Frank Ong

Robust 4D flow denoising using divergence-free wavelet transform

To investigate four‐dimensional flow denoising using the divergence‐free wavelet (DFW) transform and compare its performance with existing techniques.

Beyond Low Rank + Sparse: Multiscale Low Rank Matrix Decomposition

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multiscale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multiscale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multiscale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multiscale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multiscale modeling of the dynamic contrast enhanced magnetic resonance imaging, and collaborative filtering exploiting age information.

Motion robust high resolution 3D free-breathing pulmonary MRI using dynamic 3D image self-navigator

To achieve motion robust high resolution 3D free‐breathing pulmonary MRI utilizing a novel dynamic 3D image navigator derived directly from imaging data.

Beyond low rank + sparse: Multi-scale low rank matrix decomposition

The recent low rank + sparse matrix decomposition [1,2] enables us to decompose a matrix into sparse and globally low rank components. In this paper, we present a natural generalization and consider the decomposition of matrices into low rank components of multiple scales. The proposed multi-scale low rank decomposition is well motivated in practice, since natural data often exhibit multi-scale structure instead of globally or sparsely. Concretely, we propose a multi-scale low rank modeling to represent a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components, and approach the problem via a convex formulation. Theoretically, we show that under a deterministic incoherence condition, the convex program recovers the multi-scale low rank components exactly. Empirically, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than existing low rank methods, and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering with age information.

Improved visualization and quantification of 4D flow MRI data using divergence-freewavelet denoising

4D flow MRI is a promising method for providing global quantification of cardiac flow in a single acquisition, yet its use in clinical application suffers from low velocity-to-noise ratio. In this work, we present a novel noise reduction processing for 4D flow MRI data using divergence-free wavelet transform. Divergence-free wavelets have the advantage of enforcing soft divergence-free conditions when discretization and partial voluming result in numerical non-divergence-free components and at the same time, provide sparse representation of flow in a generally divergence-free field. Efficient denoising is achieved by appropriate shrinkage of divergence-free and non-divergence-free wavelet coefficients. To verify its performance, divergence-free wavelet denoising was performed on simulated flow and compared with existing methods. The proposed processing was also applied on in vivo data and was demonstrated to improve visualization of flow data while preserving quantifications of flow data.

Fast sparse 2-D DFT computation using sparse-graph alias codes

We present a novel algorithm, named the 2D-FFAST (Two-dimensional Fast Fourier Aliasing-based Sparse Transform), to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample and computational complexity. The proposed algorithm is based on diverse concepts from signal processing (sub-sampling and aliasing), coding theory (sparse-graph codes) and number theory (Chinese-remainder-theorem) and generalizes the 1D-FFAST algorithm recently proposed by Pawar and Ramchandran to the 2D setting. Concretely, our proposed 2D-FFAST algorithm computes a k-sparse 2D-DFT, with a uniformly random support, of size N = Nx × Ny using O(k) noiseless spatial-domain measurements in O(k log k) computational time. Our results are attractive when the sparsity is sub-linear with respect to the signal dimension, that is, when k → ∞ and k/N → 0. For the case when the spatial-domain measurements are corrupted by additive noise, our 2D-FFAST framework extends to a noise-robust version of computing a 2D-DFT using O(k log3 N) measurements in sub-linear time of O(k log4 N). Empirically, we show that the 2D-FFAST can compute a k = 3509 sparse 2D-DFT of a 508 × 508-size phantom image using only 4.75k measurements. We also empirically evaluate the 2D-FFAST algorithm on a real-world magnetic resonance brain image using a total of 60.18% of Fourier measurements to provide an almost instant reconstruction with SNR=4.5 dB. This provides empirical evidence that the 2D-FFAST architecture is applicable to a wider class of input signals than analyzed theoretically in the paper.

General phase regularized reconstruction using phase cycling: General Phase Regularized Reconstruction Using Phase Cycling

To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water–fat imaging and flow imaging.

Improved visualization and quantification of 4D flow data using divergence-free wavelets

Background 4D flow MRI has the potential to provide global quantification of cardiac flow in a single acquisition [Hsiao, 2012]. However, 4D flow data are often compromised by low velocity-to-noise ratio, potentially caused by MRI acceleration or unfitting vencs. Since blood flow is approximately divergence-free, noise level can be reduced by removing divergence from noisy flow data [Song, 1993] [Busch, 2012]. On the other hand, strict enforcement of divergence-free condition distorts flow around edges as discrete approximation of flow near edges creates divergence. In this current work, we aim to provide an adjustable and fast operation of imposing multi-scale divergence-free conditions on flow data by using divergence-free wavelets. In addition, we utilize the sparsity of flow data in divergencefree wavelet domain [Deriaz, 2006] for further denoising by performing wavelet shrinkage [Donoho, 1995].