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.
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.
@cite_1 @cite_22 @cite_12
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Magnetic Resonance Imaging (MRI) offers high-resolution in vivo imaging and rich functional and anatomical multimodality tissue contrast. In practice, however, there are challenges associated with considerations of scanning costs, patient comfort, and scanning time that constrain how much data can be acquired in clinical or research studies. In this paper, we explore the possibility of generating high-resolution and multimodal images from low-resolution single-modality imagery. We propose the weakly-supervised joint convolutional sparse coding to simultaneously solve the problems of super-resolution (SR) and cross-modality image synthesis. The learning process requires only a few registered multimodal image pairs as the training set. Additionally, the quality of the joint dictionary learning can be improved using a larger set of unpaired images. To combine unpaired data from different image resolutions modalities, a hetero-domain image alignment term is proposed. Local image neighborhoods are naturally preserved by operating on the whole image domain (as opposed to image patches) and using joint convolutional sparse coding. The paired images are enhanced in the joint learning process with unpaired data and an additional maximum mean discrepancy term, which minimizes the dissimilarity between their feature distributions. Experiments show that the proposed method outperforms state-of-the-art techniques on both SR reconstruction and simultaneous SR and cross-modality synthesis. Clinical imaging with structural MRI routinely relies on multiple acquisitions of the same region of interest under several different contrast preparations. This work presents a reconstruction algorithm based on Bayesian compressed sensing to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS. The joint inference problem is formulated in a hierarchical Bayesian setting, wherein solving each of the inverse problems corresponds to finding the parameters (here, image gradient coefficients) associated with each of the images. The variance of image gradients across contrasts for a single volumetric spatial position is a single hyperparameter. All of the images from the same anatomical region, but with different contrast properties, contribute to the estimation of the hyperparameters, and once they are found, the k-space data belonging to each image are used independently to infer the image gradients. Thus, commonality of image spatial structure across contrasts is exploited without the problematic assumption of correlation across contrasts. Examples demonstrate improved reconstruction quality (up to a factor of 4 in root-mean-square error) compared to previous compressed sensing algorithms and show the benefit of joint inversion under a hierarchical Bayesian model. 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. Motivated by a Bayesian vision of the 3D multi-view reconstruction from images problem, we propose a dense 3D reconstruction technique that jointly refines the shape and the camera parameters of a scene by minimizing the photometric reprojection error between a generated model and the observed images, hence considering all pixels in the original images. The minimization is performed using a gradient descent scheme coherent with the shape representation (here a triangular mesh), where we derive evolution equations in order to optimize both the shape and the camera parameters. This can be used at a last refinement step in 3D reconstruction pipelines and helps improving the 3D reconstruction's quality by estimating the 3D shape and camera calibration more accurately. Examples are shown for multi-view stereo where the texture is also jointly optimized and improved, but could be used for any generative approaches dealing with multi-view reconstruction settings (ie depth map fusion, multi-view photometric stereo).