ABSTRACT
This chapter explains application of thermo/photo/optoacoustic tomography to mammography. Early experimental work generated impressive reconstructions despite several simplifying assumptions about the physics of acoustic wave propagation and detection with standard ultrasound transducers. Idealized thermo- and photoacoustic data represent spherical integrals, and reconstruction requires inverting the spherical Radon transform. The chapter shows that partial-scan reconstructions of thermoacoustic computerized tomography (TCT) data agree with theoretical predictions from integral geometry. Low-frequency extension of partial-scan data by enforcing consistency conditions upon TCT data can remove low-frequency shading and therefore improve visibility of small, low-contrast inclusions. Mathematical results on tomographic inversion of partial-scan data typically focus on the ability to recover "singularities", that is, edges in the image. Reconstruction of limited angle data is highly unstable outside of the "audible zone" for both standard x-ray CT and spherical means, as measured in TCT and SONAR.
