12 research outputs found
Preconditioned ADMM with nonlinear operator constraint
We are presenting a modification of the well-known Alternating Direction
Method of Multipliers (ADMM) algorithm with additional preconditioning that
aims at solving convex optimisation problems with nonlinear operator
constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid
Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to
handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging
(MRI)
Spectral X-ray CT for fast NDT using discrete tomography
We present progress in fast, high-resolution imaging, material classification, and fault detection using
hyperspectral X-ray measurements. Classical X-ray CT approaches rely on data from many projection
angles, resulting in long acquisition and reconstruction times. Additionally, conventional CT cannot
distinguish between materials with similar densities. However, in additive manufacturing, the majority of
materials used are known a priori. This knowledge allows to vastly reduce the data collected and increase
the accuracy of fault detection. In this context, we propose an imaging method for non-destructive testing
of materials based on the combination of spectral X-ray CT and discrete tomography. We explore the
use of spectral X-ray attenuation models and measurements to recover the characteristic functions of
materials in heterogeneous media with piece-wise uniform composition. We show by means of numerical
simulation that using spectral measurements from a small number of angles, our approach can alleviate
the typical deterioration of spatial resolution and the appearance of streaking artifacts.Mechanical Engineerin
The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack
Post capture refocusing effect in smartphone cameras is achievable by using
focal stacks. However, the accuracy of this effect is totally dependent on the
combination of the depth layers in the stack. The accuracy of the extended
depth of field effect in this application can be improved significantly by
computing an accurate depth map which has been an open issue for decades. To
tackle this issue, in this paper, a framework is proposed based on
Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth
from the focal stack and synthetic defocus application. In addition to its
ability to provide high structural accuracy and occlusion handling, the
optimization function of the proposed method can, in fact, converge faster and
better than state of the art methods. The evaluation has been done on 21 sets
of focal stacks and the optimization function has been compared against 5 other
methods. Preliminary results indicate that the proposed method has a better
performance in terms of structural accuracy and optimization in comparison to
the current state of the art methods.Comment: 15 pages, 8 figure
Reconstruction Methods for Free-Breathing Dynamic Contrast-Enhanced MRI
Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) is a valuable diagnostic tool due to the combination of anatomical and physiological information it provides. However, the sequential sampling of MRI presents an inherent tradeoff between spatial and temporal resolution. Compressed Sensing (CS) methods have been applied to undersampled MRI to reconstruct full-resolution images at sub-Nyquist sampling rates. In exchange for shorter data acquisition times, CS-MRI requires more computationally intensive iterative reconstruction methods.
We present several model-based image reconstruction (MBIR) methods to improve the spatial and temporal resolution of MR images and/or the computational time for multi-coil MRI reconstruction. We propose efficient variable splitting (VS) methods for support-constrained MRI reconstruction, image reconstruction and denoising with non-circulant boundary conditions, and improved temporal regularization for breast DCE-MRI. These proposed VS algorithms decouple the system model and sparsity terms of the convex optimization problem. By leveraging matrix structures in the system model and sparsifying operator, we perform alternating minimization over a list of auxiliary variables, each of which can be performed efficiently. We demonstrate the computational benefits of our proposed VS algorithms compared to similar proposed methods. We also demonstrate convergence guarantees for two proposed methods, ADMM-tridiag and ADMM-FP-tridiag. With simulation experiments, we demonstrate lower error in spatial and temporal dimensions for these VS methods compared to other object models.
We also propose a method for indirect motion compensation in 5D liver DCE-MRI. 5D MRI separates temporal changes due to contrast from anatomical changes due to respiratory motion into two distinct dimensions. This work applies a pre-computed motion model to perform motion-compensated regularization across the respiratory dimension and improve the conditioning of this highly sparse 5D reconstruction problem. We demonstrate a proof of concept using a digital phantom with contrast and respiratory changes, and we show preliminary results for motion model-informed regularization on in vivo patient data.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138498/1/mtle_1.pd