The validity of the HELS method (Wu, 2000) for reconstructing the acoustic pressure field inside the minimum circle that encloses an arbitrary object is examined. Results show that the HELS solutions are approximate and the corresponding matrix equation is ill conditioned in general for back propagation of the acoustic field. Accordingly, the further the reconstruction point moves inside the minimum circle, the worse the reconstruction accuracy becomes. To overcome this difficulty new strategy for sensor placement is proposed. This strategy together with a constrained minimization are shown to yield satisfactory reconstruction inside the minimum circle. The same procedures can be extended to three-dimensional problems.

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