Fast and stable Bayesian image expansion using sparse edge priors

Smoothness assumptions in traditional image expansion cause blurring of edges and other high-frequency content that can be perceptually disturbing. Previous edge-preserving approaches are either ad hoc, statistically untenable, or computationally unattractive. We propose a new edge-driven stochastic prior image model and obtain the maximum a posteriori (MAP) estimate under this model. The MAP estimate is computationally challenging since it involves the inversion of very large matrices. An efficient algorithm is presented for expansion by dyadic factors. The technique exploits diagonalization of convolutional operators under the Fourier transform, and the sparsity of our edge prior, to speed up processing. Visual and quantitative comparison of our technique with other popular methods demonstrates its potential and promise.