Compressive Spectral Imaging Based on Hexagonal Blue Noise Coded Apertures

Abstract

The coded aperture snapshot spectral imager (CASSI) is a computational imaging system that acquires a three dimensional (3D) spectral data cube by a single or a few two dimensional (2D) measurements. The 3D data cube is reconstructed computationally. Binary on-off random coded apertures with square pixels are primarily implemented in CASSI systems to modulate the spectral images in the image plane. The design and optimization of coded apertures have been shown to improve the imaging performance of these systems significantly. This work proposes a different approach to code design. Instead of using traditional squared tiled coded elements, hexagonal tiled elements are used. The dislocation between the binary hexagonal coded apertures and the squared detector pixels is shown to introduce an equivalent grey-scale spatial modulation that increases the degrees of freedom in the sensing matrix, thus further improving the spectral imaging performance. Based on the restricted isometry property (RIP) of compressive sensing theory, this paper proves that optimal coded aperture patterns under a hexagonal lattice obey blue noise spatial characteristic, where "on" elements are placed as far from each other as possible. In addition, optimal coded apertures used in different snapshots are complementary to each other. This paper also proves the superiority of the hexagonal blue noise coded aperture over the traditional coded apertures with squared tiled elements. Based on a set of simulations, the proposed hexagonal tiled coded apertures are shown to effectively improve the imaging performance of CASSI systems compared to that of traditional coded apertures on rectangular lattices.

Supplementary document for Blue noise coding for coherent X-ray diffraction imaging system - 4979278.pdf

“…According to Ref. [3,4,5], the complementary BNCMs ( {0,1} | 1, , ) 8), ( 9) and (10) simultaneously. So using complementary BNCMs, the mathematical expectation of h in Eq.…”

“…(S.6). Specifically, the probability that the distance between any two elements in each coding mask is bigger than b λ should be a fixed value [4][5][6]. Thus, we…”

Signal to Noise Ratio of a Coded Slit Hyperspectral Sensor

“…The developments of the "coded aperture snapshot spectral imager" (CASSI) [1] concept and other snapshot imaging systems [2][3][4][5][6], have stimulated great interest in sensors that combine coded apertures with conventional spectrographs to enhance the throughput of conventional hyperspectral imaging systems (HSI). Such sensors make use of the compressive theory which brings their performances well beyond that of conventional imaging system for the given imaging characteristics such as frame rate and spatial resolutions.…”