Digital Image Processing 14 December 2006 Dr. ir. Aleksandra Pizurica Prof. Dr. Ir. Wilfried Philips Aleksandra.Pizurica @telin.ugent.be Tel: 09/264.3415 UNIVERSITEIT GENT Telecommunicatie en Informatieverwerking Repeating
Objectives of Image Restoration Image restoration likewise image enhancement attemts at improving the image quality Some overlap exists between image enhancement and restoration Important differences: image enhancement is largely subjective, while image restoration is mainly objective process Restoration attempts to recover an image that has been degraded by using a priori knowledge about degradation process Restoration techniques involve modelling of degradation and applying the inverse process in order to recover the image The restoration approach usually involves a criterion of goodness (e.g., mean squared error, smoothness, minimal desription length, ) that will yield an optimal estimate of the desired result 05.a3 Why is denoising important Not only visual enhancement, but also: automatic processing is facilitated! original denoised Example: edge detection 05.a4
Noise models Noise models can be categorized according to marginal statistics (first-order statistics, marginal probability density function): Gaussian, Rayleigh, Poisson, impulsive, higher-order statistics white noise (uncorrelated) colored (correlated) type of mixing with the signal additive multiplicative other (more complex) dependence on the signal statistically independent of the signal statisticaly dependent of the signal Many techniques assume additive white Gaussian noise (AWGN) model 05.a5 Noise models: marginal statistics Some common probability densitu functions (pdf s)of noise: * Gaussian e.g., thermal noise and a variety of noise sources * Rayleigh e.g. amplitude of random complex numbers whose real and imaginary components are normally and independently distributed. Examples: ultrasound imaging Rayleigh Rice Impulsive * Rice e.g., MRI image magnitude (Gaussian and Rayleigh are special cases of this distribution) * Poisson models photon noise in the sensor (an average number of photons within a given observation window) * Bipolar impulsive (e.g., salt and pepper) noise 05.a6
version: 14/12/2006 B. A. Goossens, Pizurica, Universiteit Gent, 2006 Noise models: correlation properties Original image Image with white noise Image with colored noise noise white uncorrelated colored correlated Difference with the original Difference with the original 05.a7 version: 14/12/2006 W. Philips, A. Pizurica, Universiteit Universiteit Gent, Gent, 1999-2006 Some reasons behind noise correlation Bayer pattern captured image interpolated 05.a8
Some reasons behind noise correlation Speckle noise in ultrasound images Original New filter Speckle noise affects all coheren imaging systems. Speckle arises as a consequence of constructive and destructive interference between backscattered waves. Speckle is of multiplicative and signal-dependant nature. Where the signal is stronger, speckle is also more pronounced. 05.a9 Some reasons behind noise correlation Speckle noise Synthetic Aperture Radar (SAR) images Original New filter SAR speckle is similar to ultrasound speckle, but has different correlation properties. 05.a10
version: 14/12/2006 W. Philips, A. Pizurica, Universiteit Universiteit Gent, Gent, 1999-2006 Reduction of impulse noise impulse noise median over 3x3 Median filter removes isolated noise peaks, without blurring the image 05.a11 Some simple noise filters Arithmetic mean 1 fˆ( x, y) = mn g( s, S xy Average within a local window S xy Aimed for Gaussian noise, (but blurs edges) Median Median Alpha-trimmed mean fˆ( x, y) = median{ g( s, } S xy Efficient for impulsive noise Not efficient for Gaussian noise Discard d/2 lowest and d/2 largest values in S xy Denote by g r (s, the remaining mn-d pixels 1 fˆ( x, y) = gr mn d For d=0: mean filter For d=mn-1: median filter S xy 05.a12