Poisson noise reduction with non-local PCA

Photon limitations arise in spectral imaging, nuclear medicine, astronomy and night vision. The Poisson distribution used to model this noise has variance equal to its mean so blind application of standard noise removals methods yields significant artifacts. Recently, overcomplete dictionaries combined with sparse learning techniques have become extremely popular in image reconstruction. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using small dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce patch-based denoising algorithms which perform an adaptation of PCA (Principal Component Analysis) for Poisson noise. We carry out a comprehensive empirical evaluation of the performance of our algorithms in terms of accuracy when the photon count is really low. The results reveal that, despite its simplicity, PCA-flavored denoising appears to be competitive with other state-of-the-art denoising algorithms.

1. INTRODUCTION, MODEL AND NOTATION

Since the introduction of patch based method for image denoising [1], those methods have proved to outperform previously considered approaches [2], [3]. Our work is inspired by recent combining Principal Component Analysis (PCA) with patch based approaches [4], [5], [6] for the Additive White Gaussian Noise (AWGN) model.