We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an @math minimization problem of the Jacobian of the underlying multi-modality or multi-contrast images. Derivation of data fidelity for Jacobian and transformation of noise distribution are also detailed. The new minimization problem yields an optimal @math convergence rate, where @math is the iteration number, and the per-iteration cost is low thanks to the close-form matrix-valued shrinkage. We conducted numerical tests on a number multi-contrast magnetic resonance image (MRI) datasets, which show that the proposed method significantly improves reconstruction efficiency and accuracy compared to the state-of-the-arts.
@cite_1: Imaging is a powerful tool being used in many disciplines such as engineering, physics, biology and medicine to name a few. Recent years have seen a trend that imaging modalities have been combined to create multi-modality imaging tools where different modalities acquire complementary information. For example, in medical imaging, positron emission tomography (PET) and magnetic resonance imaging (MRI) are combined to image structure and function of the human body. Another example is spectral imaging where each channel provides information about a different wave length, e.g. information about red, green and blue (RGB). Most imaging modalities do not acquire images directly but measure a quantity from which we can reconstruct an image. These inverse problems require a priori information in order to give meaningful solutions. Assumptions are often on the smoothness of the solution but other information is sometimes available, too. Many multi-modality images show a strong inter-channel correlation as they are acquired from the same anatomy in medical imaging or the same scenery in spectral imaging. However, images from different modalities are usually reconstructed separately. In this thesis we aim to exploit this correlation using the data from all modalities, that are present in the acquisition, in a joint reconstruction process with the assumption that similar structures in all channels are more likely. We propose a framework for joint reconstruction where modalities are coupled by additional information about the solution we seek. A family of priors -- called parallel level sets -- allows us to incorporate structural a priori knowledge into the reconstruction. We analyse the parallel level set priors in several aspects including their convexity and the diffusive flow generated by their variation. Several numerical examples in RGB colour imaging and in PET-MRI illustrate the gain of joint reconstruction and in particular of the parallel level set priors.
@cite_22: The combination of positron emission tomography (PET) and magnetic resonance imaging (MRI) offers unique possibilities. In this paper we aim to exploit the high spatial resolution of MRI to enhance the reconstruction of simultaneously acquired PET data. We propose a new prior to incorporate structural side information into a maximum a posteriori reconstruction. The new prior combines the strengths of previously proposed priors for the same problem: it is very efficient in guiding the reconstruction at edges available from the side information and it reduces locally to edge-preserving total variation in the degenerate case when no structural information is available. In addition, this prior is segmentation-free, convex and no a priori assumptions are made on the correlation of edge directions of the PET and MRI images. We present results for a simulated brain phantom and for real data acquired by the Siemens Biograph mMRR for a hardware phantom and a clinical scan. The results from simulations show that the new prior has a better trade-off between enhancing common anatomical boundaries and preserving unique features than several other priors. Moreover, it has a better mean absolute biasto- mean standard deviation trade-off and yields reconstructions with superior relative 2-error and structural similarity index. These findings are underpinned by the real data results from a hardware phantom and a clinical patient confirming that the new prior is capable of promoting well-defined anatomical boundaries.
@cite_12: Recent advances in technology have enabled the combination of positron emission tomography (PET) with magnetic resonance imaging (MRI). These PET-MRI scanners simultaneously acquire functional PET and anatomical or functional MRI data. As function and anatomy are not independent of one another the images to be reconstructed are likely to have shared structures. We aim to exploit this inherent structural similarity by reconstructing from both modalities in a joint reconstruction framework. The structural similarity between two modalities can be modelled in two different ways: edges are more likely to be at similar positions and or to have similar orientations. We analyse the diffusion process generated by minimizing priors that encapsulate these different models. It turns out that the class of parallel level set priors always corresponds to anisotropic diffusion which is sometimes forward and sometimes backward diffusion. We perform numerical experiments where we jointly reconstruct from blurred Radon data with Poisson noise (PET) and under-sampled Fourier data with Gaussian noise (MRI). Our results show that both modalities benefit from each other in areas of shared edge information. The joint reconstructions have less artefacts and sharper edges compared to separate reconstructions and the l2-error can be reduced in all of the considered cases of under-sampling.
There have been a significant amount effort devoted to develop models and algorithms that can effectively take the anatomy structure similarities across modalities contrasts into account during joint reconstructions. As widely accepted, these structure similarities can be exploited using the locations and directions of the edges @cite_1 @cite_22 @cite_12 characterized by the magnitude and direction of the gradient of an image. The active researches on multi-modal contrast image reconstructions have focused mainly on how to effectively utilize the complimentary information on these structure similarities to improve the accuracy and robustness of the reconstructions.