Feedback Acquisition and Reconstruction of Spectrum-Sparse Signals by Predictive Level Comparisons

TL;DR

This paper introduces a feedback-based method for sensing and reconstructing spectrally sparse signals that adaptively estimates spectral components and corrects sign bit errors, outperforming existing techniques.

Contribution

It presents a novel feedback acquisition scheme with a sliding-window algorithm for dynamic spectral estimation and an iterative error correction method for sign flip errors.

Findings

Effective spectral component estimation with a sliding-window approach.

Robustness to sign flip errors through iterative correction.

Superior performance compared to existing methods in simulations.

Abstract

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based Compressive Sensing (CS) algorithms, our proposed algorithm gradually estimates and follows slow changes in the sparse components utilizing a sliding-window technique. We also consider the scenario in which possible flipping errors in the sign bits propagate along iterations (due to the feedback loop) during reconstruction. We propose an iterative error correction algorithm to cope with this error propagation phenomenon considering a binary-sparse occurrence model on the error sequence. Simulation results show effective performance of the proposed scheme in comparison with the literature.