Recently, the ratio of l1 and l2 norms has been proposed as a sparsity inducing function for noiseless compressed sensing. In this talk, we further discuss properties of this model in the noiseless setting, and propose an algorithm for minimizing the ratio of l1 and l2 norms when the measurements are subject to noise. Specifically, we first present conditions that guarantee solution existence for these models. We then derive an explicit Kurdyka-Lojasiewicz exponent for the model in the noiseless setting, which enables us to deduce linear convergence of a recently proposed Dinkelbach type algorithm for the noiseless model. Finally, we extend this algorithm to deal with the noisy scenario by incorporating moving balls approximation techniques, and discuss its convergence.
This is joint work with Peiran Yu and Liaoyuan Zeng.
Analysis and Algorithms for Some Compressed Sensing Models Based on the Ratio of l1 and l2 Norms
15.11.2021 15:30 - 16:30
Organiser:
R. I. Boț (U Wien), S. Sabach (Technion - Israel Institute of Technology Haifa), M. Staudigl (Maastricht U)
Location:
Zoom Meeting
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