This paper introduces a variational method for destriping data acquired by pushbroom-type satellite imaging systems. The model leverages sparsity in signals and is based on current research in sparse optimization and compressed sensing. It is based on the basic principles of regularization and data fidelity with certain constraints using modern methods in variational optimization, namely, total variation (TV),
fidelity, and the alternating direction method of multipliers (ADMM). The proposed algorithm, TV–
, uses sparsity-promoting energy functionals to achieve two important imaging effects. The TV term maintains boundary sharpness of the content in the underlying clean image, while the
fidelity allows for the equitable removal of stripes without over- or under-penalization, providing a more accurate model of presumably independent sensors with an unspecified and unrestricted bias distribution. A comparison is made between the TV–
model and the proposed TV–
model to exemplify the qualitative efficacy of an
striping penalty. The model makes use of novel minimization splittings and proximal mapping operators, successfully yielding more realistic destriped images in very few iterations.