Efficient Noise Filtration of Images by Low-Rank Singular Vector Approximations of Geodesics' Gramian Matrix

Modern society is interested in capturing high-resolution and fine-quality images due to the surge of sophisticated cameras. However, the noise contamination in the images not only inferior people's expectations but also conversely affects the subsequent processes if such images are utilized in computer vision tasks such as remote sensing, object tracking, etc. Even though noise filtration plays an essential role, real-time processing of a high-resolution image is limited by the hardware limitations of the image-capturing instruments. Geodesic Gramian Denoising (GGD) is a manifold-based noise filtering method that we introduced in our past research which utilizes a few prominent singular vectors of the geodesics' Gramian matrix for the noise filtering process. The applicability of GDD is limited as it encounters $\mathcal{O}(n^6)$ when denoising a given image of size $n\times n$ since GGD computes the prominent singular vectors of a $n^2 \times n^2$ data matrix that is implemented by singular value decomposition (SVD). In this research, we increase the efficiency of our GGD framework by replacing its SVD step with four diverse singular vector approximation techniques. Here, we compare both the computational time and the noise filtering performance between the four techniques integrated into GGD.