In this paper, we present a new deep learning framework for 3-D tomographic reconstruction. To this end, we map filtered back-projection-type algorithms to neural networks. However, the back-projection cannot be implemented as a fully connected layer due to its memory requirements. To overcome this problem, we propose a new type of cone-beam back-projection layer, efficiently calculating the forward pass. We derive this layer's backward pass as a projection operation. Unlike most deep learning approaches for reconstruction, our new layer permits joint optimization of correction steps in volume and projection domain. Evaluation is performed numerically on a public data set in a limited angle setting showing a consistent improvement over analytical algorithms while keeping the same computational test-time complexity by design. In the region of interest, the peak signal-to-noise ratio has increased by 23%. In addition, we show that the learned algorithm can be interpreted using known concepts from cone beam reconstruction: the network is able to automatically learn strategies such as compensation weights and apodization windows.
We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our framework. We derive a maximal error bound for deep nets that demonstrates that inclusion of prior knowledge results in its reduction. Furthermore, we also show experimentally that known operators reduce the number of free parameters. We apply this approach to various tasks ranging from CT image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such the concept is widely applicable for many researchers in physics, imaging, and signal processing. We assume that our analysis will support further investigation of known operators in other fields of physics, imaging, and signal processing.
Compressed sensing-based Magnetic Resonance Imaging (CS-MRI) is a promising paradigm allowing to accelerate MRI acquisition by reconstructing images from only a fraction of the normally required k-space measurements. Traditionally, sparsity-based methods and their data-driven variants such as dictionary learning [10] have been popular due to their mathematically robust formulation for perfect reconstruction. However, these methods are limited in acceleration factor and also suffer from high computational complexity. More recently, several deep learning-based architectures have been proposed as an attractive alternative for CS-MRI. The advantages of these techniques are their computational efficiency, G. Yang and J. Schlemper/D. Rueckert and A. Maier share second/last coauthorship.
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