(l)(p)-multiresolution analysis: How to reduce ringing and sparsify the error
We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the l(p)-sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using shift-invariant basis functions, such as B-splines. The solution is well-defined and determined by an iterative optimization algorithm based on digital filtering. Its convergence is accelerated by the use of first and second order derivatives. For p close to 1, we show that the ringing is reduced and that the histogram of the detail image is sparse as compared with the standard case, where p = 2.
banach spaces multiresolution non-euclidean norms splines