Various Compressed Sensing Set-Ups Evaluated Against Shannon Sampling Under Constraint of Constant Illumination

TL;DR

This paper evaluates various compressed sensing setups in optical and electron microscopy under constant illumination, introducing a heuristic DQE metric to optimize measurement design and demonstrate optimal reconstruction performance.

Contribution

It develops a heuristic DQE metric for compressed sensing under illumination constraints and demonstrates its effectiveness in optimizing measurement design and reconstruction.

Findings

Compressed sensing does not increase Fisher information beyond Shannon sampling without read-out noise.

The DQE metric effectively predicts optimal measurement parameters.

Regularization improves reconstruction accuracy at DQE-predicted settings.

Abstract

Under the constraint of constant illumination, an information criterion is formulated for the Fisher information that compressed sensing measurements in optical and transmission electron microscopy contain about the underlying parameters. Since this approach requires prior knowledge of the signal's support in the sparse basis, we develop a heuristic quantity, the detective quantum efficiency (DQE), that tracks this information criterion well without this knowledge. It is shown that for the investigated choice of sensing matrices, and in the absence of read-out noise, i.e. with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of Shannon sampling. Furthermore, enabled by the DQE's analytical tractability, the experimental designs are optimized by finding out the optimal fraction of on-pixels as a function of dose and read-out noise. Finally, we introduce a regularization and demonstrate, through simulations and experiment, that it yields reconstructions attaining minimum mean squared error at experimental settings predicted by the DQE as optimal.