Real Image Denoising With a Locally-Adaptive Bitonic Filter

Image noise removal is a common problem with many proposed solutions. The current standard is set by learning-based approaches, however these are not appropriate in all scenarios, perhaps due to lack of training data or the need for predictability in novel circumstances. The bitonic filter is a non-learning-based filter for removing noise from signals, with a mathematical morphology (ranking) framework in which the signal is postulated to be locally bitonic (having only one minimum or maximum) over some domain of finite extent. A novel version of this filter is developed in this paper, with a domain that is locally-adaptive to the signal, and other adjustments to allow application to real image sensor noise. These lead 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. It also surpasses this and other more recent non-learning-based filters for two public data sets containing real image noise at various levels. This is despite an additional adjustment to the block-matching filter, 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 2.4dB lower than the best learning-based techniques when they are optimally trained. However, 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.