Removal of Artifacts

1
Removal of Artifacts

• T-61.182, Biomedical Image Analysis
• Seminar presentation 19.2.2005
• Hannu Laaksonen
• Vibhor Kumar

2
Overview, part I

• Different types of noise
• Signal dependent noise
• Stationarity
• Simple methods of noise removal
• Averaging
• Space-domain filtering
• Frequency-domain filtering
• Matrix representation of images

3
Introduction

• Noise any part of the image that is of no
  interest
• Removal of noise (artifacts) crucial for image
  analysis
• Artifact removal should not cause distortions in
  the image

4
Different types of noise

• Random noise
• Probability density function, PDF
• Gaussian, uniform, Poisson
• Structured noise
• Physiological interference
• Other

5
Signal dependent noise

• Noise might not be independent it may also
  depend on the signal itself
• Poisson noise
• Film-grain noise
• Speckle noise

An image with Poisson noise
6
Stationarity

• Strongly stationary
• Stationary in the wide sense
• Nonstationary
• Quasistationary (block-wise stationary)
• Short-time analysis
• Cyclo-stationary

7
Synchronized or multiframe averaging

• If several time instances of the image are
  available, the noise can be reduced by averaging
• Synchronized averaging frames are acquired in
  the same phase
• Changes (motion, displacement) between frames
  will cause distortion

8
Space-domain filters

• Images often nonstationary as a whole, but ma be
  stationary in small segments
• Moving-window filter
• Sizes, shapes and weights vary
• Parameters are estimated in the window and
  applied to the pixel in center

9
Examples of windows
10
Examples of space-domain filters

• Mean filter
• Mean of the values in window
• Median filter
• Median of the values in window
• Nonlinear
• Order-statistic filter
• A large class of nonlinear filters

11
Filters in use
12
Frequency-domain filters

• In natural images, usually the most important
  information is located at low frequencies
• Frequency-domain filtering
• 2D Fourier transform is calculated of the image
• The transformed image passed through a transfer
  function (filter)
• The image is then transformed back

13
Grid artifact removal
14
Matrix representation of image processing

• Image may be presented as a matrix
• f f(m,n) m 0,1,2,M-1 n 0,1,2,,N-1
• Can be converted into vector by row ordering
• f f1, f2, , fMT
• Image properties can be calculated using matrix
  notation
• Mean m Ef
• Covariance s E(f - m)(f - m)T
• Autocorrelation F Ef fT

15
Matrix representation of transforms

• Several transforms may be expressed as FA f A,
  where A is a matrix constructed using basis
  functions
• Fourier, Walsh-Hadamard and discrete cosine
  transforms