2022/09/27 by Kelum Gajamannage, Gajamannage, Kelum, Yonggi Park +3
Computer Science · Engineering · #68T10 #68U10 #94A08 #Advanced Image Fusion Techniques #Advanced Numerical Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #I.4.3 #I.4.5 #Image and Signal Denoising Methods #Image and Video Processing (eess.IV) #Numerical Analysis (math.NA) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2209.13094
openalex publication_date 2022/09/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
With the advent of sophisticated cameras, the urge to capture high-quality images has grown enormous. However, the noise contamination of the images results in substandard expectations among the people; thus, image denoising is an essential pre-processing step. While the algebraic image processing frameworks are sometimes inefficient for this denoising task as they may require processing of matrices of order equivalent to some power of the order of the original image, the neural network image processing frameworks are sometimes not robust as they require a lot of similar training samples. Thus, here we present a manifold-based noise filtering method that mainly exploits a few prominent singular vectors of the geodesics' Gramian matrix. Especially, the framework partitions an image, say that of size n × n, into n2 overlapping patches of known size such that one patch is centered at each pixel. Then, the prominent singular vectors, of the Gramian matrix of size n2 × n2 of the geodesic distances computed over the patch space, are utilized to denoise the image. Here, the prominent singular vectors are revealed by efficient, but diverse, approximation techniques, rather than explicitly computing them using frameworks like Singular Value Decomposition (SVD) which encounters O(n6) operations. Finally, we compare both computational time and the noise filtration performance of the proposed denoising algorithm with and without singular vector approximation techniques.