  Recovering clear images from blurry ones with an unknown blur kernel is a
challenging problem. Deep image prior (DIP) proposes to use the deep network as
a regularizer for a single image rather than as a supervised model, which
achieves encouraging results in the nonblind deblurring problem. However, since
the relationship between images and the network architectures is unclear, it is
hard to find a suitable architecture to provide sufficient constraints on the
estimated blur kernels and clean images. Also, DIP uses the sparse maximum a
posteriori (MAP), which is insufficient to enforce the selection of the
recovery image. Recently, variational deep image prior (VDIP) was proposed to
impose constraints on both blur kernels and recovery images and take the
standard deviation of the image into account during the optimization process by
the variational principle. However, we empirically find that VDIP struggles
with processing image details and tends to generate suboptimal results when the
blur kernel is large. Therefore, we combine total generalized variational (TGV)
regularization with VDIP in this paper to overcome these shortcomings of VDIP.
TGV is a flexible regularization that utilizes the characteristics of partial
derivatives of varying orders to regularize images at different scales,
reducing oil painting artifacts while maintaining sharp edges. The proposed
VDIP-TGV effectively recovers image edges and details by supplementing extra
gradient information through TGV. Additionally, this model is solved by the
alternating direction method of multipliers (ADMM), which effectively combines
traditional algorithms and deep learning methods. Experiments show that our
proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and
qualitatively.
