Math563 – Final Project

To get started:

• See requirements.txt for dependencies.

• See sample.py for a full working example; loads the image, applies blurring, and a implements a function for testing the algorithms. Change my_path to the path of the desired image.

blurkit

The blurkit directory contains the finalized code.

• optsolver.py: Implements main wrapper class OptSolver for the algorithms, meant to be the interface for the user.

• optutil.py: Implements a helper class, OptUtil, for OptSolver, abstracting commonly used matrix operations using the eigenvalues of the 2D DFTs of the convolution kernel and the discrete gradient operator.

• solvertemplate.py: Contains core algorithm logic, in a structure resembling pseudocode, and implements early stopping.

• periodic_mat_util.py: Various Fourier transform methods, mainly based on the provided Matlab code. Used by optutil.py.

• kernel.py: Implements 3 kernels for blurring: Gaussian, motion, and disk.

• preprocess_image.py: Methods for converting and resizing the image into a matrix.

• prox_util.py: Implements proximal operators.

• test_util.py: Helper functions for testing.

Other

• ./test: Contains an outdated version of our source code, along with some files for testing and hyperparameter tuning

Sample Usage

# usage
from blurkit.optsolver import ADMM
import matplotlib.pyplot as plt
import numpy as np

k = np.array([1, 2, 3])[:, None] # dummy kernel
b = np.random.random((128, 128)) # dummy image

# instantiate solver
params = {'deblurring_objective': 'l1', 'maxiter': 100}
solver = ADMM(k=k, shape=(128,128), **params)

recovered_image, obj_vals = solver.solve(
    b=b, # blurred image
    if_track=True, # whether or not to track objective
    stop_criterion=1e-2 # halt and return when objective reaches this value
    )

recovered_image = np.real(recovered_image) # extract real part of image

# show recovered image (doesn't look like anything special)
plt.figure('Recovered Image')
plt.imshow(recovered_image, cmap='gray')
plt.axis('off')
plt.show()

# show objective across iterations
plt.figure('Objective Across Iterations')
plt.plot(obj_vals)
plt.yscale("log")
plt.xlabel('Iteration')
plt.ylabel('Error')
plt.grid(True)
plt.show()

Tracking Loss

If one wishes to track the objective, set the solver's solve method's key word argument if_track to True, and use the list of objective values for downsteam analysis. See sample.py for details.