Adding Sparse Recovery to Projective Ray Space Analysis

Integrating sparse recovery methods into the ray space transform is a new and recent area of investigation for microphone arrays. A previous exploration using a single microphone array resulted in a new method that shows promise. Nevertheless, a primary advantage of the ray space approach derives from its robust ability to integrate information from multiple arrays and viewpoints. Therefore, in this work, we explore the integration of information across two viewpoints provided by two separate microphone arrays. Because working with multiple viewpoints in the ray space domain requires the use of methods from projective geometry, we explore the integration of sparse recovery and the ray space transform from a projective viewpoint. Numerical simulations demonstrate that integrating sparse recovery with the ray space transform improves the results of the ray space transform in the projective ray space. In particular, we show an improvement to the quality of the acoustic images. Results also indicate that the utility and extent of the projection in the projective ray space depends strongly on the distance between the source and the array.