations
Aurélien Bourquard, BIG

Seminar • 13 September 2010

Abstract
The first part of this talk addresses image acquisition and reconstruction in the framework of compressed sensing and 1-bit quantization. First, a suitable theoretical acquisition model is proposed. Then, a large-scale reconstruction algorithm that exploits bound-optimization concepts, which is the central contribution, is presented. The overall approach is finally placed in an more practical context, considering an optical device that performs several parallel acquisitions. The second part addresses image interpolation from a given subset of non-ideal samples. Based on the generalized-sampling theory, the corresponding problem is first expressed in the continuous domain. In order to make the problem well-posed, an anisotropic regularization approach is proposed. Structurally, the reconstruction algorithm is shown to be akin to IRLS methods. The multilevel resolution strategy is described, and subsequent experiments are shown and discussed.