Space-Scale Hybrid Continuous-Discrete Sliding Frank-Wolfe Method

In this letter, we focus on the challenging problem of designing an off-the-grid method for dictionaries involving both positional and scale shifts. To tackle this challenge, we introduce a novel algorithm inspired by the Sliding Frank-Wolfe approach. In our proposed algorithm, positions are treated as continuous variables, whereas scales are discretized. Such a strategy eliminates numerical instabilities inherent to the direct application of Sliding Frank-Wolfe. We successfully apply this algorithm to the study of DNA replication data.