Tensor error correction for corrupted values in visual data

ABSTRACT The multi-channel image or the video clip has the natural form of tensor. The values of the tensor can be corrupted due to noise in the acquisition process. We consider the problem of recovering a tensor L of visual data from its corrupted observations X = L + S, where the corrupted entries S are unknown and unbounded, but are assumed to be sparse. Our work is built on the recent studies about the recovery of corrupted low-rank matrix via trace norm minimization. We extend the matrix case to the tensor case by the definition of tensor trace norm i

Deep learning-based parameter mapping for joint relaxation and diffusion tensor MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) enables the simultaneous quantification of multiple properties of biological tissues. It relies on a pseudo-random acquisition and the matching of acquired signal evolutions to a precomputed dictionary. However, the dictionary is not scalable to higher-parametric spaces, limiting MRF to the simultaneous mapping of only a small number of parameters (proton density, T1 and T2 in general). Inspired by diffusion-weighted SSFP imaging, we present a proof-of-concept of a novel MRF sequence with embedded diffusion-encoding gradients along all three axes to efficiently encode orientational diffusion and T1 and T2 relaxation. We take advantage of a convolutional neural network (CNN) to reconstruct multiple quantitative maps from this single, highly undersampled acquisition. We bypass expensive dictionary matching by learning the implicit physical relationships between the spatiotemporal MRF data and the T1, T2 and diffusion tensor parameters. The predicted parameter maps and the derived scalar diffusion metrics agree well with state-of-the-art reference protocols. Orientational diffusion information is captured as seen from the estimated primary diffusion directions. In addition to this, the joint acquisition and reconstruction framework proves capable of preserving tissue abnormalities in multiple sclerosis lesions

Correcting for Motion between Acquisitions in Diffusion MR Imaging

The diffusion tensor (DT) and other diffusion models assume that each voxel corresponds to the same anatomical location in all the measurements. Movements and distortions violate this assumption and typically the images are realigned before model fitting. We propose a set of model-based methods to improve motion correction and avoid the errors that the traditional method introduces. The new methods are based on a three-step procedure to register DWI datasets, and use different reference images for DWIs with different gradient directions for registration, so the registrations take into account the contrast differences of measurements. Performance of the model-based registration techniques depends critically on outlier rejection. We develop new methods for fitting the diffusion tensor to diffusion MRI measurements in the presence of outliers by drawing on the RANSAC algorithm from computer vision. We compareone popularly used outlier rejection method RESTORE in the diffusion MRI literature with our new method. Then, we combine outlier rejection methods with model-based registration schemes, and compare the performance of motion correction with other methods. After aligning the dataset, we also update diffusion gradients for the registered datasets from both traditional and our methods, according to the transformations used in registrations. We develop and discuss a variety of registration evaluation methods using both synthetic and human-brain diffusion MRI datasets. Experiments demonstrate both quantitative and qualitative improvements using our new model-based methods