65 research outputs found
Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms
We propose to learn non-convex regularizers with a prescribed upper bound on
their weak-convexity modulus. Such regularizers give rise to variational
denoisers that minimize a convex energy. They rely on few parameters (less than
15,000) and offer a signal-processing interpretation as they mimic handcrafted
sparsity-promoting regularizers. Through numerical experiments, we show that
such denoisers outperform convex-regularization methods as well as the popular
BM3D denoiser. Additionally, the learned regularizer can be deployed to solve
inverse problems with iterative schemes that provably converge. For both CT and
MRI reconstruction, the regularizer generalizes well and offers an excellent
tradeoff between performance, number of parameters, guarantees, and
interpretability when compared to other data-driven approaches
Acceleration Methods for MRI
Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd
A Neural-Network-Based Convex Regularizer for Image Reconstruction
The emergence of deep-learning-based methods for solving inverse problems has
enabled a significant increase in reconstruction quality. Unfortunately, these
new methods often lack reliability and explainability, and there is a growing
interest to address these shortcomings while retaining the performance. In this
work, this problem is tackled by revisiting regularizers that are the sum of
convex-ridge functions. The gradient of such regularizers is parametrized by a
neural network that has a single hidden layer with increasing and learnable
activation functions. This neural network is trained within a few minutes as a
multi-step Gaussian denoiser. The numerical experiments for denoising, CT, and
MRI reconstruction show improvements over methods that offer similar
reliability guarantees
Core Imaging Library - Part II:multichannel reconstruction for dynamic and spectral tomography
The newly developed core imaging library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularized reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g. dynamic and spectral. We formalize different optimization problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL’s capabilities for designing state-of-the-art reconstruction methods through case studies and code snapshots
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