def objectiveFunctionTV(x, N, strtag, kern, dirWeight=0, dirs=None, nmins=0,
dirInfo=[None,None,None,None], a=10):
if np.max(a*x) < 10:
obj = (1/a)*np.log(np.cosh(a*tf.TV(x,N,strtag,kern,dirWeight,dirs,nmins,dirInfo)))
else:
obj = abs(tf.TV(x,N,strtag,kern,dirWeight,dirs,nmins,dirInfo))
return obj
def objectiveFunctionTV(x,
N,
strtag,
dirWeight=0,
dirs=None,
nmins=0,
dirInfo=[None, None, None, None],
a=10):
return (1 / a) * np.log(
np.cosh(a * tf.TV(x, N, strtag, dirWeight, dirs, nmins, dirInfo)))
def gTV(x, N, strtag, kern, dirWeight, dirs=None, nmins=0, dirInfo=[None,None,None], a=10):
if nmins:
Ahat = dirInfo[0]
dI = dirInfo[1]
inds = dirInfo[2]
else:
Ahat = None
dI = None
inds = None
if len(x.shape) == 2:
N = np.hstack([1,N])
x0 = x.reshape(N)
grad = np.zeros(np.hstack([N[0], len(strtag), N[1:]]))#,dtype=complex)
if kern.shape == 3:
Nkern = np.hstack(1,[kern.shape[1:]])
else:
Nkern = kern.shape[1:]
TV_data = tf.TV(x0,N,strtag,kern,dirWeight,dirs,nmins,dirInfo).real
for i in xrange(len(strtag)):
if strtag[i] == 'spatial':
kernHld = np.flipud(np.fliplr(kern[i])).reshape(Nkern)
grad[:,i,:,:] = correlate(np.tanh(a*TV_data[i]),kernHld,mode='wrap')
#grad[:,i,:,:] = np.tanh(a*TV_data[i])
#grad[:,i,:,:] = fftconvolve(np.tanh(a*TV_data[i]),kern[i].reshape(Nkern),mode='same')
elif strtag[i] == 'diff':
for nDir in xrange(N[0]):
rows = np.where(dI[nDir] == 1)[0]
dDir = np.zeros([len(rows) + 1, Ahat.shape[1], N[-2]*N[-1]],complex)
r = inds[nDir,:]
Iq = x0[nDir,:]
Ir = x0[inds[nDir],:]
Irq = (Ir - Iq).reshape(nmins,-1)
dDir[0] = -1*np.tanh(a*np.dot(Ahat[nDir],Irq))
for q in range(1,dDir.shape[0]):
#import pdb; pdb.set_trace()
diffHld = x0[nDir].flatten() - x0[rows[q-1]].flatten()
dDir[q] = np.tanh(a*np.dot(Ahat[rows[q-1]],np.dot(dI[nDir,rows[q-1],:].reshape(nmins,1),diffHld.reshape(1,-1))))
grad[nDir,i,:,:] = np.sum(dDir,axis=(0,1)).reshape(N[-2],N[-1])
grad = np.sum(grad,axis=1)
return grad
def gTV(x,N,strtag,dirWeight,dirs = None,nmins = 0, dirInfo = None, p = 1,l1smooth = 1e-15, a = 1.0):
if dirInfo:
M = dirInfo[0]
dIM = dirInfo[1]
Ause = dirInfo[2]
inds = dirInfo[3]
else:
M = None
dIM = None
Ause = None
inds = None
if len(N) == 2:
N = np.hstack([1, N])
x0 = x.reshape(N)
grad = np.zeros(np.hstack([N[0], len(strtag),N[1],N[2]]))
for kk in range(N[0]):
TV_data = tf.TV(x0[kk,:,:],N,strtag,dirWeight,dirs,nmins,M)
for i in xrange(len(strtag)):
if strtag[i] == 'spatial':
TV_dataRoll = np.roll(TV_data[i,:,:],1,axis=i)
grad[kk,i,:,:] = -np.tanh(a*(TV_data[i,:,:])) + np.tanh(a*(TV_dataRoll))
#grad[i,:,:] = -np.sign(TV_data[i,:,:]) + np.sign(TV_dataRoll)
elif strtag[i] == 'diff':
None
#for d in xrange(N[i]):
#dDirx = np.zeros(np.hstack([N,M.shape[1]])) # dDirx.shape = [nDirs,imx,imy,nmins]
#for ind_q in xrange(N[i]):
#for ind_r in xrange(M.shape[1]):
#dDirx[ind_q,:,:,ind_r] = x0[inds[ind_q,ind_r],:,:] - x0[ind_q,:,:]
#for comb in xrange(len(Ause[kk])):
#colUse = Ause[dir][comb]
#for qr in xrange(M.shape[1]):
#grad[i,d,:,:] = np.dot(dIM[d,qr,colUse],dDirx[d,:,:,qr]) + grad[i,d,:,:]
# Need to make sure here that we're iterating over the correct dimension
# As of right now, this assumes that we're working on a slice by slice basis
# I'll have to implement 3D data work soon.
grad = np.sum(grad,axis=0)
return grad
def gTV(x,
N,
strtag,
kern,
dirWeight,
dirs=None,
nmins=0,
dirInfo=[None, None, None, None],
a=10):
if nmins:
M = dirInfo[0]
dIM = dirInfo[1]
Ause = dirInfo[2]
inds = dirInfo[3]
else:
M = None
dIM = None
Ause = None
inds = None
if len(x.shape) == 2:
N = np.hstack([1, N])
x0 = x.reshape(N)
grad = np.zeros(np.hstack([N[0], len(strtag), N[1:]]), dtype=float)
if kern.shape == 3:
Nkern = np.hstack(1, [kern.shape[1:]])
else:
Nkern = kern.shape[1:]
TV_data = tf.TV(x0, N, strtag, kern, dirWeight, dirs, nmins, dirInfo)
for i in xrange(len(strtag)):
if strtag[i] == 'spatial':
grad[:, i, :, :] = convolve(np.tanh(a * TV_data[i]),
kern[i].reshape(Nkern),
mode='wrap')
elif strtag[i] == 'diff':
None
grad = np.sum(grad, axis=1)
return grad
def optfun(x, N, lam1, lam2, data, k, strtag, ph, dirWeight=0, dirs=None,
dirInfo=[None,None,None,None], nmins=0,wavelet='db4',mode="per",a=1.0):
'''
This is the optimization function that we're trying to optimize. We are optimizing x here, and testing it within the funcitons that we want, as called by the functions that we've created
'''
#dirInfo[0] is M
#import pdb; pdb.set_trace()
tv = 0
xfm = 0
data.shape = N
x.shape = N
obj_data = np.fft.fftshift(k)*(data - tf.fft2c(x,ph))
obj = np.sum(obj_data*obj_data.conj()) #L2 Norm
#tv = np.sum(abs(tf.TV(x,N,strtag,dirWeight,dirs,nmins,M))) #L1 Norm
if lam1:
tv = np.sum((1/a)*np.log(np.cosh(a*tf.TV(x,N,strtag,dirWeight,dirs,nmins,dirInfo))))
#xfm cost calc
if lam2:
if len(N) > 2:
xfm=0
for kk in range(N[0]):
wvlt = tf.xfm(x[kk,:,:],wavelet=wavelet,mode=mode)
xfm += np.sum((1/a)*np.log(np.cosh(a*wvlt[0])))
for i in xrange(1,len(wvlt)):
xfm += np.sum([np.sum((1/a)*np.log(np.cosh(a*wvlt[i][j]))) for j in xrange(3)])
else:
wvlt = tf.xfm(x,wavelet=wavelet,mode=mode)
xfm = np.sum((1/a)*np.log(np.cosh(a*wvlt[0])))
for i in xrange(1,len(wvlt)):
xfm += np.sum([np.sum((1/a)*np.log(np.cosh(a*wvlt[i][j]))) for j in xrange(3)])
x.shape = (x.size,) # Not the most efficient way to do this, but we need the shape to reset.
data.shape = (data.size,)
#output
#print('obj: %.2f' % abs(obj))
#print('tv: %.2f' % abs(lam1*tv))
#print('xfm: %.2f' % abs(lam2*xfm))
return abs(obj + lam1*tv + lam2*xfm)