简单的基追踪一维信号降噪方法（MATLAB 2018）

基本跟踪法是基于冗余完整字典下的信号稀疏表示方法。该方法具有提高信号稀疏性、降低阈值噪音、提高时频分辨率等优点。基本跟踪方法以表示系数的范数作为信号来衡量稀疏性，将信号稀疏表示问题定义为一种具有约束力的极值问题，然后转化为线性规划问题来解决。

Speech Signal Generation and Plot

M = 100;                  % length of signaln = 0:M-1;s = 0.5*sin(2*pi*0.05*n); % Speech Waveform % Plotting the speech Signal in Time Domainfigure(1)subplot(2,1,1)plot(n,s)ylabel('Amplitude');xlabel('Time');title('Speech Waveform in Time Domain')% Plotting the speech Signal in Frequency DomainY = (1/1024)*fft(s,1024);figure(1)subplot(2,1,2)plot(abs(Y))xlim([0 1024])ylabel('Amplitude');xlabel('Frequency');title('Speech Waveform in Frequency Domain')

Noisy Signal Generation and Plot

w = 0.5*randn(size(s));    % w : zero-mean Gaussian noisey = s   w;                 % y : Adding noise to speech signal% Plotting the noisy Signal in Time Domainfigure(2)subplot(2,1,1)plot(y)title('Noisy speech signal')ylabel('Amplitude');xlabel('Time');% Plotting the noisy Signal in Frequency DomainN = 2^10;                   % N : Length of Fourier coefficient vectorY = (1/N)*fft(y,N);         % Y : Spectrum of noisy signalfigure(2)subplot(2,1,2)plot(abs(Y))xlim([0 1024])title('Fourier coefficients (FFT) of noisy signal');xlabel('Frequency (index)')

[A, AH] = MakeTransforms('DFT', 100, 2^10)

% Defining algorithm parameterslambda = 7; % lambda : regularization parameterNit = 50; % Nit : number of iterationsmu = 500; % mu : ADMM parameter% Running the  BPD algorithm[c, cost] = BPD(y, A, AH, lambda, mu, Nit);figure(4)plot(cost)title('Cost function history');xlabel('Iteration')it1 = 5;del = cost(it1) - min(cost);ylim([min(cost)-0.1*del cost(it1)]xlim([0 Nit])

Denoising

% Plotting the denoised Signal in Frequency Domainfigure(5)subplot(2,1,1)plot(abs(c))xlim([0 1024])title('Fourier coefficients (BPD solution)');ylabel('Amplitude')xlabel('Frequency')% Plotting the denoised Signal in Time Domainfigure(5)subplot(2,1,2)plot(ifft(c))xlim([0 100])title('Denoised signal using BPD');ylabel('Amplitude')xlabel('Time')

完整代码：https://mbd.pub/o/bread/mbd-ZZmVmJlv

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