  We mainly analyze and solve the overfitting problem of deep image prior
(DIP). Deep image prior can solve inverse problems such as super-resolution,
inpainting and denoising. The main advantage of DIP over other deep learning
approaches is that it does not need access to a large dataset. However, due to
the large number of parameters of the neural network and noisy data, DIP
overfits to the noise in the image as the number of iterations grows. In the
thesis, we use hybrid deep image priors to avoid overfitting. The hybrid priors
are to combine DIP with an explicit prior such as total variation or with an
implicit prior such as a denoising algorithm. We use the alternating direction
method-of-multipliers (ADMM) to incorporate the new prior and try different
forms of ADMM to avoid extra computation caused by the inner loop of ADMM
steps. We also study the relation between the dynamics of gradient descent, and
the overfitting phenomenon. The numerical results show the hybrid priors play
an important role in preventing overfitting. Besides, we try to fit the image
along some directions and find this method can reduce overfitting when the
noise level is large. When the noise level is small, it does not considerably
reduce the overfitting problem.
