  Total variation regularization based on the l1 norm is ubiquitous in image
reconstruction. However, the resulting reconstructions are not always as sparse
in the edge domain as desired. Iteratively reweighted methods provide some
improvement in accuracy, but at the cost of extended runtime. In this paper we
examine these methods for the case of data acquired as non-uniform Fourier
samples. We then develop a non-iterative weighted regularization method that
uses a pre-processing edge detection to find exactly where the sparsity should
be in the edge domain. We show that its performance in terms of both accuracy
and speed has the potential to outperform reweighted TV regularization methods.
