小波去噪举例

§4.6 小波去噪举例[4]

4.6.1 MATLAB中用wnoise函数测试去噪算法

sqrt_snr=3;

init=231434;

[x,xn]=wnoise(3,11,sqrt_snr,init); % WNOISE generate noisy wavelet test data.

% X= WNOISE(FUN,N) returns values of the test function given by FUN, on a % 2^N sample of [0,1]. [X,XN] = WNOISE(FUN,N,SQRT_SNR) returns the % previous vector X rescaled such that std(x) = SQRT_SNR. The returned

% vector XN contains the same test vector X corrupted by an additive Gaussian

% white noise N(0,1). Then XN has a signal-to-noise ratio of (SQRT_SNR^2).

% [X,XN] = WNOISE(FUN,N,SQRT_SNR,INIT) returns previous vectors X and % XN, but the generator seed is set to INI value.

subplot(3,2,1),plot(x)

title('original test function')

subplot(3,2,2),plot(xn)

title('noised function')

%产生一个长为2**11点，包含高斯白噪声的正弦信号，噪声的的标准偏差为3。

lev=5;

xd=wden(x,'heursure','s','one',lev,'sym8');

% [XD,CXD,LXD] = WDEN(X,TPTR,SORH,SCAL,N,'wname')

% returns a de-noised version XD of input signal X obtained by thresholding the

% wavelet coefficients. Additional output arguments [CXD,LXD] are the wavelet

% decomposition structure of de-noised signal XD.（WDEN根据信号小波分解

% 结构[C,L]对信号进行去噪处理，返回处理信号XD，以及XD的小波分解

% 结构{CXD，LXD}）。

% TPTR(contains threshold selection rule)='heursure',

% 'heursure' is an heuristic variant of the first option

% （选择基于Stein无偏估计理论的自适应域值的启发式改进）

% SORH ('s' or 'h') is for soft or hard thresholding（决定域值的使用方式）

% SCAL(='onedefines multiplicative threshold rescaling:'one' for no rescaling

%（决定域值是否随噪声变化） 'wname'='sym8'

subplot(3,2,3),plot(xd)

title('One de-noised function')

% 利用’sym8’小波对信号分解，在分解的第5层上，利用启发式SURE 域值选择法对信号去噪。

xd=wden(x,'heursure','s','sln',lev,'sym8');

% 'sln' for rescaling using a single estimation

% of level noise based on first level coefficients（根据第一层小波分解的噪声方% 差调整域值）

subplot(3,2,4),plot(xd)

title('Sln de-noised function')

% 同上’sym8’小波对信号分解条件，但用软SURE域值选择算法对信号去噪。

xd=wden(x,'sqtwolog','s','sln',lev,'sym8');

% for universal threshold sqrt(2*log(.))（固定域值选择算法去噪）.

subplot(3,2,5),plot(xd)

title('Sqtwolog de-noised function')

% 同上’sym8’小波对信号分解条件，但用固定域值选择算法去噪。

[c,l]=wavedec(x,lev,'sym8');

% WA VEDEC performs a multilevel 1-D wavelet analysis using either a specific

% wavelet 'wname' or a specific set of wavelet decomposition filters (see

% WFILTERS).[C,L] = WA VEDEC(X,N,'wname') returns the wavelet

% decomposition of the signal X at level N, using 'wname'. The output

% decomposition structure contains the wavelet decomposition vector C（按照一

% 定顺序存储信号小波分解的阿个曾的近似分量和细节分量的系数）and the % bookkeeping vector L(各近似分量和细节分量系数的长度).

% xd=wden(c,l,'minimaxi','s','sln',lev,'sym8'); 'minimaxi' for minimax thresholding