  The deep image prior (DIP) is a well-established unsupervised deep learning
method for image reconstruction; yet it is far from being flawless. The DIP
overfits to noise if not early stopped, or optimized via a regularized
objective. We build on the regularized fine-tuning of a pretrained DIP, by
adopting a novel strategy that restricts the learning to the adaptation of
singular values. The proposed SVD-DIP uses ad hoc convolutional layers whose
pretrained parameters are decomposed via the singular value decomposition.
Optimizing the DIP then solely consists in the fine-tuning of the singular
values, while keeping the left and right singular vectors fixed. We thoroughly
validate the proposed method on real-measured $\mu$CT data of a lotus root as
well as two medical datasets (LoDoPaB and Mayo). We report significantly
improved stability of the DIP optimization, by overcoming the overfitting to
noise.
