Image wavelet threshold denoising_wavelet noise reduction function

There are many methods for wavelet denoising, such as filtering and noise reduction by wavelet decomposition and reconstruction, denoising by wavelet transform modulus maxima, spatial and spatial correlation after signal wavelet transform for signal-to-noise separation, and nonlinear wavelet. Threshold method denoising, translation invariant wavelet denoising, and multi-wavelet noise reduction and so on. There are three main categories: modulus max detection, threshold denoising, and masking (correlation) denoising. The most commonly used one is the threshold method to denoise . The basic idea is to use image wavelet decomposition to select different thresholds for different characteristics of each sub-band image, so as to achieve better noise reduction.

Image denoising in MATLAB is mainly achieved by two aspects: threshold acquisition and image denoising.

The functions that implement threshold acquisition in MATLAB are ddencmp, select, wbmpen, and wdcbm2. Here mainly introduces the function ddencmp.

The function of the function ddencmp is to get the default value of noise reduction or compression. This function is a steering function for noise reduction and compression, which gives all default values ​​for the general process of noise reduction and compression using wavelet or wavelet packets for one or two-dimensional signals.

Its syntax is:

[THR,SORH,KEEPAPP,CRIT]=ddencmp(IN1,IN2,X)

[THR,SORH,KEEPAPP]=ddencmp(IN1,'wv',X)

[THR,SORH,KEEPAPP,CRIT]=ddencmp(IN1,'wp',X)

The functions that implement threshold denoising in MATLAB are wden, wdencmp, wpdencmp, wthresh, wpthcoef, and wthcoef2. Here mainly introduces the function wdencmp.

Its syntax is:

[XC, CXC, LXC, PERF0, PERFL2]=wdencmp('gbl',X,'wname',N,THR,SORH,KEEPAPP)

[XC, CXC, LXC, PERF0, PERFL2]=wdencmp('lvd',X,'wname',N,THR,SORH)

[XC, CXC, LXC, PERF0, PERFL2]=wdencmp('lvd',C,L,'wname',N,THR,SORH)

The function of the function wdencmp is to use wavelet to reduce noise. This function is a steering function for two-dimensional wavelet denoising. It uses wavelets to perform noise reduction on signals or images. Wname is the wavelet function used. Gbl(global) means that each layer is processed with the same threshold. Lvd indicates that each layer is processed with a different threshold. N represents the number of layers of wavelet decomposition. THR is a threshold vector with a length of N. SORH indicates that a soft threshold or a hard threshold is selected (the values ​​are 's' and 'h', respectively). If the value of the parameter KEEPAPP is 1, then the low-frequency coefficient is not subjected to threshold quantization, and conversely, the low-frequency coefficient is subjected to threshold quantization. XC is the noise-reduced signal, [CXC, LXC] is the wavelet decomposition structure of XC, and PHRF0 and PERFL2 are the norm percentages of the recovered and compressed L2. If [C, L] is the wavelet decomposition structure of x, then PERFL2 = 100  (the norm of the CXC vector / the norm of the C vector) 2; if X is a one-dimensional signal and the wavelet wname is an orthogonal wavelet, then:

Noise reduction for noisy one-dimensional signals to achieve signal-to-noise separation. Noise-containing sinusoidal signal: Decomposes the noisy signal and derives the high-frequency and low-frequency coefficients from the decomposition. The high frequency coefficient corresponds to the detail signal, and the low frequency coefficient corresponds to the approximation signal. Noise is detected from the high frequency coefficients, and different frequencies of the respective component signals are identified in the low frequency coefficients. Then, the target signal is reconstructed from the denoised high frequency signal and the approximated low frequency signal.

% generates a noisy sinusoidal signal

N=1024

t=1: N;

Sig=sin(0.03*t);

figure(1);

Subplot(211); plot(t, sig); TItle('sinusoidal signal');

% superimposed noise

x=sig+randn(1,N);

Subplot(212); plot(t,x);TItle('noise sinusoidal signal');

% one-dimensional wavelet decomposition, using 'haar' for 4-layer decomposition

[c,l]=wavedec(x,4,'haar');

% Reconstruction of layer 1-4 approximation signals

A4=wrcoef('a',c,l,'haar',4);

A3=wrcoef('a',c,l,'haar',3);

A2=wrcoef('a',c,l,'haar',2);

A1=wrcoef('a',c,l,'haar',1);

% shows the approximation signal of each layer

Figure(2);

Subplot(411); plot(a4);ylabel('a4');

Subplot(412);plot(a3);ylabel('a3');

Subplot(413);plot(a2);ylabel('a2');

Subplot(414);plot(a1);ylabel('a1');

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