Image Restoration
PlugandPlay ADMM

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization
problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its
emph{modular} structure which allows one to plug in any offtheshelf image denoising algorithm for a subproblem in
the ADMM algorithm. Because of the plugin nature, this type of ADMM algorithms is coined the name “PlugandPlay
ADMM”. PlugandPlay ADMM has demonstrated promising empirical results in a number of recent papers. However, it is
unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since
PlugandPlay ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for
common Gaussian and Poissonian image restoration problems.
We propose a PlugandPlay ADMM algorithm with provable fixed point convergence. We show that for any
denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, PlugandPlay ADMM converges to
a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on
superresolution and singlephoton imaging. We compare PlugandPlay ADMM with stateoftheart algorithms in each
problem type, and demonstrate promising experimental results of the algorithm.
MATLAB Implementation
Publication:
Stanley H. Chan, Xiran Wang, and Omar Elgendy, ‘‘PlugandPlay ADMM for image
restoration: Fixed point convergence and applications’’, IEEE Trans. Comp. Imaging, vol. 3, no. 5, pp.84–98, Mar.
2017.
Xiran Wang and Stanley H. Chan, ‘‘Parameterfree PlugandPlay ADMM for image
restoration’’, accepted to IEEE ICASSP, New Orleans, Louisiana, Mar. 2017.

Total Variation Minimization

In this project, we develop a fast numerical optimization method to solve total variation image restoration problems. The method transforms the original
unconstrained problem to an equivalent constrained problem and uses an augmented Lagrangian method to handle the constraints. The transformation allows
the differentiable and nondifferentiable parts of the objective function to be separated into different subproblems where each subproblem may be solved
efficiently. An alternating strategy is then used to combine the subproblem solutions.
MATLAB Implementation
Publication:
Stanley H. Chan, Ramsin Khoshabeh, Kris B. Gibson, Philip E. Gill and Truong Q. Nguyen,
An augmented Lagrangian method for total variation video restoration, IEEE Trans Image Process., vol. 20, no. 11, pp.30973111, Nov 2011.
Stanley H. Chan, Ramsin Khoshabeh, Kris Gibson, Philip E. Gill and Truong Q. Nguyen,
An augmented Lagrangian method for video restoration, IEEE ICASSP, pp.941944, Prague, May 2011.
Daniel Pipa, Stanley H. Chan, and Truong Q. Nguyen,
Directional Decomposition Based Total Variation Image Restoration, EUSIPCO, pp.15581562, 2012.

Depth Estimation: Reconstruction and Sampling

Acquiring depth information is the first and the most important step for 3D image processing. Existing depth
acquisition methods either use expensive hardware devices and computationally intensive block matching algorithms. We
propose a compressive sensing based method to estimate the depth using a few samples. Our solution is unique in
the following sense:
We pick samples spatially without the need of mixing (a common setting in classical compressive sensing which often
requires additional hardware devices);
Our method works for both hardware devices and block matching algorithms; Given a small subset of reliable depth measurement,
we can recover the entire dense depth map;
Our optimization algorithm is based on an augmented Lagrangian method, which can be fully parallelized on GPU to achieve real time computation;
We provide practical sampling schemes to minimize the number of samples and optimize the sampling locations.
MATLAB Implementation
Publication:
LeeKang Liu, Stanley H. Chan, and Truong Q. Nguyen, ‘‘Depth Reconstruction
from Sparse Samples: Representation, Algorithm, and Sampling’’, IEEE Trans. Image Process., vol. 24, no. 6, pp.
19831996, Jun. 2015.
Ramsin Khoshabeh, Stanley H. Chan and Truong Q. Nguyen,
Spatiotemporal consistency in video disparity estimation, IEEE ICASSP, pp.885888, Prague, May 2011.

Motion Estimation

In conventional block matching motion estimation algorithms, subpixel motion accuracy is achieved by searching the best matching block in an enlarged
(interpolated) reference search area. This, however, is computationally expensive as the number of operations required is directly proportional to the
interpolation factor. For non video compression based applications, the interpolation process is even wasteful as the motion compensation frames are not
needed. This project aims at developing a fast motion estimation algorithm that achieves subpixel accuracy without interpolation. We show that by fusing
the existing integer block matching algorithm and a modified optical flow method, subpixel motion vectors can be determined at the cost of integer block
matching plus solving a 2by2 systems of linear equations. Experimental results demonstrate that the proposed method is faster than conventional method
by a factor of 2 (or more), while the motion vector quality is compatible to the benchmark full search algorithm.
MATLAB implementation
Publication:
Stanley H. Chan, Dung Vo and Truong Q. Nguyen,
Subpixel motion estimation withouth interpolation,
IEEE ICASSP, pp.722725, Dallas, March 2010.

