SPRITE: sparsity-based super-resolution algorithm
SPRITE (Sparse Recovery of InstrumenTal rEsponse, 1) aims at computing a well-resolved compact source image from several undersampled and noisy observations. SPRITE solves the succession of problems of the form
The vectors are the low resolution (LR) observations. The scalars account for possible luminosity differences between the LR images and is the noise variance in the LR image . The matrices account for the shifts between the observations and the matrix D is the downsampling operator. The vector is a rough estimate of the well-resolved image. The final image is given by , where is the minimizer of the problem solved.
is a user-chosen redundant dictionary. The method relies on the prior that a suitable solution should have a sparse decomposition into the dictionary . Finally the inequality constraint (which is element-wise) insures that the final well-resolved image has positive pixels values.
It's important to note that the only parameters to be provided by the user are $Phi$ and $kappa$. The other parameters are automatically calculated.
Please cite the reference below if you use these codes in a publication. This is a preliminary version of the SPRITE package, which may be imperfect. Please feel free to contact us if you have any problem.
-  F. M. Ngolè Mboula, J.-L. Starck, S. Ronayette, K. Okomura, J. Amiaux. Super-resolution method using sparse regularization for point spread function recovery, Astronomy and Astrophysics, 2014. Available here.