Compressive single-pixel spectral imaging with spatial-spectral modulation optimization via coherence minimization

Abstract

Compressive spectral imaging (CSI) obtains spatial-spectral information from under-sampled measurements, which solves the contradiction between imaging speed and resolution in conventional scanning-based spectral imaging systems. The spatial-spectral modulation and the corresponding sparse prior in reconstruction algorithm jointly determine the reconstruction quality of CSI systems. In this paper, a compressive single-pixel spectral imaging system with the spatial-spectral modulation and the sparse prior simultaneously optimized by coherence minimization is proposed. By formulating the modulation of the single-pixel spectral imaging system and the sensing coherence in the differentiable matrix notation, the gradients of the modulation and the sparse prior with respect to the sensing coherence are derived for both spatial and spectral dimensions. The spatial-spectral modulation and the sparse prior are optimized via gradient descent to minimize the sensing coherence, for both the decoupled CSI systems with one dimension completely sampled and the coupled CSI system with both spatial-spectral dimensions compressively sampled. For the optimized spatial-spectral modulation, high relative mutual differences in the spectral dimension as well as low redundancy patterns in the spatial dimension are achieved, and by combining with the optimized spatial-spectral sparse prior, the enhancement of 5.7 dB for PSNR compared to the unoptimized system is realized.