We consider the problem of hyperspectral cube reconstruction with a new controllable imaging system. The reconstruction with a small number of images acquired with different configurations of the imager avoids a complete scanning of the hyperspectral cube. We focus here on a quadratic penalty reconstruction approach, which provides a fast resolution thanks to the high sparsity of the involved matrices. While such a regularization is known to smooth the restored images, we propose to exploit the system capability to acquire the panchromatic image of the scene, to introduce prior information on the sharp edges of the image, leading to a fast and edge-preserved reconstruction of the image.

We present a novel acquisition scheme based on a dual disperser architecture, which can reconstruct a hyperspectral data cube using many times fewer acquisitions than spectral bands. The reconstruction algorithm follows a quadratic regularization approach, based on the assumption that adjacent pixels in the scene share similar spectra, and if they do not, this corresponds to an edge which is detectable on the panchromatic image. A digital micro-mirror device (DMD) applies reconfigurable spectral-spatial filtering to the scene for each acquisition, and the filtering code is optimized considering the physical properties of the system. The algorithm is tested on simple multi-spectral scenes with 110 wavelength bands, and is able to accurately reconstruct the hyperspectral datacube using only 10 acquisitions.

We present a fast reconstruction algorithm for hyperspectral images, utilizing a small amount of data without the need for any training. The method is implemented with a dual disperser hyperspectral imager and makes use of spatial-spectral correlations by a so-called separability assumption that assumes that the image is made of regions of homogenous spectra. The reconstruction algorithm is simple and ready-to-use and does not require any prior knowledge of the scene. A simple proof-of-principle experiment is performed, demonstrating that only a small number of acquisitions are required, and the resulting compressed data-cube is reconstructed near instantaneously.

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