Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models
This work addresses computational bottlenecks in big data applications like massive MIMO and medical data, offering incremental improvements for sparse parameter recovery in linear low-rank models.
The paper tackles the problem of recovering a sparse weight vector from noisy linear combinations with a partially known low-rank matrix, proposing methods that reduce computational cost by approximating the support of the sparse vector and unifying matrix completion with sparse recovery. Simulation results show that the augmented approach achieves the best performance, with both proposed methods outperforming a two-step technique while requiring substantially less computation.
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion on the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.