Generalized Filtered Backprojection in Nonlinear Acoustics

Abstract

The filtered backprojection algorithm (FBP) is a standard image reconstruction algorithm used in many imaging modalities. The FBP algorithm is suited for high-frequency imaging applications, that is, applications where the specimen is much larger than the wavelengths of the incident fields. However, when data is scarce due to limited view or dosage considerations, or when super-resolution is required, different techniques are needed to adequately resolve the specimen. We present a generalization of the filtered backprojection algorithm that extends the capabilities of acoustic imaging systems to limited aperture and wavelength resolution. Our principal interest is applications to acoustic (scalar) scattering, though the methodology we develop can be extended to general electromagnetic (vector) settings.