An Approximate Computing Technique for Reducing the Complexity of a Direct-Solver for Sparse Linear Systems in Real-Time Video Processing

Michael Schaffner, Frank K. Gürkaynak, Aljoscha Smolic, Hubert Kaeslin, Luca Benini

Abstract: Many video processing algorithms are formulated as least-squares problems that result in large, sparse linear systems. Solving such systems in real time is very demanding. This paper focuses on reducing the computational complexity of a direct Cholesky-decomposition-based solver. Our approximation scheme builds on the observation that, in well-conditioned problems, many elements in the decomposition nearly vanish. Such elements may be pruned from the dependency graph with mild accuracy degradation. Using an example from image-domain warping, we show that pruning reduces the amount of operations per solve by over 75%, resulting in significant savings in computing time, area or energy.