def linear_operator_from_masks(masks, weights=None):
"""Generates the linear operator for the group total variation Nesterov
function from a mask for a 3D image.
Parameters
----------
masks : List of numpy arrays. The mask for each group. Each mask is an
integer (0 or 1) or boolean numpy array or the same shape as the
actual data. The mask does not involve any intercept variables.
weights : List of floats. The weights account for different group sizes,
or incorporates some prior knowledge about the importance of the
groups. Default value is the square roots of the group sizes.
"""
import parsimony.functions.nesterov.tv as tv
if isinstance(masks, tuple):
masks = list(masks)
A = []
G = len(masks)
for g in xrange(G):
mask = masks[g]
if weights is None:
weight = np.sqrt(np.sum(mask))
else:
weight = weights[g]
# Compute group A matrix
Ag = tv.linear_operator_from_subset_mask(mask)
# Include the weights
if weight != 1.0 and weight != 1:
for A_ in Ag:
A_ *= weight
A += Ag
return A
def linear_operator_from_masks(masks, weights=None):
"""Generates the linear operator for the group total variation Nesterov
function from a mask for a 3D image.
Parameters
----------
masks : List of numpy arrays. The mask for each group. Each mask is an
integer (0 or 1) or boolean numpy array or the same shape as the
actual data. The mask does not involve any intercept variables.
weights : List of floats. The weights account for different group sizes,
or incorporates some prior knowledge about the importance of the
groups. Default value is the square roots of the group sizes.
"""
import parsimony.functions.nesterov.tv as tv
if isinstance(masks, tuple):
masks = list(masks)
A = []
G = len(masks)
for g in xrange(G):
mask = masks[g]
if weights is None:
weight = np.sqrt(np.sum(mask))
else:
weight = weights[g]
# Compute group A matrix
Ag = tv.linear_operator_from_subset_mask(mask)
# Include the weights
if weight != 1.0 and weight != 1:
for A_ in Ag:
A_ *= weight
A += Ag
return A
def linear_operator_from_rects(rects, shape, weights=None):
"""Generates the linear operator for the group total variation Nesterov
function from the rectange of a 3D image.
Parameters
----------
rects : List of lists or tuples with 2-, 4- or 6-tuple elements. The shape
of the patch of the 1D, 2D or 3D image to smooth. The elements of
rects has the form ((x1, x2),), ((y1, y2), (x1, x2)) or ((z1, z2),
(y1, y2), (x1, x2)), where z is the "layers", y rows and x is the
columns and x1 means the first column to include, x2 is one beyond
the last column to include, and similarly for y and z. The rect
does not involve any intercept variables.
shape : List or tuple with 1, 2 or 3 integers. The shape of the 1D, 2D or
3D image. shape has the form (X,), (Y, X) or (Z, Y, X), where Z is
the number of "layers", Y is the number of rows and X is the number
of columns. The shape does not involve any intercept variables.
weights : List of floats. The weights account for different group sizes,
or incorporates some prior knowledge about the importance of the
groups. Default value is the square roots of the group sizes.
"""
import parsimony.functions.nesterov.tv as tv
A = []
G = len(rects)
for g in xrange(G):
rect = rects[g]
if len(rect) == 1:
rect = [(0, 1), (0, 1), rect[0]]
elif len(rect) == 2:
rect = [(0, 1), rect[0], rect[1]]
while len(shape) < 3:
shape = tuple([1] + list(shape))
mask = np.zeros(shape, dtype=bool)
z1 = rect[0][0]
z2 = rect[0][1]
y1 = rect[1][0]
y2 = rect[1][1]
x1 = rect[2][0]
x2 = rect[2][1]
mask[z1:z2, y1:y2, x1:x2] = True
if weights is None:
weight = np.sqrt(np.sum(mask))
else:
weight = weights[g]
# Compute group A matrix
Ag = tv.linear_operator_from_subset_mask(mask)
# Include the weights
if weight != 1.0 and weight != 1:
for A_ in Ag:
A_ *= weight
A += Ag
return A
def linear_operator_from_rects(rects, shape, weights=None):
"""Generates the linear operator for the group total variation Nesterov
function from the rectange of a 3D image.
Parameters
----------
rects : List of lists or tuples with 2-, 4- or 6-tuple elements. The shape
of the patch of the 1D, 2D or 3D image to smooth. The elements of
rects has the form ((x1, x2),), ((y1, y2), (x1, x2)) or ((z1, z2),
(y1, y2), (x1, x2)), where z is the "layers", y rows and x is the
columns and x1 means the first column to include, x2 is one beyond
the last column to include, and similarly for y and z. The rect
does not involve any intercept variables.
shape : List or tuple with 1, 2 or 3 integers. The shape of the 1D, 2D or
3D image. shape has the form (X,), (Y, X) or (Z, Y, X), where Z is
the number of "layers", Y is the number of rows and X is the number
of columns. The shape does not involve any intercept variables.
weights : List of floats. The weights account for different group sizes,
or incorporates some prior knowledge about the importance of the
groups. Default value is the square roots of the group sizes.
"""
import parsimony.functions.nesterov.tv as tv
A = []
G = len(rects)
for g in xrange(G):
rect = rects[g]
if len(rect) == 1:
rect = [(0, 1), (0, 1), rect[0]]
elif len(rect) == 2:
rect = [(0, 1), rect[0], rect[1]]
while len(shape) < 3:
shape = tuple([1] + list(shape))
mask = np.zeros(shape, dtype=bool)
z1 = rect[0][0]
z2 = rect[0][1]
y1 = rect[1][0]
y2 = rect[1][1]
x1 = rect[2][0]
x2 = rect[2][1]
mask[z1:z2, y1:y2, x1:x2] = True
if weights is None:
weight = np.sqrt(np.sum(mask))
else:
weight = weights[g]
# Compute group A matrix
Ag = tv.linear_operator_from_subset_mask(mask)
# Include the weights
if weight != 1.0 and weight != 1:
for A_ in Ag:
A_ *= weight
A += Ag
return A
