Video denoising using higher order optimal space-time adaptation

The optimal spatial adaptation (OSA) method proposed by Boulanger and Kervrann (2006) has proven to be quite effective for spatially adaptive image denoising. This method, in addition to extending the non-local means (NLM) method of A. Buades et al. (2005), employs an iteratively growing window scheme, and a local estimate of the mean square error to very effectively remove noise from images. By adopting an iteratively growing space-time window, the method was recently extended to 3D for video denoising in J. Boulanger et al. (2007). In the present paper, we demonstrate a simple, but effective improvement on the OSA method in both 2- and 3D. We demonstrate that the OSA implicitly relies on a locally constant model of the underlying signal. Thereby, removing this constraint and introducing the possibility of higher order local regression models, we arrive at a relatively simple modification that results in an improvement in performance. While this improvement is observed in both 2D and 3D, we concentrate on demonstrating it in 3D for the application of video denoising.