Deriving Neural Network Architectures Using Precision Learning: Parallel-to-Fan Beam Conversion

Abstract

In this paper, we derive a neural network architecture based on an analytical formulation of the parallel-to-fan beam conversion problem following the concept of precision learning. The network allows to learn the unknown operators in this conversion in a data-driven manner avoiding interpolation and potential loss of resolution. Integration of known operators results in a small number of trainable parameters that can be estimated from synthetic data only. The concept is evaluated in the context of Hybrid MRI/X-ray imaging where transformation of the parallel-beam MRI projections to fan-beam X-ray projections is required. The proposed method is compared to a traditional rebinning method. The results demonstrate that the proposed method is superior to ray-by-ray interpolation and is able to deliver sharper images using the same amount of parallel-beam input projections which is crucial for interventional applications. We believe that this approach forms a basis for further work uniting deep learning, signal processing, physics, and traditional pattern recognition.

A gentle introduction to deep learning in medical image processing

“…They also show that their method is compatible with other approaches, such as variational networks that are able to learn an additional de-streaking sparsifying transform [118]. Syben et al drive these efforts even further and demonstrate that the concept of precision learning is able to mathematically derive a neural network structure [119]. In their work, they demonstrate that they are able to postulate that an expensive matrix inverse is a circulant matrix and hence can be replaced by a convolution operation.…”

Learning with known operators reduces maximum error bounds

“…All three applications are from the domain of medical imaging, yet the method is applicable to many more disciplines to be discovered in the future. The results presented here are based on conference contributions [ 10 , 11 , 13 ]. Note that the supplementary material contains descriptions of experiments, data, and additional figures that were omitted here for brevity.…”

“…Lastly, we discuss our observations in relation to other works in literature and give an outlook on future work. Note that some of the work presented here is based on prior conference publications [ 10 , 11 , 12 , 13 ].…”

Projection-to-Projection Translation for Hybrid X-ray and Magnetic Resonance Imaging

“…The acquisition of whole volumes and subsequent forward projection is, however, too slow to be applicable in interventional procedures. Fortunately, the direct acquisition of projection images is possible 9,10 . Yet, the resulting images are subject to a parallel-beam geometry and, therefore, incompatible with their cone-beam projected X-ray counterpart.…”