Convolutional sparse formulation of the sound field in an enclosure

Sound field analysis methods often make use of elementary wave expansions to describe the sound field in a room. A widespread rationale is to express the observed sound field as a superposition of plane, spherical or other wave bases. This is frequently a good approach when considering small apertures and the spatial variations of the sound field are similar to the chosen wave base. Yet, when considering distributed measurements over a large aperture, it becomes challenging to find analytical models that match the measured data. In practice, global wave bases can hardly account for complex sound fields that include high modal density, diffraction or scattering. This study examines methods to model the sound field in an enclosure from distributed experimental data. A methodoloy is proposed to extract the spatio-temporal properties of the sound field in a convolutionally sparse framework. To reduce model mismatch, it expresses the sound field as a set of local spatial patches that conform to the global data set. The technique is also suitable for approaching the problem as a spectro-spatial one.