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

TL;DR

This work tackles image reconstruction through multimode fibers when the measurement matrix $A_u$ is unknown and subject to bending, which breaks traditional reconstruction. It introduces mismatch reconstruction theory, centered on the mismatch equation, and develops two solution families: a matched-solution algorithm that iteratively builds a usable $A_{recv}$ from a single extra measurement, and a calibration-solution algorithm that constructs a universal $A_{recv}$ via orthogonal basis images and a QR-derived image space. Theoretical results and appendix proofs establish the mismatch equation and convergence properties, while experiments (simulations) show successful image reconstruction under low-noise conditions and reveal how noise, precision, and basis orthogonality influence performance. The approach offers a low-cost, hardware-light route to stable dynamic imaging without precise fiber models or real-time calibration, with promising applications in portable multimode-fiber endoscopy and other harsh environments where bending is unavoidable. Key contributions include the mismatch equation, the matched and calibration algorithms, and evidence of robustness and practical applicability in dynamic imaging settings.

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.

Figures (12)

• Figure 1: Results of mismatch reconstruction.
• Figure 2: Reconstruction results of Baboon image using constructed $A_{recv}$ by Algo.1 and Algo.2 on three different $PM_{image}$.
• Figure 3: Error curves of Algo.1. The horizontal axis is the number of iteration and the vertical axis is error value. Same column shows the error curve in different iteration intervals.
• Figure 4: Error curves of Algo.2. The horizontal axis is the number of iteration and the vertical axis is error value. Same column shows the error curve in different iteration intervals.
• Figure 5: Reconstruction results of seven images using constructed $A_{recv}$ by Algo.1 (first line and its error level is 1e-4) and Algo.2 (second line) on PM3.