JR2net: a joint non-linear representation and recovery network for compressive spectral imaging

Phase unwrapping for phase imaging using the plug-and-play proximal algorithm

Phase unwrapping (PU) is essential for various scientific optical applications. This process aims to estimate continuous phase values from acquired wrapped values, which are limited to the interval (-π,π]. However, the PU process can be challenging due to factors such as insufficient sampling, measurement errors, and inadequate equipment calibration, which can introduce excessive noise and unexpected phase discontinuities. This paper presents a robust iterative method based on the plug-and-play (PnP) proximal algorithm to unwrap two-dimensional phase values while simultaneously removing noise at each iteration. Using a least-squares formulation based on local phase differences and reformulating it as a partially differentiable equation, it is possible to employ the fast cosine transform to obtain a closed-form solution for one of the subproblems within the PnP framework. As a result, reliable phase reconstruction can be achieved even in scenarios with extremely high noise levels.

Computational spectral imaging: a contemporary overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow the identification of objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared with conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarizes the advances in CSI, starting with SI and its relevance and continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, as well as the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks.