Outlier deletion based improvement on the StOMP algorithm for sparse solution of large-scale underdetermined problems

StOMP algorithm is well suited to large-scale underdetermined applications in sparse vector estimations. It can reduce computation complexity and has some attractive asymptotical statistical properties. However, the estimation speed is at the cost of accuracy violation. This paper suggests an improvement on the StOMP algorithm that is more efficient in finding a sparse solution to the large-scale underdetermined problems. Also, compared with StOMP, this modified algorithm can not only more accurately estimate parameters for the distribution of matched filter coefficients, but also improve estimation accuracy for the sparse vector itself. Theoretical success boundary is provided based on a large-system limit for approximate recovery of sparse vector by modified algorithm, which validates that the modified algorithm is more efficient than StOMP. Actual computations with simulated data show that without significant increment in computation time, the proposed algorithm can greatly improve the estimation accuracy.