def build_graph(tau):
"""Builds graph where the input is an image placeholder + a perturbation variable"""
# tf_tau = tf.placeholder(tf.float32, shape=(), name='stab_tau')
tf_lam = tf.placeholder(tf.float32, shape=(), name='stab_lambda')
N = 128
wav = db4
levels = 5
# Build FISTA graph
tf_im = tf.placeholder(tf.complex64, shape=[N, N, 1], name='image')
tf_samp_patt = tf.placeholder(tf.bool,
shape=[N, N, 1],
name='sampling_pattern')
# perturbation
tf_rr_real = tf.Variable(tau * tf.random_uniform(tf_im.shape),
name='rr_real',
trainable=True)
tf_rr_imag = tf.Variable(tau * tf.random_uniform(tf_im.shape),
name='rr_imag',
trainable=True)
tf_rr = tf.complex(tf_rr_real, tf_rr_imag, name='rr')
tf_input = tf_im + tf_rr
op = MRIOperator(tf_samp_patt, wav, levels)
measurements = op.sample(tf_input)
tf_adjoint_coeffs = op(measurements, adjoint=True)
adj_real_idwt = idwt2d(tf.real(tf_adjoint_coeffs), wav, levels)
adj_imag_idwt = idwt2d(tf.imag(tf_adjoint_coeffs), wav, levels)
tf_adjoint = tf.complex(adj_real_idwt, adj_imag_idwt)
gradient = LASSOGradient(op, measurements)
alg = FISTA(gradient)
initial_x = op(measurements, adjoint=True)
result_coeffs = alg.run(initial_x)
real_idwt = idwt2d(tf.real(result_coeffs), wav, levels)
imag_idwt = idwt2d(tf.imag(result_coeffs), wav, levels)
result_image = tf.complex(real_idwt, imag_idwt)
# End build primal-dual graph
# Start building objective function for adv noise
# the output of PD with no adv. noise
tf_solution = tf.placeholder(tf.complex64, shape=[N, N, 1], name='actual')
tf_obj = tf.nn.l2_loss(
tf.abs(result_image -
tf_solution)) - tf_lam * tf.nn.l2_loss(tf.abs(tf_rr))
# End building objective function for adv noise
return tf_rr_real, tf_rr_imag, tf_input, result_image, tf_obj, tf_adjoint
def build_graph(tau):
N = 128
wav = db4
levels = 4
tf_lam = tf.placeholder(tf.float32, shape=(), name='stab_lambda')
# Build Primal-dual graph
tf_im = tf.placeholder(tf.complex64, shape=[N,N,1], name='image')
tf_samp_patt = tf.placeholder(tf.bool, shape=[N,N,1], name='sampling_pattern')
# perturbation
tf_rr_real = tf.Variable(tau*tf.random_uniform(tf_im.shape), name='rr_real', trainable=True)
tf_rr_imag = tf.Variable(tau*tf.random_uniform(tf_im.shape), name='rr_imag', trainable=True)
tf_rr = tf.complex(tf_rr_real, tf_rr_imag, name='rr')
tf_input = tf_im + tf_rr
op = MRIOperator(tf_samp_patt, wav, levels)
measurements = op.sample(tf_input)
tf_adjoint_coeffs = op(measurements, adjoint=True)
adj_real_idwt = idwt2d(tf.real(tf_adjoint_coeffs), wav, levels)
adj_imag_idwt = idwt2d(tf.imag(tf_adjoint_coeffs), wav, levels)
tf_adjoint = tf.complex(adj_real_idwt, adj_imag_idwt)
prox1 = SQLassoProx1()
prox2 = SQLassoProx2()
alg = SquareRootLASSO(op, prox1, prox2, measurements)
initial_x = op(measurements, adjoint=True)
result_coeffs = alg.run(initial_x)
real_idwt = idwt2d(tf.real(result_coeffs), wav, levels)
imag_idwt = idwt2d(tf.imag(result_coeffs), wav, levels)
result_image = tf.complex(real_idwt, imag_idwt)
tf_solution = tf.placeholder(tf.complex64, shape=[N,N,1], name='actual')
tf_obj = tf.nn.l2_loss(tf.abs(result_image - tf_solution)) - tf_lam * tf.nn.l2_loss(tf.abs(tf_rr))
# End building objective function for adv noise
return tf_rr_real, tf_rr_imag, tf_input, result_image, tf_obj, tf_adjoint
return result_image
def build_fista_graph(N, wav, levels):
tf_im = tf.compat.v1.placeholder(tf.complex64,
shape=[N, N, 1],
name='image')
tf_samp_patt = tf.compat.v1.placeholder(tf.bool,
shape=[N, N, 1],
name='sampling_pattern')
op = MRIOperator(tf_samp_patt, wav, levels)
measurements = op.sample(tf_im)
initial_x = op(measurements, adjoint=True)
gradient = LASSOGradient(op, measurements)
alg = FISTA(gradient)
result_coeffs = alg.run(op(measurements, True))
real_idwt = idwt2d(tf.math.real(result_coeffs), wav, levels)
imag_idwt = idwt2d(tf.math.imag(result_coeffs), wav, levels)
output_node = tf.complex(real_idwt, imag_idwt)
return output_node
def build_pd_graph(N, wav, levels):
'''Returns the output node of the Primal-dual algorithm'''
# Shapes must be set for the wavelet transform to be applicable
tf_im = tf.compat.v1.placeholder(tf.complex64,
shape=[N, N, 1],
name='image')
tf_samp_patt = tf.compat.v1.placeholder(tf.bool,
shape=[N, N, 1],
name='sampling_pattern')
op = MRIOperator(tf_samp_patt, wav, levels)
measurements = op.sample(tf_im)
prox_f_star = BPDNFStar(measurements)
prox_g = BPDNG()
alg = PrimalDual(op, prox_f_star, prox_g)
initial_x = op(measurements, adjoint=True)
result_coeffs = alg.run(initial_x)
return result_coeffs
pl_sigma = tf.compat.v1.placeholder(dtype, shape=(), name='sigma')
pl_tau = tf.compat.v1.placeholder(dtype, shape=(), name='tau')
pl_lam = tf.compat.v1.placeholder(dtype, shape=(), name='lambda')
# Build Primal-dual graph
tf_im = tf.compat.v1.placeholder(cdtype, shape=[N, N, 1], name='image')
tf_samp_patt = tf.compat.v1.placeholder(tf.bool,
shape=[N, N, 1],
name='sampling_pattern')
# For the weighted l^1-norm
pl_weights = tf.compat.v1.placeholder(dtype, shape=[N, N, 1], name='weights')
tf_input = tf_im
op = MRIOperator(tf_samp_patt, wav, levels, dtype=dtype)
measurements = op.sample(tf_input)
tf_adjoint_coeffs = op(measurements, adjoint=True)
adj_real_idwt = idwt2d(tf.math.real(tf_adjoint_coeffs), wav, levels)
adj_imag_idwt = idwt2d(tf.math.imag(tf_adjoint_coeffs), wav, levels)
tf_adjoint = tf.complex(adj_real_idwt, adj_imag_idwt)
prox1 = WeightedL1Prox(pl_weights, pl_lam * pl_tau, dtype=dtype)
prox2 = SQLassoProx2(dtype=dtype)
alg = SquareRootLASSO(op,
prox1,
prox2,
measurements,
sigma=pl_sigma,