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Coded aperture snap shot spectral imager (CASSI) is a potential method to get hyperspectral images. One of the latest designs of CASSI is a dual-camera design, which adds a grayscale camera to capture the same scene. In this paper, an improved method based on two-step iterative shrinkage thresholding algorithms (TwIST) is proposed to utilize the images containing the information of the structure of the objects from the grayscale camera more efficiently. The information come from the auxiliary camera and the CASSI detector is used to construct an estimated 3D hyperspectral data. Then we use TwIST and TV regularization to reconstruct the residual image based on the residual data. The final reconstructed hyperspectral image equals the sum of the estimated image and the reconstruct residual image. This method ensures that the result is more similar to the structure of the original image. The simulation results show that our method improves the image quality of the reconstructed hyperspectral images for all the data we have tried. The simulation results show that our method improves the image quality of the reconstructed hyperspectral images and use less run time compared to the original method. The corresponding peak signal-to-noise ratio (PSNR) is increased by 8.99 dB. The structural similarity (SSIM) is increased by 0.0757. The spectrum angular mapper (SAM) is reduced by 0.1987.
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