  In the classic sparsity-driven problems, the fundamental L-1 penalty method
has been shown to have good performance in reconstructing signals for a wide
range of problems. However this performance relies on a good choice of penalty
weight which is often found from empirical experiments. We propose an algorithm
called the Laplacian variational automatic relevance determination (Lap-VARD)
that takes this penalty weight as a parameter of a prior Laplace distribution.
Optimization of this parameter using an automatic relevance determination
framework results in a balance between the sparsity and accuracy of signal
reconstruction. Our algorithm is implemented in a transmission tomography model
with sparsity constraint in wavelet domain.
