Image denoising and zooming under the linear minimum mean square-error estimation framework

Most of the existing image interpolation schemes assume that the image to be interpolated is noise free. This assumption is invalid in practice because noise will be inevitably introduced in the image acquisition process. Usually, the image is denoised first and is then interpolated. The denoising process, however, may destroy the image edge structures and introduce artefacts. Meanwhile, edge preservation is a critical issue in both image denoising and interpolation. To address these problems, in this study the authors propose a directional denoising scheme, which naturally endows a subsequent directional interpolator. The problems of denoising and interpolation are modelled as to estimate the noiseless and missing samples under the same framework of optimal estimation. The local statistics is adaptively calculated to guide the estimation process. For each noisy sample, the authors compute multiple estimates of it along different directions and then fuse those directional estimates for a more accurate output. The estimation parameters calculated in the denoising processing can be readily used to interpolate the missing samples. Compared with the conventional schemes that perform denoising and interpolation in tandem, the proposed noisy image interpolation method can reduce many noise-caused interpolation artefacts and preserve well the image edge structures.