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 = [f 1, f 2, …, f M ] T Image properties can be calculated using matrix notation  Mean m = E[f]  Covariance σ = E[(f - m)(f - m) T ]  Autocorrelation Φ = E[f f T ]

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