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Removal of Artifacts

Removal of Artifacts. T-61.182, Biomedical Image Analysis Seminar presentation 19.2.2005 Hannu Laaksonen Vibhor Kumar. Overview, part I. Different types of noise Signal dependent noise Stationarity Simple methods of noise removal Averaging Space-domain filtering

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Removal of Artifacts

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  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, …, fM]T • Image properties can be calculated using matrix notation • Mean m = E[f] • Covariance σ = E[(f - m)(f - m)T] • Autocorrelation Φ = E[ffT]

  15. Matrix representation of transforms • Several transforms may be expressed as F=A f A, where A is a matrix constructed using basis functions • Fourier, Walsh-Hadamard and discrete cosine transforms

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