Singular Value Decomposition and its Applications in Image Processing

The Singular Value Decomposition (SVD) is a highlight of linear algebra and has a wide range application in computer vision, statistics and machine learning. This paper reviews the main theorem of SVD and illustrates some applications of SVD in image processing. More specifically, we focus on image compression and matrix completion. The former is to convert the original full-rank pixel matrix to a well-approximated low-rank matrix and thus dramatically save the space, the latter is to recover a pixel matrix with a large number of missing entries by using nuclear norm minimization, in which some singular value thresholding algorithm will be used. For both applications, we conduct numerical experiments to show the performance and point out some possible improvements in the future.