  Compressive sensing promises to enable bandwidth-efficient on-board
compression of astronomical data by lifting the encoding complexity from the
source to the receiver. The signal is recovered off-line, exploiting GPUs
parallel computation capabilities to speedup the reconstruction process.
However, inherent GPU hardware constraints limit the size of the recoverable
signal and the speedup practically achievable. In this work, we design parallel
algorithms that exploit the properties of circulant matrices for efficient
GPU-accelerated sparse signals recovery. Our approach reduces the memory
requirements, allowing us to recover very large signals with limited memory. In
addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc
parallelization of matrix-vector multiplications and matrix inversions.
Finally, we practically demonstrate our algorithms in a typical application of
circulant matrices: deblurring a sparse astronomical image in the compressed
domain.
