ENH: Add gaussian process DWI signal representation notebooks

Add gaussian process DWI signal representation notebooks:
- One of the notebooks uses a simulated DWI signal.
- The second notebook uses a real DWI signal.

Author: jhlegarreta

docs/notebooks/dwi_gp.ipynb

@@ -0,0 +1,186 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Gaussian process notebook",
+   "id": "486923b289155658"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "import tempfile\n",
+    "from pathlib import Path\n",
+    "\n",
+    "import numpy as np\n",
+    "from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel\n",
+    "\n",
+    "from eddymotion import model\n",
+    "from eddymotion.data.dmri import DWI\n",
+    "from eddymotion.data.splitting import lovo_split\n",
+    "\n",
+    "datadir = Path(\"../../test\")  # Adapt to your local path or download to a temp location using wget\n",
+    "\n",
+    "kernel = DotProduct() + WhiteKernel()\n",
+    "\n",
+    "dwi = DWI.from_filename(datadir / \"dwi.h5\")\n",
+    "\n",
+    "_dwi_data = dwi.dataobj\n",
+    "# Use a subset of the data for now to see that something is written to the\n",
+    "# output\n",
+    "# bvecs = dwi.gradients[:3, :].T\n",
+    "bvecs = dwi.gradients[:3, 10:13].T  # b0 values have already been masked\n",
+    "# bvals = dwi.gradients[3:, 10:13].T  # Only for inspection purposes: [[1005.], [1000.], [ 995.]]\n",
+    "dwi_data = _dwi_data[60:63, 60:64, 40:45, 10:13]\n",
+    "\n",
+    "# ToDo\n",
+    "# Provide proper values/estimates for these\n",
+    "a = 1\n",
+    "h = 1  # should be a NIfTI image\n",
+    "\n",
+    "num_iterations = 5\n",
+    "gp = model.GaussianProcessModel(\n",
+    "    dwi=dwi, a=a, h=h, kernel=kernel, num_iterations=num_iterations\n",
+    ")\n",
+    "indices = list(range(bvecs.shape[0]))\n",
+    "# ToDo\n",
+    "# This should be done within the GP model class\n",
+    "# Apply lovo strategy properly\n",
+    "# Vectorize and parallelize\n",
+    "result_mean = np.zeros_like(dwi_data)\n",
+    "result_stddev = np.zeros_like(dwi_data)\n",
+    "for idx in indices:\n",
+    "    lovo_idx = np.ones(len(indices), dtype=bool)\n",
+    "    lovo_idx[idx] = False\n",
+    "    X = bvecs[lovo_idx]\n",
+    "    for i in range(dwi_data.shape[0]):\n",
+    "        for j in range(dwi_data.shape[1]):\n",
+    "            for k in range(dwi_data.shape[2]):\n",
+    "                # ToDo\n",
+    "                # Use a mask to avoid traversing background data\n",
+    "                y = dwi_data[i, j, k, lovo_idx]\n",
+    "                gp.fit(X, y)\n",
+    "                pred_mean, pred_stddev = gp.predict(\n",
+    "                    bvecs[idx, :][np.newaxis]\n",
+    "                )  # Can take multiple values X[:2, :]\n",
+    "                result_mean[i, j, k, idx] = pred_mean.item()\n",
+    "                result_stddev[i, j, k, idx] = pred_stddev.item()"
+   ],
+   "id": "da2274009534db61",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Plot the data",
+   "id": "77e77cd4c73409d3"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "from matplotlib import pyplot as plt \n",
+    "%matplotlib inline\n",
+    "\n",
+    "s = dwi_data[1, 1, 2, :]\n",
+    "s_hat_mean = result_mean[1, 1, 2, :]\n",
+    "s_hat_stddev = result_stddev[1, 1, 2, :]\n",
+    "x = np.asarray(indices)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "ax.plot(x, s_hat_mean, c=\"orange\", label=\"predicted\")\n",
+    "plt.fill_between(\n",
+    "    x.ravel(),\n",
+    "    s_hat_mean - 1.96 * s_hat_stddev,\n",
+    "    s_hat_mean + 1.96 * s_hat_stddev,\n",
+    "    alpha=0.5,\n",
+    "    color=\"orange\",\n",
+    "    label=r\"95% confidence interval\",\n",
+    ")\n",
+    "plt.scatter(x, s, c=\"b\", label=\"ground truth\")\n",
+    "ax.set_xlabel(\"bvec indices\")\n",
+    "ax.set_ylabel(\"signal\")\n",
+    "ax.legend()\n",
+    "plt.title(\"Gaussian process regression on dataset\")\n",
+    "\n",
+    "plt.show()"
+   ],
+   "id": "4e51f22890fb045a",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "Plot the DWI signal for a given voxel\n",
+    "Compute the DWI signal value wrt the b0 (how much larger/smaller is and add that delta to the unit sphere?) for each bvec direction and plot that?"
+   ],
+   "id": "694a4c075457425d"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "# from mpl_toolkits.mplot3d import Axes3D\n",
+    "# fig, ax = plt.subplots()\n",
+    "# ax = fig.add_subplot(111, projection='3d')\n",
+    "# plt.scatter(xx, yy, zz)"
+   ],
+   "id": "bb7d2aef53ac99f0",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Plot the DWI signal brain data\n",
+   "id": "62d7bc609b65c7cf"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": "# plot_dwi(dmri_dataset.dataobj, dmri_dataset.affine, gradient=data_test[1], black_bg=True)",
+   "id": "edb0e9d255516e38",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "Plot the predicted DWI signal",
+   "id": "1a52e2450fc61dc6"
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": "# plot_dwi(predicted, dmri_dataset.affine, gradient=data_test[1], black_bg=True);",
+   "id": "66150cf337b395e0",
+   "outputs": [],
+   "execution_count": null
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}