Two-dimensional Fourier compressed sensing under a fixed readout budget per channel
This work provides theoretical and practical insights for compressed sensing in applications like MRI and radar where per-channel sampling constraints are critical, though the results are incremental.
The paper addresses the problem of reconstructing sparse 2D signals from subsampled Fourier measurements under a fixed per-channel readout budget. It derives a lower bound on mutual coherence that is tighter than the Welch bound due to the budget constraint, and constructs deterministic subsampling patterns that achieve this bound for certain dimensions and budgets, showing improved performance over random subsampling in simulations.
Recovering sparse signals from their subsampled Fourier representation is an important problem in communications, radar, and imaging. In this letter, we focus on reconstructing sparse 2D signals (matrices) under the constraint that only a fixed number of entries can be sampled from each channel, e.g., a row or a column in the Fourier domain. For a specified per-channel readout budget, we derive a lower bound on the mutual coherence of the corresponding compressed sensing matrix. We show that our bound is larger than the classical Welch bound, due to a limited readout budget. We also construct deterministic subsampling patterns that attain this bound for a class of matrix dimensions and readout budgets, and benchmark them against random subsampling through simulations.