Consistency in quantized matching pursuit

This paper explores the effects of coefficient quantization in applying the matching pursuit algorithm to source coding of vectors in R ^N. By considering the issue of consistency, we find that even though matching pursuit is designed to produce a linear combination to estimate a given source vector, optimal reconstruction in the presence of coefficient quantization requires a nonlinear algorithm. Such an algorithm was implemented and was experimentally confirmed to have superior reconstruction properties in comparison to the standard linear reconstruction. The improvement depends on the source, dictionary and operating point; in some cases the MSE was lessened by as much as a factor of five