The Adaptative 2D LMS Filter - Laboratory of Computer and 自适应二维LMS滤波器的实验室与计算机.ppt

The Adaptative 2D LMS Filter - Laboratory of Computer and 自适应二维LMS滤波器的实验室与计算机
Adaptive filtering
Linear filtering
Noise is reduced near the edges without causing blurring
Sub-areas
Updating for the filter coefficients
New coefficients determined by minimazing MSE between f(m,n) and the estimation
Steepest descent method:
μ controls the rate of convergence and filter stability.
Error is estimated using an approximation to the original signal d(m,n)
d(m,n) obtained by decorrelation from the input image g(m,n)
2D delay operator of (1,1) samples, use the previous pixel as an estimate
Advantages of the Algorithm
It does not require a priori information about:
Image
Noise statistics
Correlation properties
It does not require averaging, differentiation and matrix operations
MSE=1590
MSE=395
The Adaptative Rectangular Window LMS Filter
ARW LMS Algorithm
Same concept: 2D LMS filter based on standard Wiener filter
New Idea: use of an adaptative-sized rectangular window
Additional assumption: image processes have zero mean
Implementation
Taking into account that now we have zero mean noise, following estimate is derived:
σf2 is the variance of the original image (estimated)
Idea: globally nonstationary process can be considered locally stationary and ergodic over small regions
Target: to identify the size of a stationary square region for each pixel in the image
Sample statistics can approximate the a posteriori pareameters needed
Updating the window size
Large window It may include pixels form other ensembles
Small window The statistics needed are poorly estimated
ARW lengths (Lr and Lc) are varied using a signal activity parameter:
A similar signal activity parameter is defined in the colum direction
Updating the window size (II)
If S is large N is decremented
If S is small N is incremented
In order to make this decision, S is compared to a threshold T as follows:
Threshold is defined as:
κ controls the ra