Image Restoration
MultiAgent Consensus Equilibrium

While foreground extraction is fundamental to virtual reality systems and has
been studied for decades, majority of the professional softwares today still
rely substantially on human interventions, e.g., providing trimaps or
labeling key frames. This is not only time consuming, but is also sensitive
to human error. In this paper, we present a fully automatic foreground
extraction algorithm which does not require any trimap or scribble. Our
solution is based on a newly developed concept called the MultiAgent
Consensus Equilibrium (MACE), a framework which allows us to integrate
multiple sources of expertise to produce an overall superior result. The MACE
framework consists of three agents: (1) A new dual layer closedform matting
agent to estimate the foreground mask using the color image and a background
image; (2) A background probability estimator using color difference and
object segmentation; (3) A total variation minimization agent to control the
smoothness of the foreground masks. We show how these agents are constructed,
and how their interactions lead to better performance. We evaluate the
performance of the proposed algorithm by comparing to several
stateoftheart methods. On the real datasets we tested, our results show
less error compared to the other methods.
Publication:
Xiran Wang, Jason Juang, Stanley H. Chan, ‘‘Automatic Foreground Extraction using MultiAgent Consensus Equilibrium’’, submitted.

Theory of PlugandPlay ADMM

The PlugandPlay (PnP) ADMM algorithm is a powerful image restoration
framework that allows advanced image denoising priors to be integrated into
physical forward models to yield a provably convergent algorithm. However,
despite the enormous applications and promising results, very little is known
about why the PnP ADMM performs so well. This paper presents a formal
analysis of the performance of PnP ADMM. By restricting the denoisers to the
class of graph filters, or more specifically the symmetric smoothing filters,
we offer three contributions: (1) We rigorously show conditions under which
an equivalent maximumaposteriori (MAP) optimization exists, (2) we derive
the mean squared error of the PnP solution, and provide a simple geometric
interpretation which can explain the performance, (3) we introduce a new
analysis technique via the concept of consensus equilibrium, and provide
interpretations to general linear inverse problems and problems with multiple
priors.
Publication:
Stanley H. Chan, ‘‘Performance Analysis of PlugandPlay ADMM: A Graph Signal Processing Perspective’’, submitted.
Gregery T. Buzzard, Stanley H. Chan and Charles A. Bouman ‘‘PlugandPlay Unplugged: Optimization Free Reconstruction using Consensus Equilibrium’’, submitted. [CODE]

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’’, IEEE ICASSP,
pp.13231327, 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.

