Mismatch reconstruction theory for unknown measurement matrix in imaging through multimode fiber bending

TL;DR

This paper introduces a mismatch reconstruction theory that enables image reconstruction in multimode fiber imaging even when the measurement matrix is unknown, by constructing a new measurement matrix through proposed algorithms.

Contribution

It presents a novel mismatch equation and algorithms for constructing measurement matrices, improving image reconstruction robustness in unknown measurement scenarios.

Findings

Constructed measurement matrix enables successful image reconstruction under low noise.

Algorithms show robustness against noise, computational precision, and orthogonality issues.

Theoretical proofs and practical experiments validate the proposed methods.

Abstract

Multimode fiber imaging requires strict matching between measurement value and measurement matrix to achieve image reconstruction. However, in practical applications, the measurement matrix often cannot be obtained due to unknown system configuration or difficulty in real-time alignment after arbitrary fiber bending, resulting in the failure of traditional reconstruction algorithms. This paper presents a novel mismatch reconstruction theory for solving the problem of image reconstruction when measurement matrix is unknown. We first propose mismatch equation and design matched and calibration solution algorithms to construct a new measurement matrix. In addition, we also provide a detailed proof of these equations and algorithms in the appendix. The experimental results show that under low noise levels, constructed matrix can be used for matched pair in traditional reconstruction algorithms, and reconstruct the original image successfully. Then, we analyze the impact of noise, computational precision and orthogonality on reconstruction performance. The results show that proposed algorithms have a certain degree of robustness. Finally, we discuss the limitations and potential applications of this theory. The code is available: https://github.com/yanglebupt/mismatch-solution.