Wavelet-vaguelette restoration in photon-limited imaging

This paper studies linear shift-invariant inverse problems arising in photon-limited imaging. The problem we consider is the recovery of an intensity image from a distorted version degraded with Poisson noise. This problem arises in medical and astronomical imaging. It is shown that the wavelet-vaguelette decomposition (WVD) can provide much better estimates of the underlying intensity compared to classical frequency domain methods. The paper combines wavelet-based filtering techniques for photon imaging with new results in WVD methods for inverse problems. Furthermore, we show that the WVD can be interpreted as a prefiltered wavelet transform, and that it can be very efficiently computed. The new method is applied to nuclear medicine imaging.