SPRITE: sparsity-based super-resolution algorithm

## The method

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

with .

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.

The source code can be downloaded here: SPRITE package. The data and IDL codes used to perform the benchmark tests presented in **1** are available here: super-resolution benchmark.

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.

## Article

**[1]**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.