Adaptive frames-based denoising of confocal microscopy data

In this paper, we present a novel frames-based denoising algorithm. Using a general result on lifting frames, we construct a non-separable 3D frame capable of robust edge detection. This frame detects edge information by ensemble thresholding of the filtered data. The denoising uses a hysteresis thresholding step and an affine thresholding function, which are filter-adaptive and take full advantage of the threshold bounds. The threshold bounds are statistically determined from the given data for each directional filter. We compare our denoising method with other methods based on separable 3D wavelets and 3D median filtering, and report very encouraging results on applications to both synthetic and real confocal microscopy data.