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@miykael
Last active October 23, 2018 09:31
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Showcase for test for new `nilearn.signal.clean` implementation
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exploration of the test function for `nilearn.signal.clean`\n",
"\n",
"This is to explore the test function for `nilearn.signal.clean`, if temporal filters and confound removal is selected."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Creation of test data"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from scipy.signal import welch"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create signal\n",
"n_samples = 100\n",
"\n",
"sx = np.array([np.sin(np.linspace(0, 100, n_samples) * 1.5),\n",
" np.sin(np.linspace(0, 100, n_samples) * 3.),\n",
" np.sin(np.linspace(0, 100, n_samples) / 8.),\n",
" ])\n",
"plt.plot(sx.T);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Validate new test function\n",
"\n",
"The idea of the new test function is as follows. If we apply temporal filters to the signal and to the confounds before confound removal, than the power spectrum density for the removed frequency should be almost zero. If the confounds are not temporally filtered, they should reintroduce some of the filtered frequency.\n",
"\n",
"For this to test, let's create a simplified copy of the `clean` function and add the possibility of temporally filtering the confounds."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/line/anaconda3/lib/python3.6/site-packages/scipy/signal/spectral.py:1773: UserWarning: nperseg = 256 is greater than input length = 100, using nperseg = 100\n",
" .format(nperseg, input_length))\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot power spectrum density\n",
"f, Pxx_den = welch(sx, fs=1.0)\n",
"plt.plot(f, Pxx_den.T)\n",
"plt.xlabel('frequency [Hz]')\n",
"plt.ylabel('PSD [V**2/Hz]');"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from nilearn.tests.test_signal import generate_signals\n",
"from nilearn import signal as nisignal\n",
"from scipy import linalg"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def test_clean_frequencies_and_confounds(sx, low_pass=None, high_pass=None, new_approach=False):\n",
"\n",
" # Specify filter criterias\n",
" signals = np.copy(sx.T)\n",
" n_samples = signals.shape[0]\n",
" t_r = 1.0\n",
" standardize=False\n",
" detrend=False\n",
"\n",
" # Create confounds\n",
" _, _, confounds = generate_signals(length=n_samples, n_confounds=10, n_features=10)\n",
"\n",
"\n",
" # Perform new filtering\n",
"\n",
" # detrend\n",
" signals = nisignal._standardize(signals, normalize=False, detrend=detrend)\n",
"\n",
" # Apply low- and high-pass filters\n",
" if low_pass is not None or high_pass is not None:\n",
"\n",
" signals = nisignal.butterworth(signals, sampling_rate=1. / t_r,\n",
" low_pass=low_pass, high_pass=high_pass)\n",
"\n",
" # Remove confounds\n",
" if confounds is not None:\n",
"\n",
" if new_approach:\n",
" # Apply low- and high-pass filters to keep filters orthogonal\n",
" # (according to Lindquist et al. (2018))\n",
" if low_pass is not None or high_pass is not None:\n",
"\n",
" confounds = nisignal.butterworth(confounds, sampling_rate=1. / t_r,\n",
" low_pass=low_pass, high_pass=high_pass)\n",
"\n",
" confounds = nisignal._standardize(confounds, normalize=standardize,\n",
" detrend=detrend)\n",
"\n",
" if not standardize:\n",
" # Improve numerical stability by controlling the range of\n",
" # confounds. We don't rely on _standardize as it removes any\n",
" # constant contribution to confounds.\n",
" confound_max = np.max(np.abs(confounds), axis=0)\n",
" confound_max[confound_max == 0] = 1\n",
" confounds /= confound_max\n",
"\n",
" # Pivoting in qr decomposition was added in scipy 0.10\n",
" Q, R, _ = linalg.qr(confounds, mode='economic', pivoting=True)\n",
" Q = Q[:, np.abs(np.diag(R)) > np.finfo(np.float).eps * 100.]\n",
" signals -= Q.dot(Q.T).dot(signals)\n",
"\n",
" return signals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test old a new approach with low_pass filter only"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/line/anaconda3/lib/python3.6/site-packages/scipy/signal/spectral.py:1773: UserWarning: nperseg = 256 is greater than input length = 100, using nperseg = 100\n",
" .format(nperseg, input_length))\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.8476361229087643e-07\n",
"0.08971383946169231\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"low_pass = 0.1\n",
"high_pass = None\n",
"signals_new = test_clean_frequencies_and_confounds(sx, low_pass, high_pass, new_approach=True)\n",
"signals_old = test_clean_frequencies_and_confounds(sx, low_pass, high_pass, new_approach=False)\n",
"\n",
"# Plotting of power spectrum of new approach\n",
"f, Pxx_den_new = welch(np.mean(signals_new.T, axis=0), fs=1.0)\n",
"plt.plot(f, Pxx_den_new.T)\n",
"\n",
"# Plotting of power spectrum of old approach\n",
"f, Pxx_den_old = welch(np.mean(signals_old.T, axis=0), fs=1.0)\n",
"plt.plot(f, Pxx_den_old.T)\n",
"\n",
"plt.xlabel('frequency [Hz]')\n",
"plt.ylabel('PSD [V**2/Hz]')\n",
"plt.legend(['new', 'old'])\n",
"\n",
"# Verifying that values above 2 * low_pass are zero\n",
"print(np.sum(Pxx_den_new[f >= low_pass * 2]))\n",
"print(np.sum(Pxx_den_old[f >= low_pass * 2]))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.776521225455978e-08\n",
"0.14744215701973218\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/line/anaconda3/lib/python3.6/site-packages/scipy/signal/spectral.py:1773: UserWarning: nperseg = 256 is greater than input length = 100, using nperseg = 100\n",
" .format(nperseg, input_length))\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"low_pass = None\n",
"high_pass = 0.4\n",
"signals_new = test_clean_frequencies_and_confounds(sx, low_pass, high_pass, new_approach=True)\n",
"signals_old = test_clean_frequencies_and_confounds(sx, low_pass, high_pass, new_approach=False)\n",
"\n",
"# Plotting of power spectrum of new approach\n",
"f, Pxx_den_new = welch(np.mean(signals_new.T, axis=0), fs=1.0)\n",
"plt.plot(f, Pxx_den_new.T)\n",
"\n",
"# Plotting of power spectrum of old approach\n",
"f, Pxx_den_old = welch(np.mean(signals_old.T, axis=0), fs=1.0)\n",
"plt.plot(f, Pxx_den_old.T)\n",
"\n",
"plt.xlabel('frequency [Hz]')\n",
"plt.ylabel('PSD [V**2/Hz]')\n",
"plt.legend(['new', 'old'])\n",
"\n",
"# Verifying that values above 2 * low_pass are zero\n",
"print(np.sum(Pxx_den_new[f <= high_pass / 2.]))\n",
"print(np.sum(Pxx_den_old[f <= high_pass / 2.]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Conclusion\n",
"\n",
"Therefore, if we test both low- and high-pass filtering for a value below 1-e4, that should work."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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