Redundant representation with complex wavelets: how to achieve sparsity

Overcomplete transforms, like the Dual-Tree Complex Wavelet Transform, offer more flexible signal representations than critically-sampled transforms, due to their properties of shift invariance and directional selectivity. We show that many transform coefficients can be discarded without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We consider the convergence properties of an iterative projection system for achieving the usual coding aims of good sparsity with low reconstruction error. Results show how these measures translate to useful image compression performance.