Statistical dependencies among wavelet coefficients are commonly represented
by graphical models such as hidden Markov trees(HMTs). However, in linear
inverse problems such as deconvolution, tomography, and compressed sensing, the
presence of a sensing or observation matrix produces a linear mixing of the
simple Markovian dependency structure. This leads to reconstruction problems
that are non-convex optimizations. Past work has dealt with this issue by
resorting to greedy or suboptimal iterative reconstruction methods.