Alexey Lukin, Daria Kalinkina, Denis Kubasov

Most images coming from digital stills cameras are contaminated with noise. Here we illustrate some algorithms for suppression of white noise in digital images.

The noise is assumed stationary, white (or at least wideband), and non-correlated with image. Noise of digital cameras approximately satisfies these conditions.

Clean image

Noisy image

Simplest methods for noise reduction (or denoising) just blur the image in areas where no image details are present. Near details the blur amount is reduced or no blurring is performed at all. Usually such methods have rather low quality, they leave noisy contours around image details and blur some image details.

Most popular methods for noise reduction are wavelet thresholding methods. Wavelet transform has the energy compaction property, i.e. it compacts energy of most useful image details into relatively small number of wavelet coefficients. Therefore we can zero (or lower the magnitude of) the rest of coefficients assuming them to be noise, and perform the inverse wavelet transform to restore the denoised image. Wavelet transform allows to suppress noise across various scales, including large-scale low-frequency noises.

Noisy image

Adaptive blur

Wavelet thresholding

We propose the algorithm that is based on paper "Adaptive Principal Components and Image Denoising" (Muresan, Parks, 2003). The adaptive denoising using principal component analysis (PCA) has been improved and hybridized with wavelet transform. This has enabled us to reduce the Gibbs phenomenon (ringing) that appeared in the original PCA-denoising.

Publication

Here you can download our paper from "Lomonosov 2005" conference (in Russian): "Combining PCA and Wavelet Transforms for Image Denoising" (PDF).

The accompanying presentation (in Russian, Power Point format) can also be downloaded. 

Literature

• Pizurica, Zlokolica, Philips, "Combined Wavelet Transform and Temporal Video Denoising"
• Chang, Yu, Vetterli, "Spatially Adaptive Wavelet Thresholding with Context Modeling for Image Denoising"
• Marpe, Cycon, Zander, Barthel, "Context-based Denoising of Images Using Iterative Wavelet Thresholding"
• Muresan, Parks, "Adaptive Principal Components and Image Denoising"

Results

The proposed algorithm features high quality of PCA denoising and at the same time addresses its artifacts: significantly reduces Gibbs phenomenon and effectively suppresses large-scale low-frequency noise. If compared with wavelet thresholding methods, our algorithm better adapts to edges and lines of different orientations.

Wavelet denoising	PCA denoising	Proposed method
Wavelet denoising	PCA denoising	Proposed method
Clean image	Noisy image	Adaptive blur
Wavelet denoising	PCA denoising	Proposed method