Coded aperture design for hyper-spectral image recovery via Matrix Completion

A spectral image is a 3-dimensional spatio-spectral set with a large amount of spectral information for each spatial location of a scene. Compressive Spectral Imaging techniques (CSI) permit to capture the 3D scene in 2-dimensional coded projections. The Coded Aperture Snapshot Spectral Imager (CASSI) is an optical architecture to sense a spectral image in a single projection by applying CSI. CSI increases the sensing speed and reduces the amount of collected data compared to traditional methods. The 3D scene is then recovered by solving an ℓ₁-based optimization problem. However, this problem assumes that the scene is sparse in some known orthonormal basis. In contrast, a technique called Matrix Completion (MC) allows the recovery of a scene without such prior knowledge. The MC reconstruction algorithms rely on a low-rank structure of the scene. Moreover, the quality of the estimated scene from CASSI measurements depends on the coded aperture patterns used in the sensing process. Therefore, this paper proposes the design of an optimal coded aperture set for the MC methodology. The designed set is attained by maximizing the distance between the translucent elements in the coded aperture. Simulations show average improvement of around 5 dB when the designed set is used.

1. Introduction

Spectral Imaging (SI) techniques sense the two-dimensional spatial information across a range of spectral wavelengths of a scene [1], [6]. Knowledge of the spectral content at various spatial locations from a scene can be valuable for identifying the composition and structure of objects of interest. SI has therefore been widely used in areas such as remote sensing to exploit information about natural resources, in artwork for the conservation of paints, and in biomedical imaging for the detection of anomalies and diseases in living cells [18], [21], [22].