  Coded aperture snapshot spectral imager (CASSI) is a computational imaging
system that acquires a three dimensional (3D) spectral data cube by single or a
few two dimensional (2D) measurements. Binary random coded apertures with
square pixels are primarily implemented in CASSI systems to modulate the
spectral images in spatial domain. The design and optimization of coded
apertures was shown to improve the imaging performance of these systems
significantly. This work proposes a different approach to code design. Instead
of traditional squared tiled coded elements, hexagonal tiled elements are used.
The dislocation between the binary hexagonal pixels on coded apertures and the
square pixels on detector introduces equivalent grey-scale spatial modulation
to increase the degrees of freedom in the sensing matrix, thus further
improving the spectral imaging performance. Then, this paper presents an
optimal structure under the criterion of satisfying the restricted isometry
property (RIP) with high probability, coined blue noise (BN) coded apertures.
In addition, this paper studies and verifies the proposed hexagonal blue noise
coded aperture method on a general CASSI system, where the resolution of the
coded aperture is equivalent to that of the detector. Based on the RIP
criterion, this paper theoretically proves the superiority of the hexagonal
blue noise coded aperture over the traditional random coded aperture with
square lattice.
