8,298 research outputs found
Imaging with highly incomplete and corrupted data
We consider the problem of imaging sparse scenes from a few noisy data using an L1-minimization approach. This problem can be cast as a linear system of the form Ap = b, where A is an N x K measurement matrix. We assume that the dimension of the unknown sparse vector p E Ck is much larger than the dimension of the data vector b E Cn, i.e. K >>N. We provide a theoretical framework that allows us to examine under what conditions the L1-minimization problem admits a solution that is close to the exact one in the presence of noise. Our analysis shows that L1-minimization is not robust for imaging with noisy data when high resolution is required. To improve the performance of L1-minimization we propose to solve instead the augmented linear system [A|C]p = b, where the N = Σ matrix C is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data, a vector of dimension N, can be well approximated. Theoretically, the dimension Σ of the noise collector should be eN which would make its use not practical. However, our numerical results illustrate that robust results in the presence of noise can be obtained with a large enough number of columns Σ~10K.Part of this material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the authors were in residence at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, during the Fall 2017 semester. The work of M Moscoso was partially supported by Spanish MICINN grant FIS2016-77892-R. The work of A Novikov was partially supported by NSF grants DMS-1515187, DMS-1813943. The work of C Tsogka was partially supported by AFOSR FA9550-17-1-0238
A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography with Incomplete Data
Differential phase-contrast computed tomography (DPC-CT) is a powerful
analysis tool for soft-tissue and low-atomic-number samples. Limited by the
implementation conditions, DPC-CT with incomplete projections happens quite
often. Conventional reconstruction algorithms are not easy to deal with
incomplete data. They are usually involved with complicated parameter selection
operations, also sensitive to noise and time-consuming. In this paper, we
reported a new deep learning reconstruction framework for incomplete data
DPC-CT. It is the tight coupling of the deep learning neural network and DPC-CT
reconstruction algorithm in the phase-contrast projection sinogram domain. The
estimated result is the complete phase-contrast projection sinogram not the
artifacts caused by the incomplete data. After training, this framework is
determined and can reconstruct the final DPC-CT images for a given incomplete
phase-contrast projection sinogram. Taking the sparse-view DPC-CT as an
example, this framework has been validated and demonstrated with synthetic and
experimental data sets. Embedded with DPC-CT reconstruction, this framework
naturally encapsulates the physical imaging model of DPC-CT systems and is easy
to be extended to deal with other challengs. This work is helpful to push the
application of the state-of-the-art deep learning theory in the field of
DPC-CT
Deep Learning using K-space Based Data Augmentation for Automated Cardiac MR Motion Artefact Detection
Quality assessment of medical images is essential for complete automation of
image processing pipelines. For large population studies such as the UK
Biobank, artefacts such as those caused by heart motion are problematic and
manual identification is tedious and time-consuming. Therefore, there is an
urgent need for automatic image quality assessment techniques. In this paper,
we propose a method to automatically detect the presence of motion-related
artefacts in cardiac magnetic resonance (CMR) images. As this is a highly
imbalanced classification problem (due to the high number of good quality
images compared to the low number of images with motion artefacts), we propose
a novel k-space based training data augmentation approach in order to address
this problem. Our method is based on 3D spatio-temporal Convolutional Neural
Networks, and is able to detect 2D+time short axis images with motion artefacts
in less than 1ms. We test our algorithm on a subset of the UK Biobank dataset
consisting of 3465 CMR images and achieve not only high accuracy in detection
of motion artefacts, but also high precision and recall. We compare our
approach to a range of state-of-the-art quality assessment methods.Comment: Accepted for MICCAI2018 Conferenc
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
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