## Frank Ong

 Hi! I am a fourth-year EECS graduate student working with Professor Michael (Miki) Lustig. My research interest lies in magnetic resonance imaging and image reconstruction in general. Here are some of my info: Email: frankong@berkeley.edu Github: https://github.com/frankong Linkedin: http://www.linkedin.com/in/frank-ong Callsign: KK6KJT

## Projects

### Multi-scale Low Rank Matrix Decomposition

• Slides: BASP’15, ISMRM’15

• Matlab/C Code: https://github.com/frankong/multi_scale_low_rank

• Multi-scale low rank matrix decomposition is a matrix decomposition method that decomposes an input matrix into a sum of block-wise low rank matrices with increasing scales of block sizes. It captures the intuitive notion that data matrices are often correlated at multiple scales. The additional multi-scale structure also allows us to obtain a more accurate and compact signal representation than conventional low rank methods whenever the signal exhibits multi-scale structures. Here are some multi-scale low rank decomposition examples:

### Two-Dimensional Sparse Fast Fourier Transform with 2D-FFAST

• Slides: ICASSP’16

• Matlab Code: https://github.com/frankong/FFAST

• Collaborators: Sameer Pawar, and Kannan Ramchandran

• The 2D-FFAST (Two-Dimensional Fast Fourier Aliasing-Based Sparse Transform) is an algorithm that can compute a sparse 2D-Discrete Fourier Transform (2D-DFT) with both low sample complexity and low computational complexity. Concretely, the 2D-FFAST algorithm computes a k-sparse 2D-DFT, of size N = Nx × Ny using O(k) noiseless spatial-domain measurements in O(k log k) computational time. For the case when the spatial-domain measurements are corrupted by additive noise, the 2D-FFAST framework extends to a noise-robust version in sub-linear time of O(k log^4 N) using O(k log^3 N) measurements. Below is a simplified illustration of how the 2D-FFAST algorithm computes a 2D sparse DFT:

• The 2D-FFAST algorithm uniformly subsamples the 2D signal with different sampling factors, thereby producing different aliasing patterns in the DFT domain. Each aliased DFT provides unique information about the sparse DFT coefficient locations and can be viewed as a sparse graph. The aliased DFT are used together to reconstruct the full 2D spectrum via an onion-peeling algorithm.

### Berkeley Advanced Reconstruction Toolbox (BART)

• Collaborators: Martin Uecker, Jon Tamir and many more.

• The Berkeley Advanced Reconstruction Toolbox (BART) is a free and open-source image-reconstruction framework for Computational Magnetic Resonance Imaging. It consists of a programming library and a toolbox of command-line programs. The library provides common operations on multi-dimensional arrays, Fourier and wavelet transforms, as well as generic implementations of iterative optimization algorithms. The command-line tools provide direct access to basic operations on multi-dimensional arrays as well as efficient implementations of many calibration and reconstruction algorithms for parallel imaging and compressed sensing.

• I am one of the active developers for BART and have developed fast C and CUDA codes for wavelet transform, non-uniform fast Fourier transform, and singular value thresholding.

### Sparse Representation for 4D Flow MRI with Divergence-free Wavelet Transform

• Collaborators: Martin Uecker, Umar Tariq, Albert Hsiao, Shreyas Vasanawala and Michael Lustig

• Divergence-free wavelet is a vector-wavelet that provides a sparse representation of 4D flow data. It can be used to enforce “soft” divergence-free conditions when discretization and partial voluming result in numerical non-divergence-free components. Efficient 4D flow denoising is achieved by appropriate shrinkage of divergence-free and non-divergence-free wavelet coefficients. It can also be used in compressed sensing reconstruction. Here is a denoising result:

## Publications

### Conference Proceedings

• Nicholas R. Zwart, Ashley G. Anderson III, Ryan K. Robison, Andrew Li, Mariya Doneva, Frank Ong, Martin Uecker, Michael Lustig, and James G. Pipe
Uniting Reconstruction Software for Native Use in GPI
In proceedings of the 24th ISMRM Annual Meeting and Exhibition, Singapore, 2016.

• Martin Uecker, Frank Ong, Jonathan I Tamir, Dara Bahri, Patrick Virtue, Joseph Y Cheng, Tao Zhang, and Michael Lustig