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

Compressive spectral imaging based on hexagonal blue noise coded apertures