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| #!/usr/bin/env python | |
| # Simple example of Wiener deconvolution in Python. | |
| # We use a fixed SNR across all frequencies in this example. | |
| # | |
| # Written 2015 by Dan Stowell. Public domain. | |
| import numpy as np | |
| from numpy.fft import fft, ifft, ifftshift | |
| import matplotlib | |
| #matplotlib.use('PDF') # http://www.astrobetter.com/plotting-to-a-file-in-python/ | |
| import matplotlib.pyplot as plt | |
| import matplotlib.cm as cm | |
| from matplotlib.backends.backend_pdf import PdfPages | |
| plt.rcParams.update({'font.size': 6}) | |
| ########################## | |
| # user config | |
| sonlen = 128 | |
| irlen = 64 | |
| lambd_est = 1e-3 # estimated noise lev | |
| ########################## | |
| def gen_son(length): | |
| "Generate a synthetic un-reverberated 'sound event' template" | |
| # (whitenoise -> integrate -> envelope -> normalise) | |
| son = np.cumsum(np.random.randn(length)) | |
| # apply envelope | |
| attacklen = length / 8 | |
| env = np.hstack((np.linspace(0.1, 1, attacklen), np.linspace(1, 0.1, length - attacklen))) | |
| son *= env | |
| son /= np.sqrt(np.sum(son * son)) | |
| return son | |
| def gen_ir(length): | |
| "Generate a synthetic impulse response" | |
| # First we generate a quietish tail | |
| son = np.random.randn(length) | |
| attacklen = length / 2 | |
| env = np.hstack((np.linspace(0.1, 1, attacklen), np.linspace(1, 0.1, length - attacklen))) | |
| son *= env | |
| son *= 0.05 | |
| # Here we add the "direct" signal | |
| son[0] = 1 | |
| # Now some early reflection spikes | |
| for _ in range(10): | |
| son[ int(length * (np.random.rand()**2)) ] += np.random.randn() * 0.5 | |
| # Normalise and return | |
| son /= np.sqrt(np.sum(son * son)) | |
| return son | |
| def wiener_deconvolution(signal, kernel, lambd): | |
| "lambd is the SNR" | |
| kernel = np.hstack((kernel, np.zeros(len(signal) - len(kernel)))) # zero pad the kernel to same length | |
| H = fft(kernel) | |
| deconvolved = np.real(ifft(fft(signal)*np.conj(H)/(H*np.conj(H) + lambd**2))) | |
| return deconvolved | |
| if __name__ == '__main__': | |
| "simple test: get one soundtype and one impulse response, convolve them, deconvolve them, and check the result (plot it!)" | |
| son = gen_son(sonlen) | |
| ir = gen_ir(irlen) | |
| obs = np.convolve(son, ir, mode='full') | |
| # let's add some noise to the obs | |
| obs += np.random.randn(*obs.shape) * lambd_est | |
| son_est = wiener_deconvolution(obs, ir, lambd=lambd_est)[:sonlen] | |
| ir_est = wiener_deconvolution(obs, son, lambd=lambd_est)[:irlen] | |
| # calc error | |
| son_err = np.sqrt(np.mean((son - son_est) ** 2)) | |
| ir_err = np.sqrt(np.mean((ir - ir_est) ** 2)) | |
| print("single_example_test(): RMS errors son %g, IR %g" % (son_err, ir_err)) | |
| # plot | |
| pdf = PdfPages('wiener_deconvolution_example.pdf') | |
| plt.figure(frameon=False) | |
| # | |
| plt.subplot(3,2,1) | |
| plt.plot(son) | |
| plt.title("son") | |
| plt.subplot(3,2,3) | |
| plt.plot(son_est) | |
| plt.title("son_est") | |
| plt.subplot(3,2,2) | |
| plt.plot(ir) | |
| plt.title("ir") | |
| plt.subplot(3,2,4) | |
| plt.plot(ir_est) | |
| plt.title("ir_est") | |
| plt.subplot(3,1,3) | |
| plt.plot(obs) | |
| plt.title("obs") | |
| # | |
| pdf.savefig() | |
| plt.close() | |
| pdf.close() |
@jlandercy well spotted, the
lambdshould certainly be described more precisely as the inverse of SNR; and probably expressed in amplitude given that it gets squared. I don't however have a record of any reference for this code, I'm afraid.
Thank you for answering @danstowell.
Yes, doing some dimensional analysis trying to derive your formulae from Wiener Filter I found that might be the case.
Anyway I could not get your version from the initial formulae, any chance you remember how you derived it?
Best regards.
I found my notes. It was at least partly taken from a posting here http://blog.gmane.org/gmane.comp.python.scientific.user/month=20110801 though that archive seems to be offline now.
My expression seems to fit closely with the following line from the wikipedia article:
and then the estimate is given in the spectral domain as G(f)Y(f)
Hallo i tried to run these code but unfortunately it gives me some errors. i put them in one single cell together just want to see exactly what happen by using these. would you mind to take a look? thank you
It's probably a Python 2 versus Python 3 issue. I wrote this code using Python 2. In Python 3, integer division is changed so that it doesn't necessarily return an integer, might return a float. Can you fix it by changing some e.g. length / 8 to int(length / 8)?
This code is merely a simple, minimal example of Wiener filtering. You could certainly use it as a template from which to make other things, but that's not the goal here, and I'm afraid here is not the right place to ask.
Hi, I am certainly trying to hijack your code and you use it for a completely different purpose compared to what it was designed initially... but, I would like to perform a wiener deconvolution of a signal made of several Gaussians that are simply convolved with an ellipsoide profile. In this case though, the algorithm seems to completely fail the reconstruction, do you have any idea what could be wrong ? Is there any assumptions behind the shape of the signals (length, positivity,...) ?
@jlandercy well spotted, the
lambdshould certainly be described more precisely as the inverse of SNR; and probably expressed in amplitude given that it gets squared. I don't however have a record of any reference for this code, I'm afraid.