# Calculate complex reordering
idx_bu = bulk_up(prior, sparsify, unsparsify, k)
idx_bu = idx_bu + 1j * idx_bu
pbar.update()
reorder_bu = lambda x: idx_bu
# Calculate real/imag reordering
idx_r = whittle_down(prior.real, sparsify, unsparsify, 1 - k)
pbar.update()
idx_i = whittle_down(prior.imag, sparsify, unsparsify, 1 - k)
pbar.update()
idx_wd = idx_r + 1j * idx_i
reorder_wd = lambda x: idx_wd
# Do 2d reordering
_, reordering_r = sort2d(prior.real)
_, reordering_i = sort2d(prior.imag)
idx_ro = reordering_r + 1j * reordering_i
reorder_ro = lambda x: idx_ro
## Col/row-wise seem to do the best in general.
# Column wise reordering
idx_r = colwise(prior.real)
idx_i = colwise(prior.imag)
idx_cw = idx_r + 1j * idx_i
reorder_cw = lambda x: idx_cw
# Row wise reordering
idx_r = rowwise(prior.real)
idx_i = rowwise(prior.imag)
idx_rw = idx_r + 1j * idx_i
inverse_fun=lambda x0: np.fft.ifft2(x0), #uft.inverse,
sparsify=sparsify,
unsparsify=unsparsify,
reorder_fun=None,
alpha=.05,
thresh_sep=thresh_sep,
x=im,
ignore_residual=ignore_residual,
ignore_mse=ignore_mse,
ignore_ssim=ignore_ssim,
disp=disp,
maxiter=maxiter,
strikes=strikes)
# Do recon doing 2d monotonic sort
idx_mono = sort2d(recon.real)[1] + 1j * (sort2d(recon.imag)[1])
# from mr_utils.utils import avg_patch_vals as avp
# idx_mono_r = sort2d(avp(recon.real))[1]
# idx_mono_i = sort2d(avp(recon.imag))[1]
# idx_mono = idx_mono_r + 1j*idx_mono_i
recon_mono = proximal_GD(
kspace_u.copy(),
forward_fun=lambda x0: np.fft.fft2(x0) * samp, #uft.forward,
inverse_fun=lambda x0: np.fft.ifft2(x0), #uft.inverse,
sparsify=sparsify,
unsparsify=unsparsify,
reorder_fun=lambda x0: idx_mono,
alpha=.03,
thresh_sep=thresh_sep,
x=im,
ignore_residual=ignore_residual,
print(res)
# assert not np.allclose(res['x'], cs[idx])
H3 = make_hist(res['x'], idx)
# We can get a bit closer with clever choice of histogram metric
plt.plot(H1, '--', label='Target')
plt.plot(H2, '.', label='Truncated')
plt.plot(H3, '.', label='Fit')
plt.legend()
plt.show()
# Could we pick better indices? Try sorting in 2-dimensions, then
# truncating. Obviously, the histograms between sorted and unsorted x will
# be the same
from mr_utils.utils.sort2d import sort2d
x_2d, idx_2d = sort2d(x)
wvlt_2d = T(x_2d).flatten()
assert np.count_nonzero(wvlt_2d) > k, \
'We are trying to do better than sort2d!'
idx = np.argsort(-np.abs(wvlt_2d))[:k]
cs = wvlt_2d[idx]
H4 = make_hist(cs, idx)
plt.plot(H1)
plt.plot(H4)
plt.show()
# Try the same tuning technique
x0 = cs.copy()
res = least_squares(
lambda y: H_metric(H1, make_hist(y, idx), H_metrics[h_met]), x0)
print(res)
def reorder_every_iter(x_hat):
'''Update reordering every iteration based on current estimate.'''
_, reordering_r = sort2d(x_hat.real)
_, reordering_i = sort2d(x_hat.imag)
return reordering_r + 1j * reordering_i
def reorder_once(_x_hat):
'''True reordering.'''
_, reordering_r = sort2d(uft.inverse_ortho(y).real)
_, reordering_i = sort2d(uft.inverse_ortho(y).imag)
reordering = reordering_r + 1j * reordering_i
return reordering
def true_reorder(_x_hat):
'''True reordering.'''
_, reordering_r = sort2d(x.real)
_, reordering_i = sort2d(x.imag)
reordering = reordering_r + 1j * reordering_i
return reordering
unsparsify,
reorder_fun=None,
mode='soft',
alpha=alpha0,
thresh_sep=True,
selective=None,
x=x,
ignore_residual=False,
disp=True,
maxiter=500)
view(recon_none)
if 'monosort' in run:
# We need to find the best alpha for the monotonically sorted
# recon, use the recon_none as the CS reconstruction prior
_, reordering_r = sort2d(recon_none.real)
_, reordering_i = sort2d(recon_none.imag)
idx_ro = reordering_r + 1j * reordering_i
monosort = lambda x: idx_ro
# alpha = 0.05
# pGD = partial(
# proximal_GD, y=kspace_u, forward_fun=uft.forward_ortho,
# inverse_fun=uft.inverse_ortho, sparsify=sparsify,
# unsparsify=unsparsify, reorder_fun=monosort,
# mode='soft', thresh_sep=True, selective=None, x=x,
# ignore_residual=False, disp=False, maxiter=200)
# obj = lambda alpha0: compare_mse(
# np.abs(x), np.abs(pGD(alpha=alpha0)))
# res = minimize(obj, alpha0)
# print(res)
# # Best alpha0 = 0.09299786 for 500 iterations, N=64
def GD_TV(y,
forward_fun,
inverse_fun,
alpha=.5,
lam=.01,
do_reordering=False,
x=None,
ignore_residual=False,
disp=False,
maxiter=200):
r'''Gradient descent for a generic encoding model and TV constraint.
Parameters
==========
y : array_like
Measured data (i.e., y = Ax).
forward_fun : callable
A, the forward transformation function.
inverse_fun : callable
A^H, the inverse transformation function.
alpha : float, optional
Step size.
lam : float, optional
TV constraint weight.
do_reordering : bool, optional
Whether or not to reorder for sparsity constraint.
x : array_like, optional
The true image we are trying to reconstruct.
ignore_residual : bool, optional
Whether or not to break out of loop if resid increases.
disp : bool, optional
Whether or not to display iteration info.
maxiter : int, optional
Maximum number of iterations.
Returns
=======
x_hat : array_like
Estimate of x.
Notes
=====
Solves the problem:
.. math::
\min_x || y - Ax ||^2_2 + \lambda \text{TV}(x)
If `x=None`, then MSE will not be calculated.
'''
# Make sure compare_mse is defined
if x is None:
compare_mse = lambda xx, yy: 0
logging.info('No true x provided, MSE will not be calculated.')
xabs = 0
else:
from skimage.measure import compare_mse
xabs = np.abs(x) # Precompute absolute value of true image
# Get the reordering indicies ready, both for real and imag parts
if do_reordering:
from mr_utils.utils.sort2d import sort2d
from mr_utils.utils.orderings import inverse_permutation
_, reordering_r = sort2d(x.real)
_, reordering_i = sort2d(x.imag)
inverse_reordering_r = inverse_permutation(reordering_r)
inverse_reordering_i = inverse_permutation(reordering_i)
# Get some display stuff happening
if disp:
from mr_utils.utils.printtable import Table
table = Table(['iter', 'norm', 'MSE'], [len(repr(maxiter)), 8, 8],
['d', 'e', 'e'])
hdr = table.header()
for line in hdr.split('\n'):
logging.info(line)
# Initialize
x_hat = np.zeros(y.shape, dtype=y.dtype)
r = -y.copy()
prev_stop_criteria = np.inf
norm_y = np.linalg.norm(y)
# Do the thing
for ii in range(int(maxiter)):
# Fidelity term
fidelity = inverse_fun(r)
# Let's reorder if we said that was going to be a thing
if do_reordering:
# real part
xr = x_hat.real.flatten()[reordering_r].reshape(x.shape)
second_term_r = dTV(xr).flatten()[inverse_reordering_r] \
.reshape(x.shape)
# imag part
xi = x_hat.imag.flatten()[reordering_i].reshape(x.shape)
second_term_i = dTV(xi).flatten()[inverse_reordering_i] \
.reshape(x.shape)
# put it all together...
second_term = second_term_r + 1j * second_term_i
else:
# Sparsity term
second_term = dTV(x_hat)
# Compute stop criteria
stop_criteria = np.linalg.norm(r) / norm_y
if not ignore_residual and stop_criteria > prev_stop_criteria:
logging.warning(('Breaking out of loop after %d iterations. '
'Norm of residual increased!'), ii)
break
prev_stop_criteria = stop_criteria
# Take the step
x_hat -= alpha * (fidelity + lam * second_term)
# Tell the user what happened
if disp:
logging.info(
table.row(
[ii, stop_criteria,
compare_mse(np.abs(x_hat), xabs)]))
# Compute residual
r = forward_fun(x_hat) - y
return x_hat