Exploitation of symmetries for image reconstruction in linearized variable density diffraction tomography

The problem of reconstructing an object's weakly varying compressibility and density distributions in three-dimensional (3D) acoustic diffraction tomography is studied. Based on the Fourier diffraction projection theorem for acoustic media, it is demonstrated that the 3D Fourier components of an object's compressibility and density distributions can be decoupled algebraically, thereby providing a method for separately reconstructing the distributions. This is facilitated by the identification and exploitation of tomographic symmetries and the rotational invariance of the imaging model. The developed reconstruction methods are investigated by use of computer- simulation studies. The application of the proposed image reconstruction strategy to other tomography problems is discussed.