Optimization method for the total variational joint equivalent source of sound field

The sparse equivalent source method (L₁-ESM) can effectively sparsely reconstruct the sound field of a simple sound sources with high reconstruction accuracy, but due to the limitation of sparsity, the effect of reconstructing coherent sound field is poor. Therefore, a optimization method for the total variational joint equivalent source method (TV-ESM) of sound field is proposed, the distances from the array microphones to the equivalent source point and the distance difference from the array surface to the center equivalent source point are used to evaluate the contribution of the equivalent source point sound field and screen the number and position of equivalent sources for constructing the sound field transfer matrix; then, with the number of matrix conditions as the goal, the equivalent source structure is optimized, which combines the equivalent source structure characteristics and L₁ norm to constructs the total variational constraint matrix and the total variational regularized sound field sparse reconstruction model, and analyzes the strong sparse expression of the source by the convex optimization. Through numerical analysis and method comparison, the sound field reconstruction error of a wide-band coherent sound source is less than 10%, the acoustic image area error is less than 5%, and the sound pressure amplitude error of multiple reconstruction points at a single frequency is less than 4%. Compared with the L₁-ESM method, the reconstruction accuracy of the simple source sound field is consistent, and the reconstruction error is less than 5%, and the sound field reconstruction error of the TV-ESM method for coherent sources is 20% lower than that of the L₁-ESM method.This method expands the application scope of the sparse equivalent source method, which can not only effectively reconstructs the simple source field, but also has a good reconstruction effect on the non-strict sparse coherent sound fields such as the spatially extension source field, near field and reflection field.