Comments On "Multipath Matching Pursuit" by Kwon, Wang and Shim

Straightforward combination of tree search with matching pursuits, which was suggested in 2001 by Cotter and Rao, and then later developed by some other authors, has been revisited recently as multipath matching pursuit (MMP). In this comment, we would like to point out some major issues regarding this publication. First, the idea behind MMP is not novel, and the related literature has not been properly referenced. MMP has not been compared to closely related algorithms such as A⋆orthogonal matching pursuit (A⋆OMP). The theoretical analyses do ignore the pruning strategies applied by the authors in practice. All these issues have the potential to mislead the reader and lead to misinterpretation of the results. With this short paper, we intend to clarify the relation of MMP to existing literature in the area and compare its performance with A⋆OMP.