Oversampled Adaptive Sensing

TL;DR

This paper introduces a Bayesian adaptive sensing framework that dynamically adjusts sensing parameters based on real-time quality measures, significantly improving efficiency and accuracy for sparse Gaussian sources compared to traditional methods.

Contribution

It presents a novel Bayesian adaptive sensing method that reduces sensing time and error for sparse sources, outperforming existing techniques with polynomial complexity.

Findings

Achieves about 2 dB gain over optimal compressive sensing at a compression ratio of 3.

Improves approximately 3 dB over non-adaptive oversampled orthogonal sensing.

Gains 6-7 dB compared to LASSO-based recovery schemes.

Abstract

We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant reduction in average sensing time and/or mean-squared error is achieved in comparison to non-adaptive sensing. For compression ratio 3, a sparse 10% Gaussian source and equal average sensing times, the proposed method gains about 2 dB over the performance bound of optimum compressive sensing, about 3 dB over non-adaptive 3-fold oversampled orthogonal sensing and about 6 to 7 dB to LASSO-based recovery schemes while enjoying polynomial time complexity. We utilize that in the presence of Gaussian noise the mean-squared error conditioned on the current observation is proportional to the derivative of the conditional mean estimate with respect to this observation.