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A new numerical procedure (SVD-tail) is proposed for the reconstruction of the shape and volume of unknown objects from measurements of their radiation in the far field. This efficient procedure is a variant and the linear sampling method and has a very acceptable computational load. At variance with previously published techniques where the solution is constructed as a regularized solution of the far-field equations using a variant of the Tikhonov-Morozov type, the new method uses a newdoi:10.1088/0266-5611/25/9/095013 fatcat:zgnsq5eizje5xpkdj6u6b3isqa