Poisson Noise Reduction with Non-local PCA

• Published in: Journal of mathematical imaging and vision Vol. 48; no. 2; pp. 279 - 294
• Main Authors: Salmon, Joseph, Harmany, Zachary, Deledalle, Charles-Alban, Willett, Rebecca
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.02.2014; Springer Verlag
• Subjects: Applications of Mathematics; Computer Science; Computer Vision and Pattern Recognition; Image Processing; Image Processing and Computer Vision; Machine Learning; Mathematical Methods in Physics; Signal,Image and Speech Processing; Gradient methods; Newton’s method; Signal representations; Image denoising; PCA; Newton's method
• DOI: 10.1007/s10851-013-0435-6
• ISSN: 0924-9907

Photon-limited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denoising methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.