Interferometric single-pixel imaging with a multicore fiber

TL;DR

This paper introduces a novel interferometric single-pixel imaging method using a multicore fiber that efficiently reconstructs images with fewer measurements by leveraging spectral content encoding and rank-one projections.

Contribution

The work presents a new sensing scheme for lensless imaging with multicore fibers, combining interferometric matrix encoding and compressed sensing principles, validated through theory and experiments.

Findings

Efficient image reconstruction with fewer measurements than traditional methods.

Theoretical analysis shows the sensing scheme satisfies restricted isometry properties.

Experimental validation confirms the method's effectiveness on real MCF systems.

Abstract

Lensless illumination single-pixel imaging with a multicore fiber (MCF) is a computational imaging technique that enables potential endoscopic observations of biological samples at cellular scale. In this work, we show that this technique is tantamount to collecting multiple symmetric rank-one projections (SROP) of a Hermitian \emph{interferometric} matrix -- a matrix encoding the spectral content of the sample image. In this model, each SROP is induced by the complex \emph{sketching} vector shaping the incident light wavefront with a spatial light modulator (SLM), while the projected interferometric matrix collects up to $O(Q^2)$ image frequencies for a $Q$-core MCF. While this scheme subsumes previous sensing modalities, such as raster scanning (RS) imaging with beamformed illumination, we demonstrate that collecting the measurements of $M$ random SLM configurations -- and thus acquiring $M$ SROPs -- allows us to estimate an image of interest if $M$ and $Q$ scale linearly (up to log factors) with the image sparsity level, hence requiring much fewer observations than RS imaging or a complete Nyquist sampling of the $Q \times Q$ interferometric matrix. This demonstration is achieved both theoretically, with a specific restricted isometry analysis of the sensing scheme, and with extensive Monte Carlo experiments. Experimental results made on an actual MCF system finally demonstrate the effectiveness of this imaging procedure on a benchmark image.