Learning sparse structures for physics-inspired compressed sensing
This work is significant for researchers in underwater acoustics and signal processing, offering an improved method for environmental and source characterization by better modeling the frequency dependence of wavenumbers.
The paper addresses the problem of estimating wavenumbers in underwater acoustics for broadband sources, where signals are described as a sum of modal components. It proposes a new approach using a restricted Boltzmann machine to model the structured sparsity of wavenumbers across frequencies.
In underwater acoustics, shallow water environments act as modal dispersive waveguides when considering low-frequency sources. In this context, propagating signals can be described as a sum of few modal components, each of them propagating according to its own wavenumber. Estimating these wavenumbers is of key interest to understand the propagating environment as well as the emitting source. To solve this problem, we proposed recently a Bayesian approach exploiting a sparsity-inforcing prior. When dealing with broadband sources, this model can be further improved by integrating the particular dependence linking the wavenumbers from one frequency to the other. In this contribution, we propose to resort to a new approach relying on a restricted Boltzmann machine, exploited as a generic structured sparsity-inforcing model. This model, derived from deep Bayesian networks, can indeed be efficiently learned on physically realistic simulated data using well-known and proven algorithms.