  Deep convolutional neural networks have recently shown promising results in
compressive spectral reconstruction. Previous methods, however, usually adopt a
single mapping function for sparse representation. Considering that different
regions have distinct characteristics, it is desirable to apply various mapping
functions to adjust different regions' transformations dynamically. With this
in mind, we first introduce a regional dynamic way of using Fast Iterative
Shrinkage-Thresholding Algorithm (FISTA) to exploit regional characteristics
and derive dynamic sparse representations. Then, we propose to unfold the
process into a hierarchical dynamic deep network, dubbed RDFNet. The network
comprises multiple regional dynamic blocks and corresponding pixel-wise
adaptive soft-thresholding modules, respectively in charge of region-based
dynamic mapping and pixel-wise soft-thresholding selection. The regional
dynamic block guides the network to adjust the transformation domain for
different regions. Equipped with the adaptive soft-thresholding, our proposed
regional dynamic architecture can also learn appropriate shrinkage scale in a
pixel-wise manner.
  Extensive experiments on both simulated and real data demonstrate that our
method outperforms prior state-of-the-arts.
