A Haar-wavelet-based Lucy-Richardson algorithm for positron emission tomography image restoration

Deconvolution is an ill-posed problem that requires regularization. Noise would inevitably be enhanced during the iterative deconvolution process. The enhanced noise degrades the image quality, causing mistakes in clinical interpretations. This paper introduced a Haar-wavelet-based Lucy-Richardson algorithm (HALU) for positron emission tomography (PET) image restoration based on a spatially variant point spread function. After wavelet decomposition, Lucy-Richardson algorithm was applied to each approximation matrix with different iteration numbers. Thus, this enhanced the contrasts of our images without amplifying much of the noise level. The results showed that HALU can be able to recover the resolution and yield better contrast and lower noise level than the Lucy-Richardson algorithm.