Random projections in gravitational wave searches from compact binaries II: efficient reconstruction of detection statistic within LLOID framework

Low-latency gravitational wave search pipelines such as LLOID take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in advanced-LIGO and Virgo detectors, one expects several orders of magnitude increase in the size of template banks. This poses a formidable computational challenge in factorizing extremely large matrices. Previously, [in Kulkarni et al. [6]], we introduced the idea of random projection (RP)-based matrix factorization as a computationally viable alternative to SVD, for such large template banks. In this follow-up paper, we demonstrate the application of a block-wise randomized matrix factorization (RMF) scheme using which one can compute the desired low-rank factorization corresponding to a fixed average SNR loss (h{\delta}\r{ho}/\r{ho}i). Unlike the SVD approach, this new scheme affords a much more efficient way of matrix factorization especially in the context of LLOID search pipelines. It is a well-known fact that for very large template banks, the total computational cost is dominated by the cost of reconstruction of the detection statistic and that the cost of filtering the data is insignificant in comparison. We are unaware of any previous work in literature that has tried to squarely address this issue of optimizing the reconstruction cost. We provide a possible solution to reduce the reconstruction cost using the matching pursuit(MP) algorithm. We show that it is possible to approximately reconstruct the time-series of the detection statistic at a fraction of the total cost using our MP algorithm. The combination of RMF along with MP can handle large template banks more efficiently in comparison to the direct application of SVD. Results from several numerical simulations have been presented to demonstrate their efficacy.