Highly Constrained Coded Aperture Imaging Systems Design Via a Knowledge Distillation Approach

TL;DR

This work addresses the challenge of designing physically constrained computational optical imaging systems, where traditional end-to-end optimization is hampered by binary coding and limited snapshots. It introduces a knowledge distillation framework that transfers performance from a high-quality, unconstrained teacher to a restricted student using an unrolled ADMM-based recovery network and dual losses (imitation and correlation congruence) to align outputs and feature dynamics. The approach is validated on single-pixel cameras for monochromatic and multispectral reconstruction, showing KD can outperform E2E baselines and enable efficient OCE design under tight physical constraints. The findings demonstrate that sparse representations of teacher features yield the best knowledge transfer, and that a less complex teacher can sometimes outperform a more powerful one for KD, with implications for faster, storage-efficient COI systems in practical settings.

Abstract

Computational optical imaging (COI) systems have enabled the acquisition of high-dimensional signals through optical coding elements (OCEs). OCEs encode the high-dimensional signal in one or more snapshots, which are subsequently decoded using computational algorithms. Currently, COI systems are optimized through an end-to-end (E2E) approach, where the OCEs are modeled as a layer of a neural network and the remaining layers perform a specific imaging task. However, the performance of COI systems optimized through E2E is limited by the physical constraints imposed by these systems. This paper proposes a knowledge distillation (KD) framework for the design of highly physically constrained COI systems. This approach employs the KD methodology, which consists of a teacher-student relationship, where a high-performance, unconstrained COI system (the teacher), guides the optimization of a physically constrained system (the student) characterized by a limited number of snapshots. We validate the proposed approach, using a binary coded apertures single pixel camera for monochromatic and multispectral image reconstruction. Simulation results demonstrate the superiority of the KD scheme over traditional E2E optimization for the designing of highly physically constrained COI systems.

Figures (3)

• Figure 1: Proposed KD framework, the yellow color is associated with the high-constrained COI system model (student), and the green color is associated with the high-performance, low-constrained COI system model (teacher).
• Figure 2: Comparison of the reconstruction performance among the E2E baseline, the student models trained without optimizing their OCEs, i.e., employing random binary CAs, and the KD approach. a) Teachers with $\gamma_t=0.8$ and b) Teachers with $\gamma_t=0.9$. Teacher A is a real-valued CA SPC, Teacher B is a binary CA SPC, and Students A and B are binary CA SPCs distilled from teachers A and B, respectively.
• Figure 3: Comparison of the reconstruction performance among the teacher model, E2E baseline, and the proposed KD approach for reconstructing eight spectral bands. a) Displays the RGB representation of the reconstructed SI of the baseline and the proposed method. Also, the eight bands are plotted. b) shows the recovery performance of the test dataset along the stages.