Removal of Artifacts

T-61.182, Biomedical Image AnalysisSeminar presentation 19.2.2005

Hannu LaaksonenVibhor Kumar

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

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

Different types of noise

Random noise Probability density function, PDF Gaussian, uniform, Poisson

Structured noise Physiological interference Other

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

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Stationarity

Strongly stationary Stationary in the wide sense Nonstationary Quasistationary (block-wise stationary)

Short-time analysis Cyclo-stationary

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

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

Examples of windows

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

Filters in use

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

Grid artifact removal

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[f fT]

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