  Two complementary approaches have been extensively used in signal and image
processing leading to novel results, the sparse representation methodology and
the variational strategy. Recently, a new sparsity based model has been
proposed, the cosparse analysis framework, which may potentially help in
bridging sparse approximation based methods to the traditional total-variation
minimization. Based on this, we introduce a sparsity based framework for
solving overparameterized variational problems. The latter has been used to
improve the estimation of optical flow and also for general denoising of
signals and images. However, the recovery of the space varying parameters
involved was not adequately addressed by traditional variational methods. We
first demonstrate the efficiency of the new framework for one dimensional
signals in recovering a piecewise linear and polynomial function. Then, we
illustrate how the new technique can be used for denoising and segmentation of
images.
