Pinv-Recon: Generalized MR Image Reconstruction via Pseudoinversion of the Encoding Matrix

Purpose: To present a novel generalized MR image reconstruction based on pseudoinversion of the encoding matrix (Pinv-Recon) as a simple yet powerful method, and demonstrate its computational feasibility for diverse MR imaging applications. Methods: MR image encoding constitutes a linear mapping of the unknown image to the measured k-space data mediated via an encoding matrix ($ data = Encode \times image$). Pinv-Recon addresses MR image reconstruction as a linear inverse problem ($image = Encode^{-1} \times data$), explicitly calculating the Moore-Penrose pseudoinverse of the encoding matrix using truncated singular value decomposition (tSVD). Using a discretized, algebraic notation, we demonstrate constructing a generalized encoding matrix by stacking relevant encoding mechanisms (e.g., gradient encoding, coil sensitivity encoding, chemical shift inversion) and encoding distortions (e.g., off-center positioning, B$_0$ inhomogeneity, spatiotemporal gradient imperfections, transient relaxation effects). Iterative reconstructions using the explicit generalized encoding matrix, and the computation of the spatial-response-function (SRF) and noise amplification, were demonstrated. Results: We evaluated the computation times and memory requirements (time ~ (size of the encoding matrix)$^{1.4}$). Using the Shepp-Logan phantom, we demonstrated the versatility of the method for various intertwined MR image encoding and distortion mechanisms, achieving better MSE, PSNR and SSIM metrics than conventional methods. A diversity of datasets, including the ISMRM CG-SENSE challenge, were used to validate Pinv-Recon. Conclusion: Although pseudo-inversion of large encoding matrices was once deemed computationally intractable, recent advances make Pinv-Recon feasible. It has great promise for both research and clinical applications, and for educational use.

Region of Interest focused MRI to Synthetic CT Translation using Regression and Classification Multi-task Network

In this work, we present a method for synthetic CT (sCT) generation from zero-echo-time (ZTE) MRI aimed at structural and quantitative accuracies of the image, with a particular focus on the accurate bone density value prediction. We propose a loss function that favors a spatially sparse region in the image. We harness the ability of a multi-task network to produce correlated outputs as a framework to enable localisation of region of interest (RoI) via classification, emphasize regression of values within RoI and still retain the overall accuracy via global regression. The network is optimized by a composite loss function that combines a dedicated loss from each task. We demonstrate how the multi-task network with RoI focused loss offers an advantage over other configurations of the network to achieve higher accuracy of performance. This is relevant to sCT where failure to accurately estimate high Hounsfield Unit values of bone could lead to impaired accuracy in clinical applications. We compare the dose calculation maps from the proposed sCT and the real CT in a radiation therapy treatment planning setup.

Unsupervised-learning-based method for chest MRI-CT transformation using structure constrained unsupervised generative attention networks

The integrated positron emission tomography/magnetic resonance imaging (PET/MRI) scanner facilitates the simultaneous acquisition of metabolic information via PET and morphological information with high soft-tissue contrast using MRI. Although PET/MRI facilitates the capture of high-accuracy fusion images, its major drawback can be attributed to the difficulty encountered when performing attenuation correction, which is necessary for quantitative PET evaluation. The combined PET/MRI scanning requires the generation of attenuation-correction maps from MRI owing to no direct relationship between the gamma-ray attenuation information and MRIs. While MRI-based bone-tissue segmentation can be readily performed for the head and pelvis regions, the realization of accurate bone segmentation via chest CT generation remains a challenging task. This can be attributed to the respiratory and cardiac motions occurring in the chest as well as its anatomically complicated structure and relatively thin bone cortex. This paper presents a means to minimise the anatomical structural changes without human annotation by adding structural constraints using a modality-independent neighbourhood descriptor (MIND) to a generative adversarial network (GAN) that can transform unpaired images. The results obtained in this study revealed the proposed U-GAT-IT + MIND approach to outperform all other competing approaches. The findings of this study hint towards possibility of synthesising clinically acceptable CT images from chest MRI without human annotation, thereby minimising the changes in the anatomical structure.