CS: Dequantizing Compressed Sensing with Non-Gaussian Constraints, A request for Collaboration.

Laurent Jacques just let me know of a paper and companion technical report on CS and the quantization of measurements. Here they are:

Dequantizing Compressed Sensing with Non-Gaussian Constraints by Laurent Jacques, David Hammond, and M. Jalal Fadili

In this paper, following the Compressed Sensing paradigm, we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment p (BPDQp), that model the quantization distortion more faithfully than the commonly used Basis Pursuit DeNoise (BPDN) program. Our decoders proceed by minimizing the sparsity of the signal to be reconstructed while enforcing a data fidelity term of bounded l_p-norm, for 2 \lt p \le \infty. We show that in oversampled situations the performance of the BPDQp decoders are significantly better than that of BPDN, with reconstruction error due to quantization divided by sqrt(p + 1). This reduction relies on a modified Restricted Isometry Property of the sensing matrix expressed in the l_p-norm (RIP_p); a property satisfied by Gaussian random matrices with high probability. We conclude with numerical experiments comparing BPDQp and BPDN for signal and image reconstruction problems.

and the attendant technical report: Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine by Laurent Jacques, David Hammond, and M. Jalal Fadili

After inquiring on the subject, David Hammond also let me know that:

We are planning on releasing the BPDQ solver code upon acceptance of a journal paper; so the time is unclear.

In a different direction, Brien Housand sent the following request on both this blog and the linkedin group discussion forum:

Seeking partner from Academic or non-profit research institute for multi-spectral Compressive Sensing project – paper study. Combine your knowledge of Compressive Sensing algorithms with our skills at Electro-Optical sensor design.

Contact: Brien Housand
Email: bhousand@dsci.com

After 6 months since its inception, the Compressive Sensing Study Group on LinkedIn now has 100 members.

Credit photo: me. A view of Geneva and the Mont-Blanc mountain.