Alternative approach for the formulation of the optimal image reconstruction algorithm for finite-size objects

Abstract

In a recent paper, the formulation of the optimal image reconstruction algorithm for finite-size objects with discrete data acquisition systems was introduced [J. Acoust. Soc. Am. 80, 195–198 (1986)]. The construction of the algorithm included the use of dual vector spaces and an inner product pair, and the formation of the adjoint operator of the linear continuous-discrete mapping associated with the wave propagation and data acquisition. In this article, an alternative derivation for the formulation of the optimal algorithm is provided. This approach bypasses the formation of the adjoint operator and therefore significantly reduces the complexity of the derivation. This method performs the entire derivation in a single inner product space and achieves the same optimal filter structure.