RF: Simplify high-pass filtering in algorithms.confounds

Legendre and cosine detrending are implemented almost identically,
although with several minor variations. Here I separate regressor
creation from detrending to unify the implementations.

This now uses `np.linalg.pinv(X)` to estimate the betas in both cases,
rather than using `np.linalg.lstsq` in the cosine filter. lstsq uses SVD
and can thus fail to converge in rare cases. Under no circumstances
should (X.T @ X) be singular, so the pseudoinverse is unique and
precisely what we want.

nipype/algorithms/confounds.py

@@ -1185,31 +1185,61 @@ def is_outlier(points, thresh=3.5):
     return timepoints_to_discard
 
 
-def cosine_filter(
-    data, timestep, period_cut, remove_mean=True, axis=-1, failure_mode="error"
+def _make_cosine_regressors(ntimepoints, timestep, period_cut):
+    return _full_rank(_cosine_drift(period_cut, timestep * np.arange(ntimepoints)))[0]
+
+
+def _make_legendre_regressors(ntimepoints, degree):
+    X = np.ones((ntimepoints, 1))  # quick way to calc degree 0
+    for i in range(degree):
+        polynomial_func = Legendre.basis(i + 1)
+        value_array = np.linspace(-1, 1, ntimepoints)
+        X = np.hstack((X, polynomial_func(value_array)[:, np.newaxis]))
+    return X
+
+
+def _high_pass_filter(
+    data, *args, filter_type, remove_mean=True, axis=-1, failure_mode="error"
 ):
     datashape = data.shape
     timepoints = datashape[axis]
     if datashape[0] == 0 and failure_mode != "error":
         return data, np.array([])
 
-    data = data.reshape((-1, timepoints))
+    filters = {
+        'cosine': _make_cosine_regressors,
+        'legendre': _make_legendre_regressors,
+    }
 
-    frametimes = timestep * np.arange(timepoints)
-    X = _full_rank(_cosine_drift(period_cut, frametimes))[0]
+    X = filters[filter_type](timepoints, *args)
     non_constant_regressors = X[:, :-1] if X.shape[1] > 1 else np.array([])
 
-    betas = np.linalg.lstsq(X, data.T)[0]
+    data = data.reshape((-1, timepoints))
+
+    betas = np.linalg.pinv(X) @ data.T
 
     if not remove_mean:
         X = X[:, :-1]
         betas = betas[:-1]
 
-    residuals = data - X.dot(betas).T
-
+    residuals = data - (X @ betas).T
     return residuals.reshape(datashape), non_constant_regressors
 
 
+def cosine_filter(
+    data, timestep, period_cut, remove_mean=True, axis=-1, failure_mode="error"
+):
+    return _high_pass_filter(
+        data,
+        timestep,
+        period_cut,
+        filter_type='cosine',
+        remove_mean=remove_mean,
+        axis=axis,
+        failure_mode=failure_mode,
+    )
+
+
 def regress_poly(degree, data, remove_mean=True, axis=-1, failure_mode="error"):
     """
     Returns data with degree polynomial regressed out.
@@ -1221,36 +1251,14 @@ def regress_poly(degree, data, remove_mean=True, axis=-1, failure_mode="error"):
     IFLOGGER.debug(
         "Performing polynomial regression on data of shape %s", str(data.shape)
     )
-
-    datashape = data.shape
-    timepoints = datashape[axis]
-    if datashape[0] == 0 and failure_mode != "error":
-        return data, np.array([])
-
-    # Rearrange all voxel-wise time-series in rows
-    data = data.reshape((-1, timepoints))
-
-    # Generate design matrix
-    X = np.ones((timepoints, 1))  # quick way to calc degree 0
-    for i in range(degree):
-        polynomial_func = Legendre.basis(i + 1)
-        value_array = np.linspace(-1, 1, timepoints)
-        X = np.hstack((X, polynomial_func(value_array)[:, np.newaxis]))
-
-    non_constant_regressors = X[:, :-1] if X.shape[1] > 1 else np.array([])
-
-    # Calculate coefficients
-    betas = np.linalg.pinv(X).dot(data.T)
-
-    # Estimation
-    if remove_mean:
-        datahat = X.dot(betas).T
-    else:  # disregard the first layer of X, which is degree 0
-        datahat = X[:, 1:].dot(betas[1:, ...]).T
-    regressed_data = data - datahat
-
-    # Back to original shape
-    return regressed_data.reshape(datashape), non_constant_regressors
+    return _high_pass_filter(
+        data,
+        degree,
+        filter_type='legendre',
+        remove_mean=remove_mean,
+        axis=axis,
+        failure_mode=failure_mode,
+    )
 
 
 def combine_mask_files(mask_files, mask_method=None, mask_index=None):