Reweighted thresholding and orthogonal projections for simultaneous source separation
Satyakee Sen, Zhaojun Liu, James J. Sheng, Bin Wang · 2014
Summary The key to success for simultaneous source separation is the ability to formulate an appropriate sparse inversion problem so that nontrivial solutions to a highly under-determined system can be found. An important issue with the sparse inversion is the potential of energy leakage between the component shots that need to be deblended. In this paper we identify leakage as a basis misidentification problem and provide a reweighted thresholding method to reduce the leakage. Further, our study of the iterative thresholding and subtraction class of methods for source separation, indicate that existing model update procedures are suboptimal. We propose an updating step based on orthogonalization that has strong theoretical guarantees for improved convergence and is potentially more robust to leakage issues.