Image Denoising and Restoration
Fast and Robust Recursive Filters

Image denoising on mobile cameras requires low complexity, but many
stateoftheart denoising methods are computationally intensive. We present
a low complexity denoising algorithm using an edgeaware recursive filter
(RF). We make two contributions. First, we modify the original RF so that it
is significantly more robust when estimating the gradients from noisy inputs.
We extend the RF to highorder for texture and heavy noise images. Second, we
introduce a SUREbased image fusion technique. We show that while individual
RFs have different performance, the fused result is often better.
Experimental results show that the new RF performs much faster than other
denoisers while providing good quality images.
MATLAB Implementation (1.2MB)
Publication:
Yiheng Chi and Stanley H. Chan, ‘‘Fast and robust recursive filter for image denoising’’, IEEE ICASSP, pp. 1708 1712, Calgary, Canada, Apr.
2018.

Symmetric Smoothing Filters

We study a class of smoothing filters for image denoising. Expressed as matrices, these smoothing filters must be row
normalized so that each row sums to unity. Surprisingly, if one applies a column normalization to the matrix before the
row normalization, the denoising quality can often be significantly improved. This columnrow normalization corresponds
to one iteration of a symmetrization process called the SinkhornKnopp balancing algorithm. However, a complete
understanding of the performance gain phenomenon is lacking.
Our Contribution: We analyze the performance gain from a Gaussian mixture model (GMM) perspective. We show that the
symmetrization is equivalent to an expectationmaximization (EM) algorithm for learning the GMM. Moreover, we make
modifications to the symmetrization procedure and present a new denoising algorithm. Experimental results show that the
new algorithm achieves comparable denoising results to some stateoftheart methods.
Publication:
Stanley H. Chan, Todd Zickler, and Yue M. Lu, ‘‘Understanding symmetric smoothing
filters: A Gaussian mixture model perspective’’, IEEE Trans. Image Process., vol. 26, no. 11, pp. 5107–5121, Nov. 2017.
Stanley H. Chan, Todd Zickler, Yue M. Lu, ‘‘Understanding symmetric
smoothing filters via Gaussian mixtures’’, IEEE ICIP, pp. 25002504, Quebec City, Canada, Sep. 2015.

MonteCarlo Nonlocal Means

Nonlocal means (Buades et al 2005) is a simple yet effective image denoising algorithm. More strikingly, Levin and
Nadler (2012) showed that nonlocal means are indeed the optimal denoising algorithm in the mean squared sense when
we have an infinitely large database of clean patches. While these results are beautiful, in reality such computation
are very difficult due to its scale. MCNLM is the first practical solution towards this problem.
Our contributions: We show that only a small subset of patches are sufficient to produce the denoising result. We provide rigorous
proofs using probabilistic largedeviation theory. We derive optimal sampling schemes and implemented a method for the denoising problem. We demonstrate orders of magnitude in speed up
with minimal degradation in quality.
MATLAB Implementation
Publication:
Stanley H. Chan, Todd Zickler, and Yue M. Lu, ‘‘Monte Carlo non local means:
Random sampling for largescale image filtering’’, IEEE Trans. Image Process., vol. 23, no. 8, pp. 37113725, Aug.
2014.
Stanley H. Chan, Todd Zickler and Yue M. Lu, ‘‘Fast nonlocal filtering by
random sampling: it works, especially for large images,’’ IEEE ICASSP, pp.16031607, Vancouver, Canada, May 2013.

Image Denoising by Prior Adaptation

Effective image prior is a key factor for successful image denoising. Existing learningbased priors require a large
collection of images for training. Besides being computationally expensive, these training images do not necessarily
correspond to the noisy image of interest.
Our Contribution: We propose an adaptive learning procedure for learning image patch priors. The new algorithm, called
the ExpectationMaximization (EM) adaptation, maps a generic prior to a targeted image to create a specific prior. EM
adaptation requires significantly less amount of training data compared to the standard EM, and can be applied to
prefiltered images in the absence of clean databases. Experimental results show that the adapted prior is consistently
better than the originally unadapted prior, and has superior performance than some stateoftheart algorithms.
MATLAB Implementation
Publication:
Enming Luo, Stanley H. Chan, and Truong Q. Nguyen, ‘‘Adaptive image denoising by
mixture adaptation’’, IEEE Trans. Image Process., vol. 25, no. 10., pp.4489–4503, Oct. 2016.
Stanley H. Chan, Enming Luo, and Truong Q. Nguyen, ‘‘Adaptive
patchbased image denoising by EM adaptation’’, IEEE GlobalSIP, pp. 810814, Orlando, Florida, Dec. 2015.

Image Denoising by Targeted External Databases

Human uses prior knowledge to analyze an image; So is our desire to put on a computer. However, the priors we use to
train the computers today are perhaps too generic. In many image denoising methods, the priors are learned from a large
collection of natural images comprising of a huge diversity of scenes. Of course, in the asymptotic limit such kind of
priors will work. Yet for a particular image denoising task with only limited computing budget this can be far from
optimal. To address this problem we propose to study the optimal denoising algorithm using a specific (or targeted)
database. For example, if we want to denoise a text document, then we shall use priors of the text. Surprisingly, this
simple idea is sufficient to outperform some of the stateoftheart denoising algorithms.
MATLAB Implementation
Publication:
Enming Luo, Stanley H. Chan, and Truong Q. Nguyen, ‘‘Adaptive image denoising by
targeted databases’’, IEEE Trans. Image Process., vol. 24, no. 7, pp.21672181, Jul. 2015.
Enming Luo, Stanle H. Chan, and Truong Q. Nguyen, ‘‘Image Denoising by
Targeted External Databases’’, IEEE ICASSP, 2014, pp. 30193023. (NSF student travel award, ICASSP student travel award)

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.

