"""

===============================================

Demo of denoising of synthetic signal iwth BIRD

===============================================

Reference:

Blind Denoising with Random Greedy Pursuits.

Moussallam, M., Gramfort, A., Daudet, L., & Richard, G. (2014).

IEEE Signal Processing Letters, 21(11), 1341-1345

"""

# Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>

# Manuel Moussallam <manuel.moussallam@gmail.com>

# License: BSD 3 clause

print(__doc__)

import numpy as np

from scipy import linalg

from joblib import Memory

from bird import bird

print("Decomposing a signal + noise at 0dB of SNR")

# will stop whenever the components can't be tell appart from noise anymore

# We could increase the number of runs to improve results

N = 2048

scales = [32, 64, 128, 256, 512, 1024]

# Size of the Shift-Invariant dictionary

M = np.sum(np.array(scales) // 2) * N

n_runs = 30

verbose = False

# tolerated probability of appearance under noise hypothesis

# A good first choice for p_above is arguably 1/M

p_above = 1.0 / M

# creating noisy mix using classic doppler signal

rng = np.random.RandomState(42)

x = np.linspace(0, 1, N)

doppler = np.sqrt(x * (1 - x)) * np.sin((2.1 * np.pi) / (x + .05))

X = doppler.reshape((1, N))

X /= linalg.norm(X)

truth = X.copy()

noise = rng.randn(*truth.shape)

noise *= .3 / linalg.norm(noise)

snr = 20. * np.log10(linalg.norm(X) / linalg.norm(noise))

data = X + noise

memory = Memory(None)

print("SNR = %s." % snr)

print("Dictionary of {0} atoms with {1} runs: chose "

"p_above={2}".format(M, n_runs, p_above))

X_denoised = bird(data, scales, n_runs, p_above=p_above, random_state=42,

n_jobs=-1, verbose=verbose, memory=memory)

residual = X_denoised - truth

print("Noisy Signal at %1.3f dB gave a RMSE of "

"%1.3f" % (snr, linalg.norm(residual)))

import matplotlib.pyplot as plt

plt.close('all')

plt.figure()

plt.plot(data.T, 'k', alpha=0.5)

plt.plot(truth.T, 'r:', linewidth=2.0)

plt.plot(X_denoised.T, 'b', linewidth=2.0)

plt.legend(('Noisy', 'Clean', 'BIRD Estimate'))

plt.title('Noisy at %d dB' % snr)

plt.show()