2017/05/23 by Janis Nötzel, Nötzel, Janis, Andreas Winter +1 · 1 citation
Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1705.08394
openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Today, the internet makes tremendous amounts of data widely available. Often, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person or object, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, we assume that the distorted image is corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA). In the case of binary data and binary symmetric noise, we develop a simplified variant of the algorithm, dubbed BUDDA, which we prove to attain universal denoising uniformly.