Signal and image denoising without regularization

This paper proposes a novel approach for image and signal denoising that does not need any classical regularization. It subtracts a sorted realization of noise to the sorted noisy signal. The similarity between the noise that corrupted the signal and the selected noise realization allows us to denoise monotonic signals. The Minimum Description Length (MDL) is then adopted to get a piecewise monotonic representation of the original signal. Experimental results show that the proposed approach outperforms most of the classical denoising approaches, even though it is based on very simple operations.