israeljsf95/c-scsa

Signal denoising based on SCSA and a curvature constraint (C-SCSA)

Matlab implementation of the C-SCSA method.

Modules

Pre-requisite

Download the project to your local Matlab directory and include all folders and subfolders in the project. No other dependencies are needed.

Data generation

There are different types of signals you can generate, including:

Types	Description
Gaussian	The Gaussian signal is recommended to be used in simulation, which SCSA is good at characterizing. Signals such as chromatography spectral peaks can be modeled by Gaussian peaks generation function. The users will be able to change the amplitude(hgt), position(pos) and width(wdt) of peak [f, yf, yf0]=Gaussian_signal_generation(pos,hgt,wdt,0) in favor of their options. Output of the function is yf0. To adjust output signal length, change x = linspace(0,1,#{length});in line 2 of Gaussian_signal_generation.m
Regular	key='regular' or key='Piece-Regular'(options.alpha gives regularity). The users will be able to generate by y = load_signal(key, signal_length, options).
Bumps	key='Bumps'. The users will be able to generate by y = load_signal(key, signal_length, options).
Sing	key='Sing'. The users will be able to generate by y = load_signal(key, signal_length, options).
Noise(Gaussian)	Gaussian noise is statistical noise having a probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution. key='gaussiannoise' (options.sigma gives width of filtering in pixels). The users will be able to generate by y = load_signal(key, signal_length, options).
Noise(Uniform)	Uniform noise refers to random noise generated in the interval (0,level), user can also specify the number of noise samples by [n] = uniformNoise(length,level)).

If we want to create a piece-wise regular signal (around 500 samples) with uniform noise (distrubuted between (0,10), use the following command:

y_clean = load_signal('Piece-Regular', 500);
n = uniformNoise(length(y_clean),10)';
y_noisy=y_clean+n;

More specifically, if we are generating gaussian signals with uniform noise (level%), use the following command:

[f, yf, yf0]=Gaussian_signal_generation(pos,hgt,wdt,level);

For example, let's say we want to generate a 4-peak gaussian signal, with 50% of noise, we can simply type:

pos=[2,3.6,7,9];
hgt= [2,4,4.5,7];
wdt=[2,3,3,4];
[f, yf, yf0]=Gaussian_signal_generation(pos,hgt,wdt,50);
plotGenFig(yf,yf0);

The generated 4-peak signal will look like below:

Signal denoising with C-SCSA

To perform SCSA utilities, use the following function with the specifications:

Utilities	Description
C-SCSA	Our main C-SCSA implementation. It is the entry point into the denoising algorithm, capable of taking any noisy signal as input (signals with 300-10000 samples are recommended for computing time perspectives). To peform denoising, simply use [ yscsa,mse,snr ,psnr] = SCSAden( yf,yf0,v ) function Input: v is a smoothness parameter related to eq. (11) in our paper. yf is the noisy signal and yf0 is the clean signal, with possible values between (-5,5). v varies with input signal types, signal length and sampling frequencies. function Output: yscsa is the denoised signal. snr and mse is the SNR and mean squared error (MSE) of the denoised signal for evaluation purposes. In the case where clean signal is not available, use [ yscsa] = SCSAden( yf,yf,v ) to get the denoised signal.
Fast	C-SCSA fast version. We are currenlty using fminsearch to speed up the searching process in eq. (10) in our paper, which uses the simplex search method of Lagarias et al. This version is currently in the research process and not available in the repository.
h_Select	Optimal h selection for denoising. This function is for testing purposes. Users will be able to extract the optimal h that bestly denoise a noisy signal yf by running:[ de,h_optimal,snr ] = SCSA_H_Select( yf,yf0 ). function Input: yf is the noisy signal and yf0 is the clean signal. function Output: de is the denoised signal. h_optimal is the h that provides the best denoising performance and snr is the highest SNR that SCSA method can achieve.
Assembly	Denoise signal by separating whole signal into regions of interest and apply C-SCSA on each. This module is currently in its testing stages and is not available in the repository.
Others	Other methods reconstruction are also available. EMD-IT can be implemented by [ de,mse,snr ,psnr] = emd_den( yf,yf0,c,k) and wavelet denoising can be implemented by [de, mse,snr,psnr ] = wa( yf,yf0 )
SCSA	SCSA reconstruction. Users can decompose the signal with a positive h value, by [yscsa,Nh,EigV,EigF] = scsa_build(h,y). function Input: h is a positive value, also known as the SCSA semi-classical constant. It can be selected by Quantum-based interval selection. y is the input signal to be decomposed. function Output: yscsa is the decomposed signal, Nh is the number of eigenfunctions. EigV is a matrix with eigenvalues on its diagonal (you can export the eigenvalues by diag(EigV). EigF is the matrix of eigenfunctions. UI interface of this tool is also available.

Run a Demo (A quick start)

There is a quick start guide in demo.m which involves signal generation and C-SCSA denoising at different noise levels (small noise, median noise, high noise). In the command window, simply run:

demo

The demo will plot the C-SCSA denoising figure:

About the project code

The original source is developed in Matlab 2016a. An equaling or higher version is recommended.

License

The C-SCSA library (i.e. all code inside of the functions directory) is licensed under the GNU General Public License v3.0, also included in our repository in the COPYING file.