A learned filtered backprojection method for use with half-time circular Radon transform data

The circular Radon transform (CRT) has been widely employed as an imaging model for wave-based tomographic bioimaging modalities such as photoacoustic computed tomography (PACT) and ultrasound reflectivity tomography. The CRT data function corresponds to the set of all integrals of the object function over circular paths, centered on a scanning aperture, that have radii less than or equal to the diameter of the scanning aperture. It is known that a complete set of CRT data function has redundancies, which enabled the development of so-called half-time reconstruction methods that can stably reconstruct object estimates from temporally-truncated data. These methods are known to be effective in mitigating artifacts caused by acoustic heterogeneities in PACT. However, these methods are iterative and/or involve the solution of an optimization problem. Therefore, they possess a significant computational burden. To date, because symmetries in the CRT data function are not simple, no explicit image reconstruction formula is known for inverting the half-time CRT. To address this, in this work, a learning-based approach is proposed to establish a half-time filtered backprojection (FBP) method. Because the proposed method approximates a mapping that is known to exist in theory, it is fundamentally different than many deep-learning based image reconstruction methods that seek to establish an inverse mapping that does not exist. Therefore, the proposed method performs well on unforeseen data. The learned half-time FBP achieves image quality comparable to a conventional full-time FBP method although it uses half of the complete data.