Integrating flexible tree searches to orthogonal matching pursuit algorithm

The orthogonal matching pursuit (OMP) algorithm employs an overcomplete dictionary in an adaptive nonlinear process for signal decomposition. An efficient tree-search-based OMP algorithm is considered for sparse signal representations, namely the flexible tree-search-based OMP (FTB-OMP). The algorithm makes use of an extended tree-search structure for finding good approximations. It allows a tradeoff between approximation performance and experimental time complexity by providing various design parameters. The efficiency is achieved by reducing the number of children as the depth of nodes increases via the exponentially decaying characteristics of the search algorithm. Further time efficiency is achieved by using a correlation-based pruning in the search tree. Through the use of the design parameters, FTB-OMP offers numerous variations that range from OMP to optimum solution. It is experimentally verified that a good approximation performance can be achieved by the exponentially decaying tree structure of FTB-OMP with much lower time complexity. This is shown for several signals and for the component detection problem. As an application example, the angle-of-arrival estimation problem is considered