  Snapshot Compressive Imaging (SCI) relies on decoding algorithms such as CNN
or Transformer to reconstruct the hyperspectral image (HSI) from its compressed
measurement. Although existing CNN and Transformer-based methods have proven
effective, CNNs are limited by their inadequate modeling of long-range
dependencies, while Transformer ones face high computational costs due to
quadratic complexity. Recent Mamba models have demonstrated superior
performance over CNN and Transformer-based architectures in some visual tasks,
but these models have not fully utilized the local similarities in both spatial
and spectral dimensions. Moreover, the long-sequence modeling capability of SSM
may offer an advantage in processing the numerous spectral bands for HSI
reconstruction, which has not yet been explored. In this paper, we introduce a
State Space Model with Across-Scanning and Local Enhancement, named ASLE-SSM,
that employs a Spatial-Spectral SSM for global-local balanced context encoding
and cross-channel interaction promoting. Specifically, we introduce local
scanning in the spatial dimension to balance the global and local receptive
fields, and then propose our across-scanning method based on spatial-spectral
local cubes to leverage local similarities between adjacent spectral bands and
pixels to guide the reconstruction process. These two scanning mechanisms
extract the HSI's local features while balancing the global perspective without
any additional costs. Experimental results illustrate ASLE-SSM's superiority
over existing state-of-the-art methods, with an inference speed 2.4 times
faster than Transformer-based MST and saving 0.12 (M) of parameters, achieving
the lowest computational cost and parameter count.
