Traditional acoustic camera methods had been advanced significantly with the advent of compressed sensing techniques, which reconstruct the original signals successfully by means of hand-crafted features or functions with nonlinear optimization, e.g., proximal gradient descent. However, the performance of the reconstruction process has been significantly slow due to nonlinear optimization steps. This paper proposes a new approach that substitutes the traditional nonlinear optimization approach with recurrent network architecture, i.e., by unrolling the iterative convex optimization algorithm in a form of neural network architecture. This paper takes a two-layered design, where a bias and back-projection gradient, and deblurring matrix are learned. As described in the paper, the recurrent architecture has been proposed to substitute the signal reconstruction problem for other field applications of compressive sensings, such as compressive imaging.

The paper proposes a RNN LISTA architecture to the problem of real-time acoustic imaging and a novel parametrization leading to a number of parameters that grow linearly wrt resolution instead of quadratically, as well as a novel initialization scheme. Some Experiments comparing this approach to the state-of-art in the field validate the proposed model. While the paper may of of narrow interest for the ML community, it presents some interesting contributions.

We propose a recurrent neural-network for real-time reconstruction of acoustic camera spherical maps. The network, dubbed DeepWave, is both physically and algorithmically motivated: its recurrent architecture mimics iterative solvers from convex optimisation, and its parsimonious parametrisation is based on the natural structure of acoustic imaging problems. Each network layer applies successive filtering, biasing and activation steps to its input, which can be interpreted as generalised deblurring and sparsification steps. To comply with the irregular geometry of spherical maps, filtering operations are implemented efficiently by means of graph signal processing techniques. Unlike commonly-used imaging network architectures, DeepWave is moreover capable of directly processing the complex-valued raw microphone correlations, learning how to optimally back-project these into a spherical map.

We propose a recurrent neural-network for real-time reconstruction of acoustic camera spherical maps. The network, dubbed DeepWave, is both physically and algorithmically motivated: its recurrent architecture mimics iterative solvers from convex optimisation, and its parsimonious parametrisation is based on the natural structure of acoustic imaging problems. Each network layer applies successive filtering, biasing and activation steps to its input, which can be interpreted as generalised deblurring and sparsification steps. To comply with the irregular geometry of spherical maps, filtering operations are implemented efficiently by means of graph signal processing techniques. Unlike commonly-used imaging network architectures, DeepWave is moreover capable of directly processing the complex-valued raw microphone correlations, learning how to optimally back-project these into a spherical map.