/
deblur.py
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/
deblur.py
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import time
import numpy as np
from scipy.ndimage import convolve, correlate
from scipy.sparse.linalg import aslinearoperator, cg
from skimage.measure import compare_psnr, compare_ssim
## define linear operator P * x
class Blur():
def __init__(self, kernel, spatial_size):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
def matvec(self, x):
# conv(x, kernel)
return convolve(x.reshape(self.spatial_size), self.kernel).flatten()
def deblur(kernel, blurred):
image_size = blurred.shape
A = aslinearoperator(Blur(kernel, image_size))
b = blurred.copy()
x, _ = cg(A, b.flatten(), maxiter=200)
x.resize(image_size)
return x.clip(0, 1)
## define linear operator P^T * P * x + mu * x
class BlurNormal():
def __init__(self, kernel, spatial_size, mu=0):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
self.mu = mu
def matvec(self, x):
return correlate(
convolve(x.reshape(self.spatial_size), self.kernel),
self.kernel).flatten() + self.mu * x
def deblur_normal(kernel, blurred, mu=0):
image_size = blurred.shape
A = aslinearoperator(BlurNormal(kernel, image_size, mu=mu))
b = correlate(blurred, kernel)
x, _ = cg(A, b.flatten(), maxiter=200)
x.resize(image_size)
return x.clip(0, 1)
## define linear operator P^T * P * x + lambda * D^T * W * D * x
class ITVReweight():
def __init__(self,
kernel,
spatial_size,
weight,
lmbda=1e-5,
kernel_h=[[-1, 1]],
kernel_v=[[-1], [1]]):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
self.weight = weight
self.lmbda = lmbda
self.kernel_h = kernel_h
self.kernel_v = kernel_v
def matvec(self, x):
x = x.copy()
x.resize(self.spatial_size)
Dh = convolve(x, self.kernel_h)
Dv = convolve(x, self.kernel_v)
W_Dh = np.multiply(self.weight, Dh)
Dht_W_Dh = correlate(W_Dh, self.kernel_h)
W_Dv = np.multiply(self.weight, Dv)
Dvt_W_Dv = correlate(W_Dv, self.kernel_v)
return (correlate(convolve(x, self.kernel), self.kernel) + self.lmbda *
(Dht_W_Dh + Dvt_W_Dv)).flatten()
def deblur_itv_reweight(kernel,
blurred,
p=1,
lmbda=1e-5,
irls_iters=10,
cg_iters=100,
groundtruth=None,
verbose=False):
image_size = blurred.shape
kernel_h = [[-1, 1]]
kernel_v = [[-1], [1]]
b = correlate(blurred, kernel)
# W = np.ones(image_size)
x = blurred.copy()
t = []
loss = []
for irls_iter in range(irls_iters):
x_old = x
t0 = time.time()
Dh_x = convolve(x, kernel_h)
Dv_x = convolve(x, kernel_v)
W = np.power(
np.maximum(np.power(Dh_x, 2) + np.power(Dv_x, 2), 1e-4), p / 2 - 1)
A = aslinearoperator(
ITVReweight(
kernel,
image_size,
W,
lmbda=lmbda,
kernel_h=kernel_h,
kernel_v=kernel_v))
x, _ = cg(A, b.flatten(), maxiter=cg_iters)
x = x.clip(0, 1)
x.resize(image_size)
t1 = time.time()
obj = 0.5 * np.sum(np.power(
convolve(x, kernel) - blurred, 2)) + lmbda * (np.sum(
np.sqrt(
np.power(convolve(x, kernel_h), 2) +
np.power(convolve(x, kernel_v), 2))))
if verbose:
if groundtruth is not None:
print(
'IRLS Iter: {}; Cost Funcitonal: {:.6f}; PSNR: {:.6f}; SSIM: {:.6f}'.
format(irls_iter + 1, obj, compare_psnr(x, groundtruth),
compare_ssim(x, groundtruth)))
else:
print('IRLS Iter: {}; Cost Funcitonal: {:.6f};'.format(
irls_iter + 1, obj))
t.append(t1 - t0)
loss.append(obj)
if np.sum(np.power(x_old - x, 2)) < 1e-2:
break
return x, t, loss
## define linear operator P^T * P * x + lambda * D^T * W * D * x
class ATVReweight():
def __init__(self,
kernel,
spatial_size,
weight_h,
weight_v,
lmbda=1e-5,
kernel_h=[[-1, 1]],
kernel_v=[[-1], [1]]):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
self.weight_h = weight_h
self.weight_v = weight_v
self.lmbda = lmbda
self.kernel_h = kernel_h
self.kernel_v = kernel_v
def matvec(self, x):
x = x.copy()
x.resize(self.spatial_size)
Dh = convolve(x, self.kernel_h)
Dv = convolve(x, self.kernel_v)
W_Dh = np.multiply(self.weight_h, Dh)
Dht_W_Dh = correlate(W_Dh, self.kernel_h)
W_Dv = np.multiply(self.weight_v, Dv)
Dvt_W_Dv = correlate(W_Dv, self.kernel_v)
return (correlate(convolve(x, self.kernel), self.kernel) + self.lmbda *
(Dht_W_Dh + Dvt_W_Dv)).flatten()
def deblur_atv_reweight(kernel,
blurred,
lmbda=1e-5,
irls_iters=10,
cg_iters=100,
groundtruth=None,
verbose=False):
image_size = blurred.shape
kernel_h = [[-1, 1]]
kernel_v = [[-1], [1]]
b = correlate(blurred, kernel)
# W = np.ones(image_size)
x = blurred.copy()
t = []
loss = []
for irls_iter in range(irls_iters):
x_old = x
t0 = time.time()
Dh_x = convolve(x, kernel_h)
Dv_x = convolve(x, kernel_v)
Wh = 1 / np.maximum(np.abs(Dh_x), 1e-4)
Wv = 1 / np.maximum(np.abs(Dv_x), 1e-4)
A = aslinearoperator(
ATVReweight(
kernel,
image_size,
Wh,
Wv,
lmbda=lmbda,
kernel_h=kernel_h,
kernel_v=kernel_v))
x, _ = cg(A, b.flatten(), maxiter=cg_iters)
x = x.clip(0, 1)
x.resize(image_size)
t1 = time.time()
obj = 0.5 * np.sum(np.power(convolve(x, kernel) - blurred, 2)
) + lmbda * (np.sum(np.abs(convolve(x, kernel_h))) +
np.sum(np.abs(convolve(x, kernel_v))))
if verbose:
if groundtruth is not None:
print(
'IRLS Iter: {}; Cost Funcitonal: {:.6f}; PSNR: {:.6f}; SSIM: {:.6f}'.
format(irls_iter + 1, obj, compare_psnr(x, groundtruth),
compare_ssim(x, groundtruth)))
else:
print('IRLS Iter: {}; Cost Funcitonal: {:.6f};'.format(
irls_iter + 1, obj))
t.append(t1 - t0)
loss.append(obj)
if np.sum(np.power(x_old - x, 2)) < 1e-2:
break
return x, t, loss
## define linear operator P^T * P * x + mu * x
class ADMMLinearize():
def __init__(self, kernel, spatial_size, mu):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
self.mu = mu
def matvec(self, x):
# the linear operator is (P^T * P + mu * I)
return correlate(
convolve(x.reshape(self.spatial_size), self.kernel),
self.kernel).flatten() + self.mu * x
def deblur_admm_linearized(kernel,
blurred,
lmbda=1e-5,
mu=1e-4,
rho=1e-4,
admm_iters=10,
cg_iters=100,
groundtruth=None):
image_size = blurred.shape
kernel_h = [[-1, 1]]
kernel_v = [[-1], [1]]
def update_x(x, z, y, rho, mu):
b = correlate(blurred, kernel) # P^T * b
b += mu * x # mu * x
## rho * D * x - rho * z + y
# horizontal part
b -= correlate(rho * convolve(x, kernel_h) -
rho * z[:z.shape[0] // 2, :] + y[:y.shape[0] // 2, :],
kernel_h)
# vertitcal part
b -= correlate(rho * convolve(x, kernel_v) -
rho * z[z.shape[0] // 2:, :] + y[y.shape[0] // 2:, :],
kernel_v)
A = aslinearoperator(ADMM(kernel, image_size, mu))
x, _ = cg(A, b.flatten(), maxiter=cg_iters)
x.resize(image_size)
return x
def update_z(x, y, lmbda, rho):
z = np.vstack([convolve(x, kernel_h), convolve(x, kernel_v)]) + y / rho
threshold = lmbda / rho
j = np.abs(z) <= threshold
z[j] = 0
k = np.abs(z) > threshold
z[k] = z[k] - np.sign(z[k]) * threshold
return z
def update_y(x, z, y, rho):
return y + rho * (
np.vstack([convolve(x, kernel_h),
convolve(x, kernel_v)]) - z)
x = blurred.copy()
# x = np.zeros(blurred.shape)
z = np.vstack([np.zeros(x.shape), np.zeros(x.shape)])
y = np.vstack([np.zeros(x.shape), np.zeros(x.shape)])
t = []
loss = []
for admm_iter in range(admm_iters):
x_old = x
t0 = time.time()
x = update_x(x, z, y, rho, mu)
x = x.clip(0, 1)
z = update_z(x, y, lmbda, rho)
y = update_y(x, z, y, rho)
rho = min(5, rho * 1.1)
mu = min(5, mu * 1.1)
t1 = time.time()
obj = 0.5 * np.sum(np.power(convolve(x, kernel) - blurred, 2)
) + lmbda * (np.sum(np.abs(convolve(x, kernel_h))) +
np.sum(np.abs(convolve(x, kernel_v))))
if groundtruth is not None:
print(
'ADMM Iter: {}; Cost Functional: {:.6f}; PSNR: {:.6f}; SSIM: {:.6f}'.
format(admm_iter + 1, obj, compare_psnr(x, groundtruth),
compare_ssim(x, groundtruth)))
else:
print('ADMM Iter: {}; Cost Functional: {:.6f}; '.format(
admm_iter + 1, obj))
t.append(t1 - t0)
loss.append(obj)
if np.sum(np.power(x_old - x, 2)) < 1e-2:
break
return x, t, loss
## define linear operator P^T * P * x + mu * D^T * D * x
class ADMM():
def __init__(self, kernel, spatial_size, kernel_h, kernel_v, rho):
self.kernel = kernel
self.shape = (spatial_size[0] * spatial_size[1],
spatial_size[0] * spatial_size[1])
self.spatial_size = spatial_size
self.rho = rho
self.kernel_h = kernel_h
self.kernel_v = kernel_v
def matvec(self, x):
# the linear operator is P^T * P * x + mu * D^T * D * x
x = x.copy()
x.resize(self.spatial_size)
return correlate(convolve(x, self.kernel), self.kernel).flatten(
) + self.rho * correlate(convolve(
x, self.kernel_h), self.kernel_h).flatten() + self.rho * correlate(
convolve(x, self.kernel_v), self.kernel_v).flatten()
def deblur_admm(kernel,
blurred,
lmbda=1e-5,
rho=1e-4,
admm_iters=25,
cg_iters=100,
groundtruth=None,
verbose=False):
image_size = blurred.shape
kernel_h = [[-1, 1]]
kernel_v = [[-1], [1]]
def update_x(z, y, rho):
b = correlate(blurred, kernel) # P^T * b
## D^T * (rho * z - y)
# horizontal part
b += correlate(rho * z[:z.shape[0] // 2, :] - y[:y.shape[0] // 2, :],
kernel_h)
# vertitcal part
b += correlate(rho * z[z.shape[0] // 2:, :] - y[y.shape[0] // 2:, :],
kernel_v)
A = aslinearoperator(ADMM(kernel, image_size, kernel_h, kernel_v, rho))
x, _ = cg(A, b.flatten(), maxiter=cg_iters)
x.resize(image_size)
return x
def update_z(x, y, lmbda, rho):
z = np.vstack([convolve(x, kernel_h), convolve(x, kernel_v)]) + y / rho
threshold = lmbda / rho
j = np.abs(z) <= threshold
z[j] = 0
k = np.abs(z) > threshold
z[k] = z[k] - np.sign(z[k]) * threshold
return z
def update_y(x, z, y, rho):
return y + rho * (
np.vstack([convolve(x, kernel_h),
convolve(x, kernel_v)]) - z)
x = blurred.copy()
# x = np.zeros(blurred.shape)
z = np.vstack([np.zeros(x.shape), np.zeros(x.shape)])
y = np.vstack([np.zeros(x.shape), np.zeros(x.shape)])
t = []
loss = []
for admm_iter in range(admm_iters):
x_old = x
t0 = time.time()
x = update_x(z, y, rho)
x = x.clip(0, 1)
z = update_z(x, y, lmbda, rho)
y = update_y(x, z, y, rho)
rho = min(5, rho * 1.1)
t1 = time.time()
obj = 0.5 * np.sum(np.power(convolve(x, kernel) - blurred, 2)
) + lmbda * (np.sum(np.abs(convolve(x, kernel_h))) +
np.sum(np.abs(convolve(x, kernel_v))))
if verbose:
if groundtruth is not None:
print(
'ADMM Iter: {}; Cost Functional: {:.6f}; PSNR: {:.6f}; SSIM: {:.6f}'.
format(admm_iter + 1, obj, compare_psnr(x, groundtruth),
compare_ssim(x, groundtruth)))
else:
print('ADMM Iter: {}; Cost Functional: {:.6f};'.format(
admm_iter + 1, obj))
t.append(t1 - t0)
loss.append(obj)
if np.sum(np.power(x_old - x, 2)) < 1e-2:
break
return x, t, loss