def landweber(A, W, y, mu=1., nu=None, threshold=thresholding.hard, x0=None,
maxiter=100, callback=None):
"""Landweber algorithm
Input
-----
A : measurement matrix
W : wavelet transform
y : data
mu : step of the gradient update
nu : thresholding coefficient
threshold : thresholding function
maxiter : number of iterations
callback : callback function
Output
------
x : solution
"""
if callback is None:
callback = lo.CallbackFactory(verbose=True)
if x0 is None:
x = A.T * y
else:
x = copy(x0)
for iter_ in xrange(maxiter):
r = A * x - y
x += .5 * mu * A.T * (r)
x = W.T * threshold(W * x, nu)
resid = lo.norm2(r) + 1 / (2 * nu) * lo.normp(p=1)(x)
callback(x)
return x
def fista(A,
W,
y,
mu=1.,
nu=None,
threshold=thresholding.hard,
x0=None,
maxiter=100,
callback=None):
""" Fista algorithm
"""
if callback is None:
callback = lo.CallbackFactory(verbose=True)
if x0 is None:
x = A.T * y
else:
x = copy(x0)
x_old = np.zeros(x.shape)
t_old = 1.
for iter_ in xrange(maxiter):
t = (1 + np.sqrt(1 + 4 * t_old**2)) / 2
a = (t_old - 1) / t
t_old = copy(t)
z = x + a * (x - x_old)
g = A.T * (A * z - y)
x = z - .5 * mu * g
x = W.T * threshold(W * x, nu)
x_old = copy(x)
resid = lo.norm2(A * x - y) + 1 / (2 * nu) * lo.normp(p=1)(x)
callback(x)
return x
def fista(A, W, y, mu=1., nu=None, threshold=thresholding.hard, x0=None,
maxiter=100, callback=None):
""" Fista algorithm
"""
if callback is None:
callback = lo.CallbackFactory(verbose=True)
if x0 is None:
x = A.T * y
else:
x = copy(x0)
x_old = np.zeros(x.shape)
t_old = 1.
for iter_ in xrange(maxiter):
t = (1 + np.sqrt(1 + 4 * t_old ** 2)) / 2
a = (t_old - 1) / t
t_old = copy(t)
z = x + a * (x - x_old)
g = A.T * (A * z - y)
x = z - .5 * mu * g
x = W.T * threshold(W * x, nu)
x_old = copy(x)
resid = lo.norm2(A * x - y) + 1 / (2 * nu) * lo.normp(p=1)(x)
callback(x)
return x
def landweber(A,
W,
y,
mu=1.,
nu=None,
threshold=thresholding.hard,
x0=None,
maxiter=100,
callback=None):
"""Landweber algorithm
Input
-----
A : measurement matrix
W : wavelet transform
y : data
mu : step of the gradient update
nu : thresholding coefficient
threshold : thresholding function
maxiter : number of iterations
callback : callback function
Output
------
x : solution
"""
if callback is None:
callback = lo.CallbackFactory(verbose=True)
if x0 is None:
x = A.T * y
else:
x = copy(x0)
for iter_ in xrange(maxiter):
r = A * x - y
x += .5 * mu * A.T * (r)
x = W.T * threshold(W * x, nu)
resid = lo.norm2(r) + 1 / (2 * nu) * lo.normp(p=1)(x)
callback(x)
return x