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 column-row normalization corresponds to one iteration of a symmetrization process called the Sinkhorn-Knopp 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 expectation-maximization (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 state-of-the-art methods.


  1. Stanley H. Chan, Todd Zickler, and Yue M. Lu, ‘‘Understanding symmetric smoothing filters: A Gaussian mixture model perspective’’, submitted, Jan. 2016.

  2. Stanley H. Chan, Todd Zickler, Yue M. Lu, ‘‘Understanding symmetric smoothing filters via Gaussian mixtures’’, IEEE ICIP, pp. 2500-2504, Quebec City, Canada, Sep. 2015.

Monte-Carlo Non-local Means


Non-local means (Buades et al 2005) is a simple yet effective image denoising algorithm. More strikingly, Levin and Nadler (2012) showed that non-local 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 large-deviation 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


  1. Stanley H. Chan, Todd Zickler, and Yue M. Lu, ‘‘Monte Carlo non local means: Random sampling for large-scale image filtering’’, IEEE Trans. Image Process., vol. 23, no. 8, pp. 3711-3725, Aug. 2014.

  2. Stanley H. Chan, Todd Zickler and Yue M. Lu, ‘‘Fast non-local filtering by random sampling: it works, especially for large images,’’ IEEE ICASSP, pp.1603-1607, Vancouver, Canada, May 2013.

Image Denoising by Prior Adaptation


Effective image prior is a key factor for successful image denoising. Existing learning-based 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 Expectation-Maximization (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 pre-filtered images in the absence of clean databases. Experimental results show that the adapted prior is consistently better than the originally un-adapted prior, and has superior performance than some state-of-the-art algorithms.

MATLAB Implementation


  1. 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.

  2. Stanley H. Chan, Enming Luo, and Truong Q. Nguyen, ‘‘Adaptive patch-based image denoising by EM adaptation’’, IEEE GlobalSIP, pp. 810-814, 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 state-of-the-art denoising algorithms.

MATLAB Implementation


  1. Enming Luo, Stanley H. Chan, and Truong Q. Nguyen, ‘‘Adaptive image denoising by targeted databases’’, IEEE Trans. Image Process., vol. 24, no. 7, pp.2167-2181, Jul. 2015.

  2. Enming Luo, Stanle H. Chan, and Truong Q. Nguyen, ‘‘Image Denoising by Targeted External Databases’’, IEEE ICASSP, 2014, pp. 3019-3023. (NSF student travel award, ICASSP student travel award)

Image Denoising for Hyperspectral Imagign Data


High-speed 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 shot-noise-limited detection sensitivity.

Our contribution: We demonstrate a denoising algorithm that removes the noise in both spatial and spectral domains by total variation minimization. The signal-to-noise 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 protein-rich organelles in Caenorhabditis elegans.

MATLAB Implementation


  1. Chien-Sheng Liao, Joon Hee Choi, Delong Zhang, Stanley H. Chan, and Ji-xin Cheng, ‘‘Denoising Stimulated Raman Spectroscopic Images by Total Variation Minimization’’, Journal of Physical Chemistry C, vol. 119, no. 33, pp.19397–19403, Jul. 2015.