A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from curved line artefacts and blurring, especially in case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge on the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography. It enables easy comparisons between regularisers with different properties, e.g. nonlinear, higher-order or directional. We solve the underlying minimisation problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator dependent preconditioning strategy. Our reconstruction methods are tested on challenging 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements, offering immediate benefits in terms of acquisition time and quality. This work provides a basic platform for the investigation of future advanced regularisation methods in photoacoustic tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to v2: regularisation with directional wavelet has been added; new experimental tests have been include

Noise2Filter: fast, self-supervised learning and real-time reconstruction for 3D Computed Tomography

At X-ray beamlines of synchrotron light sources, the achievable time-resolution for 3D tomographic imaging of the interior of an object has been reduced to a fraction of a second, enabling rapidly changing structures to be examined. The associated data acquisition rates require sizable computational resources for reconstruction. Therefore, full 3D reconstruction of the object is usually performed after the scan has completed. Quasi-3D reconstruction -- where several interactive 2D slices are computed instead of a 3D volume -- has been shown to be significantly more efficient, and can enable the real-time reconstruction and visualization of the interior. However, quasi-3D reconstruction relies on filtered backprojection type algorithms, which are typically sensitive to measurement noise. To overcome this issue, we propose Noise2Filter, a learned filter method that can be trained using only the measured data, and does not require any additional training data. This method combines quasi-3D reconstruction, learned filters, and self-supervised learning to derive a tomographic reconstruction method that can be trained in under a minute and evaluated in real-time. We show limited loss of accuracy compared to training with additional training data, and improved accuracy compared to standard filter-based methods

A computationally efficient reconstruction algorithm for circular cone-beam computed tomography using shallow neural networks

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper we introduce the Neural Network Feldkamp-Davis-Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy

Directional Sinogram Inpainting for Limited Angle Tomography

In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition lead to regions of data which cannot be sampled. Depending on the severity of the restriction, reconstructions can contain severe, characteristic, artefacts. Our model aims to address these artefacts by inpainting the missing data simultaneously with the reconstruction. Numerically, this problem naturally evolves to require the minimisation of a non-convex and non-smooth functional so we review recent work in this topic and extend results to fit an alternating (block) descent framework. \oldtext{We illustrate the effectiveness of this approach with numerical experiments on two synthetic datasets and one Electron Microscopy dataset.} \newtext{We perform numerical experiments on two synthetic datasets and one Electron Microscopy dataset. Our results show consistently that the joint inpainting and reconstruction framework can recover cleaner and more accurate structural information than the current state of the art methods

A Computationally Efficient Reconstruction Algorithm for Circular Cone-Beam Computed Tomography Using Shallow Neural Networks

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper, we introduce the Neural Network Feldkamp–Davis–Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high-throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy

Directional Sinogram Inpainting for Limited Angle Tomography

In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition lead to regions of data which cannot be sampled. Depending on the severity of the restriction, reconstructions can contain severe, characteristic, artefacts. Our model aims to address these artefacts by inpainting the missing data simultaneously with the reconstruction. Numerically, this problem naturally evolves to require the minimisation of a non-convex and non-smooth functional so we review recent work in this topic and extend results to fit an alternating (block) descent framework. \oldtext{We illustrate the effectiveness of this approach with numerical experiments on two synthetic datasets and one Electron Microscopy dataset.} \newtext{We perform numerical experiments on two synthetic datasets and one Electron Microscopy dataset. Our results show consistently that the joint inpainting and reconstruction framework can recover cleaner and more accurate structural information than the current state of the art methods