def quantitative_fm(Mxys, dfs, T1s, T2s, PDs, TR, alpha, phase_cyc, mask=None):
'''Find field map given quantitative maps.
'''
resps = {}
orig_size = np.asarray(T1s).shape
if mask is None:
mask = np.ones(Mxys.shape)
Mxys = np.asarray(Mxys).flatten()
T1s = np.asarray(T1s).flatten()
T2s = np.asarray(T2s).flatten()
PDs = np.asarray(PDs).flatten()
mask = np.asarray(mask).flatten()
fm = np.zeros(Mxys.size)
for ii in range(Mxys.size):
if mask[ii]:
# Cache results for later in case we come across the same T1,T2,PD
if (PDs[ii], T1s[ii], T2s[ii]) not in resps:
resps[(PDs[ii], T1s[ii],
T2s[ii])] = get_df_responses(T1s[ii], T2s[ii], PDs[ii],
TR, alpha, phase_cyc, dfs)
# Find the appropriate off-resonance value for this T1,T2,PD,Mxy
idx, val = find_nearest(resps[(PDs[ii], T1s[ii], T2s[ii])],
Mxys[ii])
fm[ii] = dfs[idx]
else:
fm[ii] = 0
return (fm.reshape(orig_size))
def quantitative_fm(Mxys, dfs, T1s, T2s, PDs, TR, alpha, phase_cyc, mask=None):
'''Find field map given quantitative maps.
Parameters
==========
Mxys : array_like
Complex transverse signal we measure.
dfs : array_like
Off-resonance values to simulate over.
T1s : array_like
scalar T1 longitudinal recovery value in seconds.
T2s : array_like
scalar T2 transverse decay value in seconds.
PDs : array_like
scalar proton density value scaled the same as acquisiton.
TR : float
Repetition time in seconds.
alpha : float
Flip angle in radians.
phase_cyc : float
RF phase cycling in radians.
mask : array_like
Boolean mask to tell which pixels we should compute df for.
Returns
=======
fm : array_like
Field map.
'''
resps = {}
orig_size = np.asarray(T1s).shape
if mask is None:
mask = np.ones(Mxys.shape)
Mxys = np.asarray(Mxys).flatten()
T1s = np.asarray(T1s).flatten()
T2s = np.asarray(T2s).flatten()
PDs = np.asarray(PDs).flatten()
mask = np.asarray(mask).flatten()
fm = np.zeros(Mxys.size)
for ii in range(Mxys.size):
if mask[ii]:
# Cache results for later in case we come across the same T1,T2,PD
if (PDs[ii], T1s[ii], T2s[ii]) not in resps:
resps[(PDs[ii], T1s[ii],
T2s[ii])] = get_df_responses(T1s[ii], T2s[ii], PDs[ii],
TR, alpha, phase_cyc, dfs)
# Find the appropriate off-resonance value for this T1,T2,PD,Mxy
idx, _val = find_nearest(resps[(PDs[ii], T1s[ii], T2s[ii])],
Mxys[ii])
fm[ii] = dfs[idx]
else:
fm[ii] = 0
return fm.reshape(orig_size)
def random_match_by_col(x, T, return_sorted=False):
'''Given matrix T, choose reordering of x that matches it col by col.
Parameters
==========
x : array_like
Array to find ordering of.
T : array_like
Target matrix.
return_sorted : bool, optional
Whether or not to return the sorted matrix.
Returns
=======
idx : array_like
Flattened indices giving sorted order.
array_like, optional
Sorted array.
'''
# Find number of basis functions, fi, and number of samples, M
M, N = T.shape[:]
# Keep a list of fij that we haven't done yet
fijs = list(range(M))
# Find a good ordering for each basis function
done = False
xk = x.copy()
f = np.zeros(T.shape, dtype=x.dtype)
indices = np.arange(x.size).reshape(x.shape)
with tqdm(desc='Matching', total=M, leave=False) as pbar:
while not done:
# Choose a row
idx = np.random.choice(np.arange(len(fijs)))
jj = fijs[idx]
# Choose a column
for ii in np.random.permutation(list(range(N))):
ind, f[ii, jj] = find_nearest(xk, T[ii, jj])
indices[ii, jj] = ind
xk[np.unravel_index(ind, x.shape)] = np.inf
# Finalize the best fit, i.e., min || f[:, jj] - X[jj] ||
min_err = np.abs((f - T)**2).mean(axis=0).argsort().tolist()
min_err = [me for me in min_err if me in fijs]
fijs.remove(min_err[0])
# Check the stopping condition
if not fijs:
done = True
pbar.update(1)
# If we asked for the sorted matrix, send it back, too
if return_sorted:
return(indices.flatten(), f)
return indices.flatten()
def quantitative_fm_scalar(Mxy, dfs, T1, T2, PD, TR, alpha, phase_cyc):
'''For scalar T1,T2,PD'''
# Simulate over the total range of off-resonance values
resp = get_df_responses(T1, T2, PD, TR, alpha, phase_cyc, dfs)
# Find the response that matches Mxy most closely
idx, val = find_nearest(resp, Mxy)
# Return the df's value, because that's really what the caller wanted
return (dfs[idx])
def gen_sort1d(x, T):
'''Given 1D transform T, sort 1d signal, x.
Parameters
==========
x : array_like
1D signal to find ordering of.
T : array_like
Transform matrix.
Returns
=======
array_like
Flattened indices giving sorted order.
'''
M, N = T.shape[:]
assert x.size == N, 'T, x must be conformal!'
# Get a list of all columns
cols = list(range(N))
f = np.zeros(T.shape, dtype=x.dtype)
indices = np.tile(np.arange(x.size)[:, None], (1, N))
# Order x to approximate a single column of T
for col in cols:
xk = x.copy()
for row in range(M):
ind, f[row, col] = find_nearest(xk, T[row, col])
indices[row, col] = ind
xk[ind] = np.inf
min_err = np.abs((f - T)**2).mean(axis=0).argsort()
return indices[:, min_err[0]]
def quantitative_fm_scalar(Mxy, dfs, T1, T2, PD, TR, alpha, phase_cyc):
'''For scalar T1, T2, PD.
Parameters
==========
Mxy : float
Complex transverse signal we measure.
dfs : array_like
Off-resonance values to simulate over.
T1 : float
scalar T1 longitudinal recovery value in seconds.
T2 : float
scalar T2 transverse decay value in seconds.
PD : float
scalar proton density value scaled the same as acquisiton.
TR : float
Repetition time in seconds.
alpha : float
Flip angle in radians.
phase_cyc : float
RF phase cycling in radians.
Returns
=======
float
Off-resonace value that most closely matches Mxy prior.
'''
# Simulate over the total range of off-resonance values
resp = get_df_responses(T1, T2, PD, TR, alpha, phase_cyc, dfs)
# Find the response that matches Mxy most closely
idx, _val = find_nearest(resp, Mxy)
# Return the df's value, because that's really what the caller wanted
return dfs[idx]