Oversampled Adaptive Sensing

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 nonadaptive 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.

An Adaptive Bayesian Framework for Recovery of Sources with Structured Sparsity

“…Note that in our simplified framework, A m+1 is restricted to be chosen from O F . We hence employ the worstcase adaptation strategy proposed in [1] and utilized in [2]: In subframe m, the adaptation function finds the permutation…”

“…The sensing matrix in each subframe is adapted based on some posterior information determined from the measurements of previous subframes. In [1], it has been demonstrated that OAS achieves a considerable performance gain, when some prior information on the signal is available. The most well-known form of such prior information is sparsity which was explicitly studied in [1], [2].…”

Oversampled Adaptive Sensing with Random Projections: Analysis and Algorithmic Approaches

“…T m , and hence increases the noise power in each individual sensing. Investigations have demonstrated that while this belief is true for signals with absolutely continuous priors, sequential adaptation is in fact beneficial when the signal has a mixture prior; see discussions in [1] and [11]. This is illustrative by considering an example from sparse recovery.…”

“…The initial study on OAS in [1] considered scenarios with orthogonal and deterministic projections. Such an assumption was primarily taken for sake of analytical tractability.…”

“…In oversampled adaptive sensing (OAS) [1], K sensors observe N signal samples linearly. The projections from the samples to the observations are modifiable and corrupted with noise.…”