Image Denoising
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)

Image Denoising for Hyperspectral Imagign Data

Highspeed coherent Raman scattering imaging is an important technique to unveil cellular machinery by visualizing the
spatiotemporal dynamics of target molecules or intracellular organelles. By extracting signals from the laser at
megahertz modulation frequency, current stimulated Raman scattering (SRS) microscopy has reached shotnoiselimited
detection sensitivity.
Our contribution: We demonstrate a denoising algorithm that removes the noise in both spatial and spectral domains by
total variation minimization. The signaltonoise ratio of SRS spectroscopic images was improved by up to 57 times for
diluted dimethyl sulfoxide solutions and by 15 times for biological tissues. Coupling the denoising algorithm with
multivariate curve resolution allowed discrimination of fat stores from proteinrich organelles in Caenorhabditis
elegans.
MATLAB Implementation
Publication:
ChienSheng Liao, Joon Hee Choi, Delong Zhang, Stanley H. Chan, and Jixin Cheng,
‘‘Denoising Stimulated Raman Spectroscopic Images by Total Variation
Minimization’’, Journal of Physical Chemistry C, vol. 119, no. 33, pp.19397–19403, Jul. 2015.

