def reconstruct_map(data, noise_est, layout, psf=None, psf_pcs=None,
psf_coef=None, wavelet_levels=1, wavelet_opt=None,
wave_thresh_factor=1, lowr_thresh_factor=1,
n_reweights=0, mode='all'):
######
# SET THE GRADIENT OPERATOR
if not isinstance(psf, type(None)):
grad_op = FixedPSF(data, psf)
else:
grad_op = PixelVariantPSF(data, psf_pcs, psf_coef)
print ' - Spetral Radius:', grad_op.spec_rad
######
# SET THE LINEAR OPERATOR
# linear_op = LinearCombo([Identity()])
# linear_op = LinearCombo([Wavelet(data.shape, wavelet_levels, wavelet_opt)])
linear_op = LinearCombo([Wavelet(data.shape, wavelet_levels, wavelet_opt),
Identity])
# print linear_op.operators[0].filters.shape
# exit()
######
# ESTIMATE THE NOISE
if not isinstance(psf, type(None)):
noise_est *= norm(convolve_mr_filters(np.rot90(psf, 2), linear_op.operators[0].filters))
# noise_est *= norm(linear_op.operators[0].op(np.rot90(psf, 2)))
noise_est *= np.ones(linear_op.operators[0].filters.shape)
else:
noise_est = np.sqrt(convolve_mr_filters(noise_est,
linear_op.operators[0].filters ** 2))
print noise_est.shape
######
# SET THE WEIGHTS
rw = cwbReweight(wave_thresh_factor * noise_est)
######
# SET RHO, SIGMA AND TAU
l1norm_filters = linear_op.operators[0].l1norm
tau = 1.0 / (grad_op.spec_rad + l1norm_filters)
sigma = tau
rho = 0.5
print ' - 1/tau - sigma||L||^2 >= beta/2:', (1 / tau - sigma *
l1norm_filters ** 2 >=
grad_op.spec_rad / 2)
######
# SET THE SHAPE OF THE DUAL
dual_shape = [linear_op.operators[0].filters.shape[0]] + list(data.shape)
######
# INITALISE THE PRIMAL AND DUAL VALUES
primal = np.ones(data.shape)
# dual = np.array([np.ones(dual_shape)])
dual = np.array([np.ones(dual_shape), np.ones(data.shape)])
grad_op.get_grad(primal)
######
# SET THE PROXIMITY OPERATORS
# prox_op = Identity()
prox_op = Positive()
# prox_dual_op = ProximityCombo([LowRankMatrix(layout, thresh_factor=3,
# grad_class=grad_op,
# grad_factor=1/sigma)])
# prox_dual_op = ProximityCombo([Threshold(rw.weights / sigma)])
prox_dual_op = ProximityCombo([Threshold(rw.weights / sigma),
LowRankMatrix(layout,
thresh_factor=lowr_thresh_factor,
grad_class=grad_op,
grad_factor=1/sigma)])
######
# SET THE COST FUNCTION.
cost_op = costTest(data, grad_op.MX)
# cost_op = posThresh(data, sigma, (grad_op, linear_op), rw.weights)
######
# PERFORM THE OPTIMISATION
opt = Condat(primal, dual, grad_op, prox_op, prox_dual_op, linear_op,
cost_op, sigma=sigma, tau=tau, print_cost=True,
auto_iterate=False)
opt.iterate(max_iter=150)
######
# REWEIGHTING
# for i in range(n_reweights):
#
# rw.reweight(linear_op.op(opt.x_new))
# prox_dual_op.update_weights(rw.weights / sigma)
# cost_op.update_weights(rw.weights)
# opt.iterate()
return opt.x_final
def reconstruct(data, noise_est, layout, psf=None, psf_pcs=None,
psf_coef=None, wavelet_levels=1, wavelet_opt=None,
wave_thresh_factor=1, lowr_thresh_factor=1,
n_reweights=0, mode='all', data_format='cube'):
######
# SET THE GRADIENT OPERATOR
if not isinstance(psf, type(None)):
grad_op = FixedPSF(data, psf, data_format=data_format)
else:
grad_op = PixelVariantPSF(data, psf_pcs, psf_coef,
data_format=data_format)
print ' - Spetral Radius:', grad_op.spec_rad
######
# SET THE LINEAR OPERATOR
if mode == 'all':
linear_op = LinearCombo([Wavelet(data.shape, wavelet_levels,
wavelet_opt, data_format=data_format),
Identity()])
elif mode == 'lowr':
linear_op = LinearCombo([Identity()])
elif mode == 'wave':
linear_op = LinearCombo([Wavelet(data.shape, wavelet_levels,
wavelet_opt, data_format=data_format)])
######
# ESTIMATE THE NOISE
if mode in ('all', 'wave'):
if not isinstance(psf, type(None)):
noise_est *= norm(convolve_mr_filters(np.rot90(psf, 2),
linear_op.operators[0].filters))
# noise_est *= norm(linear_op.operators[0].op(np.rot90(psf, 2)))
if data_format == 'map':
noise_est *= np.ones(linear_op.operators[0].filters.shape)
else:
noise_est *= np.ones([data.shape[0]] +
list(linear_op.operators[0].filters.shape))
else:
noise_est = np.sqrt(convolve_cube(noise_est,
linear_op.operators[0].filters ** 2))
print noise_est.shape
######
# SET THE WEIGHTS
rw = cwbReweight(wave_thresh_factor * noise_est)
######
# SET THE SHAPE OF THE DUAL
dual_shape = [linear_op.operators[0].filters.shape[0]] + list(data.shape)
if data_format == 'cube':
dual_shape[0], dual_shape[1] = dual_shape[1], dual_shape[0]
######
# SET RHO, SIGMA AND TAU
l1norm_filters = linear_op.operators[0].l1norm
tau = 1.0 / (grad_op.spec_rad + l1norm_filters)
sigma = tau
rho = 0.5
print ' - 1/tau - sigma||L||^2 >= beta/2:', (1 / tau - sigma *
l1norm_filters ** 2 >=
grad_op.spec_rad / 2)
######
# INITALISE THE PRIMAL AND DUAL VALUES
# 1 Primal Operator (Positivity or Identity)
primal = np.ones(data.shape)
if mode == 'all':
# 2 Dual Operators (Wavelet + Threshold and Identity + LowRankMatrix)
dual = np.empty(2, dtype=np.ndarray)
dual[0] = np.ones(dual_shape)
dual[1] = np.ones(data.shape)
elif mode == 'lowr':
# 1 Dual Operator (Identity + LowRankMatrix)
dual = np.empty(1, dtype=np.ndarray)
dual[0] = np.ones(data.shape)
elif mode == 'wave':
# 1 Dual Operator (Wavelet + Threshold or Identity + LowRankMatrix)
dual = np.empty(1, dtype=np.ndarray)
dual[0] = np.ones(dual_shape)
# Get the initial gradient value
grad_op.get_grad(primal)
print ' - Primal Variable Shape:', primal.shape
print ' - Dual Variable Shape:', dual.shape
######
# SET THE PROXIMITY OPERATORS
# prox_op = Identity()
prox_op = Positive()
if mode == 'all':
prox_dual_op = ProximityCombo([Threshold(rw.weights / sigma),
LowRankMatrix(layout,
thresh_factor=lowr_thresh_factor,
grad_class=grad_op,
grad_factor=1/sigma,
data_format=data_format)])
elif mode == 'lowr':
prox_dual_op = ProximityCombo([LowRankMatrix(layout,
thresh_factor=lowr_thresh_factor,
grad_class=grad_op,
grad_factor=1/sigma,
data_format=data_format)])
elif mode == 'wave':
prox_dual_op = ProximityCombo([Threshold(rw.weights / sigma),])
######
# SET THE COST FUNCTION.
cost_op = costTest(data, grad_op.MX)
# cost_op = posThresh(data, sigma, (grad_op, linear_op), rw.weights)
######
# PERFORM THE OPTIMISATION
opt = Condat(primal, dual, grad_op, prox_op, prox_dual_op, linear_op,
cost_op, sigma=sigma, tau=tau, print_cost=True,
auto_iterate=False)
opt.iterate(max_iter=150)
######
# REWEIGHTING
# for i in range(n_reweights):
#
# rw.reweight(linear_op.op(opt.x_new))
# prox_dual_op.update_weights(rw.weights / sigma)
# cost_op.update_weights(rw.weights)
# opt.iterate()
return opt.x_final, opt.y_final
