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
import lo.pywt_lo as pywt_lo
# data
pacs = PacsObservation(filename=tamasis_dir + 'tests/frames_blue.fits',
fine_sampling_factor=1,
keep_bad_detectors=False)
tod = pacs.get_tod()
# projector
projection = Projection(pacs,
resolution=3.2,
oversampling=False,
npixels_per_sample=6)
model = projection
# naive map
backmap = model.transpose(tod)
# mask
M = lo.mask(backmap < 0).T
#M = lo.identity(2 * (backmap.size,))
# transform to lo
P = lo.aslinearoperator(model.aslinearoperator()) * M
# prior
Dx = lo.diff(backmap.shape, axis=0, dtype=np.float64) * M
Dy = lo.diff(backmap.shape, axis=1, dtype=np.float64) * M
Dw = pywt_lo.wavelet2(backmap.shape, "haar") * M
# inversion
y = tod.flatten()
callback = lo.CallbackFactory(verbose=True)
x = it.rirls(P, (Dx, Dy, Dw), y, p=1.5, maxiter=100, callback=callback)
sol = backmap.zeros(backmap.shape)
sol[:] = (M * x).reshape(sol.shape)