Exploration of SVD for Image Compression and Time Series Processing

This paper explores the block-based singular-value-decomposition (SVD) with applications to image compression and processing in both static and dynamic cases. Results include a comprehensive performance study of rank-1 asymmetric block sizes in comparison to conventional uniform square blocks for static image compression. In addition, a method of movement detection for video streaming applications are presented and discussed in this paper. We show that by tracking the Frobenius norm of the derivatives of sequential images, represented as a time series matrix, allows one to infer change points in varying lighting conditions and foreground movement in video sequences. We show that by combining SVD background subtraction we can create clearer distinction between movements and changes in lighting intensity. It is also demonstrated that one can maintain the original derivative feature after re-scaling the images of the video stream to a fraction of their original resolution via local averaging.