Download Wavelet Denoising

Wavelet 1-D Denoising
Wavelet Toolbox™ software enables you to analyze signals, images, and 3-D data using orthogonal and biorthogonal
critically-sampled discrete wavelet analysis. Critically-sampled discrete wavelet analysis is also known
as decimateddiscrete wavelet analysis. Decimated discrete wavelet analysis is most appropriate for data
compression, denoising, and the sparse representation of certain classes of signals and images.
In decimated discrete wavelet analysis, the scales and translations are dyadic.
You can perform 1-D, 2-D, and 3-D decimated discrete wavelet analysis using the interactive tool, wavemenu, by
entering
wavemenu
at the command line and clicking Wavelet 1-D, Wavelet 2-D, or Wavelet 3-D.
1-D Wavelet Denoising
This example shows how to denoise a signal using discrete wavelet analysis.
1.
Create a reference signal.
len = 2^11;
h = [4 -5 3 -4 5 -4.2
2.1
4.3 -3.1
5.1 -4.2];
t = [0.1 0.13 0.15 0.23 0.25 0.40 0.44 0.65 0.76 0.78
h = abs(h);
w = 0.01*[0.5 0.5 0.6 1 1 3 1 1 0.5 0.8 0.5];
tt = linspace(0,1,len); xref = zeros(1,len);
for j=1:11
xref = xref + ( h(j) ./ (1+ ((tt-t(j))/w(j)).^4));
end
Click Enter, See xref by plot
Proper fractions – правильные дроби
Improper fractions – неправильные дроби
Mixed fractions – смешанные дроби
Decimal fractions – десятичные дроби
Numerator – числитель
Denominator – знаменатель
One half –
Two thirds – 2/3
Five sevenths – 5/7
Five sixths – 5/6
Four and one twentieth – 4 1/20
Nought point five – 0.5
Nought point nought five – 0.05
Square brackets – []
Parentheses – ()
Plus – a sign of addition - плюс
0.81];
Minus – a sign of subtraction – минус
Plus or minus - a sign of plus or minus – плюс минус
Times (by) - a sign of multiplication – знак умножения
Divided by – a sign of division – знак деления
Is to - a ratio sign – знак принадлежности
Equals – знак равно
Not equal – не равно
Approximately equals – приблизительно равно
Greater than – больше чем
Equal or greater than – больше равно
Less than – меньше чем
Equal or less than – меньше или равно
Infinity – бесконечность
Square root of – квадратный корень из
Braces – фигурные скобки
Length of line from A to B – длина линии от A в B
Parallel - параллель
Angle – угол
Right angle – прямой угол
Perpendicular – перпендикуляр
Percent (Per cent) – процент
Cube root of – корень кубический из
nth root of – корень n-й степени из
nought – ноль, читается как [оу]
Add zero-mean white Gaussian noise with a variance of 0.25.
rng default;
x = xref + 0.5*randn(size(xref));
plot(x); set(gca,'xlim',[1 2048]);
Denoise the signal down to level 3 using the Daubechies least asymmetric wavelet with 4 vanishing moments. Use
the universal threshold selection rule of Donoho and Johnstone with soft thresholding based on the DWT coefficients
at level 1. Use the periodization signal extension mode — dwtmode('per'). Plot the result along with the reference
signal for comparision.
dwtmode('per');
[xd,cxd,lxd] = wden(x,'sqtwolog','s','sln',4,'sym4');
plot(xd);
set(gca,'xlim',[1 2048]); hold on;
plot(xref,'r');