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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 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 article derives optimal coded aperture patterns under a hexagonal lattice which obey blue noise spatial characteristics, 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. The superiority of hexagonal blue noise coded apertures over the traditional coded apertures with squared tiled elements is shown.
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