Real image denoising with a locally-adaptive bitonic filter

The bitonic filter is a non-learning-based filter for removing noise from signals, following mathematical morphology (ranking) approaches, relying on a novel presumption in which the signal is postulated to be locally bitonic (having only one minimum or maximum) over some domain of finite extent. It is here developed specifically for image noise so that the domain is locallyadaptive, leading to significant improvements in noise reduction performance at no cost to processing times. The new bitonic filter performs better than the block-matching 3D filter for high levels of additive white Gaussian noise, and over all noise levels for two public data sets containing real image noise. This is despite an additional adjustment to the block-matching filter for real image noise, which leads to significantly better performance than has previously been cited on these data sets. The new bitonic filter has a signal-to-noise ratio only 2.4 dB lower than the best learning-based techniques when they are optimally trained. The performance gap is closed completely when these techniques are trained on data sets not directly related to the benchmark data. This demonstrates what can be achieved with a predictable, explainable, entirely local technique, which makes no assumptions of repeating patterns either within an image or across images, and hence creates residual images which are well behaved even in very high noise. Since the filter does not require training, it can still be used in situations where training is either difficult or inappropriate