def setsolver(self):
n = self.n
op = SimpleLinearOperator(
n,
n,
lambda u: np.asarray(u * self.K)[0],
matvec_transp=lambda u: np.asarray(u * self.K.T)[0],
symmetric=False,
)
self.solver = LSQRFramework(op)
class Image1D:
def __init__(self, n=80, sig=0.05, err=2, **kwargs):
self.n = n # Number of grid points
self.sig = float(sig) # Gaussian kernel width
self.err = float(err) / 100 # Percent error in data
# Setup grid
h = 1.0 / n
z = np.arange(h / 2, 1 - h / 2 + h, h)
# Compute nxn matrix K = convolution with Gaussian kernel
gaussKernel = 1 / sqrt(np.pi) / self.sig * np.exp(-(z - h / 2) ** 2 / self.sig ** 2)
self.K = h * np.matrix(toeplitz(gaussKernel))
# Setup true solution, blurred and noisy data
trueimg = 0.75 * np.where((0.1 < z) & (z < 0.25), 1, 0)
trueimg += 0.25 * np.where((0.3 < z) & (z < 0.32), 1, 0)
trueimg += np.where((0.5 < z) & (z < 1), 1, 0) * np.sin(2 * np.pi * z) ** 4
blurred = self.K * np.asmatrix(trueimg).T
blurred = np.asarray(blurred.T)[0] # np.matrix messes up your data
noise = self.err * np.linalg.norm(blurred) * np.random.random(n) / sqrt(n)
self.data = blurred + noise
self.z = z
self.trueimg = trueimg
self.blurred = blurred
self.setsolver()
def setsolver(self):
n = self.n
op = SimpleLinearOperator(
n,
n,
lambda u: np.asarray(u * self.K)[0],
matvec_transp=lambda u: np.asarray(u * self.K.T)[0],
symmetric=False,
)
self.solver = LSQRFramework(op)
def deblur(self, **kwargs):
"Deblur image with specified solver"
self.solver.solve(self.data, **kwargs)
return self.solver.x
