Learning a Filtered Backprojection Reconstruction Method for Photoacoustic Computed Tomography with Hemispherical Measurement Geometries

In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including in vivo breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for data acquisition. Data acquired with such measurement geometries are referred to as half-scan data, as only half of a complete spherical measurement aperture is employed. Although previous studies have shown that half-scan data can uniquely and stably reconstruct the sought-after object, no associated closed-form reconstruction formula has been reported. To accurately reconstruct images from half-scan data, optimization-based iterative reconstruction methods can be employed; however, they are computationally expensive. To address this limitation, a learning-based filtered backprojection (FBP) reconstruction method, referred to as the half-scan FBP method, is developed in this work. Because the explicit form of the filtering operation in the half-scan FBP method is not currently known, a learning-based method is proposed to approximate it. The proposed method is systematically investigated by use of virtual imaging studies of 3D breast PACT that employ ensembles of numerical breast phantoms and a physics-based model of the data acquisition process. The method is subsequently applied to experimental data acquired in an in vivo breast PACT study. The results confirm that the half-scan FBP method can accurately reconstruct 3D images from half-scan data, while offering a substantial computational speed-up over iterative methods. Importantly, because the sought-after inverse mapping is well-posed, the reconstruction method remains accurate even when applied to data that differ considerably from those employed to learn the filtering operation.