All-Addition Hyperspectral Compressed Sensing for Metasurface-Driven Miniaturized Satellite

Hyperspectral compressed sensing (HCS) for the miniaturized satellite is challenging mainly due to the required lightweight onboard hardware and the necessary low sampling rate. Optical devises involved in conventional HCS include spectral splitter (SS), digital micromirror device (DMD) array, and cylindrical lens (CL), while DMD array (used for implementing random projections) is known to be bulky. We are, hence, thinking of the possibility of just using SS and CL, mathematically meaning that only the deterministic addition operator is available in the coding stage. Another recent advance in the multifunctional metamaterial also motivates us to solve such mathematical challenges. Specifically, SS and CL can be designed on a single nanoscale metasurface (flat), more in line with the miniaturized satellite application. We show that this all-addition coding scheme is achievable though it induces a far more challenging decoding stage, for which a convex decoding criterion is proposed based on self-similarity, a well-known property in imaging inverse problems. Self-similarity regularizer has recently been explicitly defined as a convex function and is demonstrated to be effective in decoding even with a low sampling rate. In addition, as the fundamental role of the John ellipsoid (JE) has been revealed in recent hyperspectral analysis literature, we build a JE-based convex analysis framework to ensure exact recovery even with low data purity. Experimental evidence shows the superiority of the proposed method.