08. Scaling Dependent Stepsize Problem

In earlier tests it was noticed that the size of the weighting parameters has an effect on the solution while keeping the ratio constant. Meanwhile the problem has been identified as a too small number of iterations. Overall, the default parameters have been adjusted, but in this example, we will briefly show what the effect looks like.

A grey image is created and viewed in an area [0, 1]. The relation of the weighting between dataterm and regularization remains the same, but is adjusted in its absolute value too.

import numpy as np
import matplotlib.pyplot as plt

from recon.interfaces import Smoothing
from recon.utils.images import two_smooth_squares

scaled_image = two_smooth_squares(256, 200)

sigma = 0.3  # the percentage portion standard deviation for normal (Gaussian) distribution.

noise_image = scaled_image + np.random.normal(0, sigma*np.max(scaled_image), size=scaled_image.shape)

weights = [(0.2, 0.2), (1, 1), (2, 2)]

rows = ['{}'.format(row) for row in weights]

f = plt.figure(figsize=(6, 3*len(weights)))

for i, weight in enumerate(weights):
    tv_scaled_obj = Smoothing(domain_shape=scaled_image.shape,
                              reg_mode='tv',
                              lam=weight[0],
                              alpha=weight[1],
                              tau="calc")
    scaled_tv_solution = tv_scaled_obj.solve(noise_image, max_iter=5550, tol=1e-4)

    tv_unscaled_obj = Smoothing(domain_shape=scaled_image.shape,
                                reg_mode='tv',
                                lam=weight[0],
                                alpha=weight[1],
                                tau="calc")
    unscaled_tv_solution = tv_unscaled_obj.solve(noise_image, max_iter=550, tol=1e-4)

    f.add_subplot(3, 2, i*2+1)
    plt.gray()
    plt.axis('off')
    plt.imshow(scaled_tv_solution)
    plt.title("Long-Run: weight " + str(weight))
    f.add_subplot(3, 2, (i+1)*2)

    plt.gray()
    plt.imshow(unscaled_tv_solution)
    plt.title("Short-Run: weight " + str(weight))
    plt.axis('off')
plt.tight_layout()
plt.show()

Out:

Early stopping.
Early stopping.
Early stopping.
Early stopping.
Early stopping.
Early stopping.

Conclusion Be careful with max_iter and tol parameter or with the interpretation of result if the number of iteration is too small.