Brief review of image denoising techniques

https://github.com/kanavalau/EE367_Project_WNNM_denoising

Methods can be roughly classified as:

• spatial domain methods
• transform domain methods.

Spatial domain (Classical) methods

Filter-based

Eliminate noise to a reasonable extent but at the cost of image blurring, which in turn loses sharp edges.

• Wiener filter:
  • • can easily blur sharp edges
  • linear
• Bilateral filter
  • non-linear, edge-preserving, and noise-reducing smoothing filter
  • intensity value of each pixel is replaced with a weighted average of intensity values from nearby pixels
  • • inefficient

Variational

use image priors, minimize energy function goal is to find the a good prior different approaches - different definitions of prior

• Total Variation
  • based on the statistical fact that natural images are locally smooth and the pixel intensity gradually varies in most regions
  • • retain sharp edges
  • • textures tend to be over-smoothed
  • • flat areas are approximated by a piecewise constant surface resulting in a stair-casing effect
  • • the image suffers from losses of contrast
• Non-local reguralization
  • weighted filtering of the NSS prior
  • build a pointwise estimation of the image, where each pixel is obtained as a weighted average of pixels centered at regions that are similar to the region centered at the estimated pixel.
  • structural information is not well preserved
• R-NL
  • combination of NLM and TV
  • structural information is not well preserved problem not solved
• K-singular Value Decomposition
  • local
  • based on the sparsity of natural images
  • each image patch can be represented as a linear combination of several patches from an over-complete dictionary
• Non-local sparse representation model
  • integrates NSS into the sparse representation framework
  • very effective in reconstructing both smooth and textured regions
  • inefficient
• Low-rank minimalization
  • low rank matrix factorization
    • approximate a given data matrix as a product of two matrices of fixed low rank
    • • rank must be provided
  • nuclear norm minimization
    • Weighted Nuclear Norm Minimalization (WNNM)
      • non-local
      • achieves advanced denoising performance and is more robust to noise strength than other NNMs

Transform domain methods

Transform domain methods employ the following observation: the characteristics of image information and noise are different in the transform domain

Transform domain filtering

first transform the given noisy image to another domain, and then they apply a denoising procedure on the transformed image according to the different characteristics of the image and its noise

• Data adaptive transform
  • ICA, PCA
  • high-computational cost because they use sliding windows
  • require a sample of noise-free data or at least two image frames from the same scene
• Non-data adaptive transform
  • spatial frequency domain (cut-off frequency transformation -> remove high freq noise)
  • or wavelet domain
    • can successfully remove noise while preserving the image characteristics, regardless of its frequency content
    • heavily relies on the selection of wavelet bases.
• BM3D
  • two stage non-locally collaborative filtering method in the transform domain
  • when the noise increases gradually, the denoising performance of BM3D decreases greatly and artifacts are introduced, especially in flat areas

CNN and Deep Learning based methods

• optimizing a loss function on a training set that contains degraded-clean image pairs

Comparision

• « BM3D, WNNM