B1873
Title: Efficient convolutional sparse coding with a $L_0$ constraint
Authors: Charles Truong - Paris-Saclay University (France) [presenting]
Abstract: Identifying characteristic patterns in time series, such as heartbeats or brain responses to a stimulus, is critical to understanding the physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which aim to approximate signals by a sparse combination of short signal templates (also called atoms), are well-suited for this task. However, enforcing sparsity leads to non-convex and untractable optimization problems. Numerous works have proposed greedy approaches or convex relaxations based on $L_1$ regularization, but this often leads to sub-optimal results. The purpose is to find the optimal solution to the original and non-convex CSC problem when the atoms do not overlap. Specifically, it is shown that the reconstruction error satisfies a simple recursive relationship in this setting, which leads to an efficient detection algorithm. In addition, it is demonstrated that the estimated sparse support of the atoms converges asymptotically to the true support. In a thorough empirical study, with simulated and real-world physiological data sets, the method is shown to be more accurate than existing algorithms at detecting the patterns' onsets.
