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Recently, Deep Image Prior (DIP) has emerged as an effective unsupervised one-shot learner, delivering competitive results across various image recovery problems. This method only requires the noisy measurements and a forward operator, relying solely on deep networks initialized with random noise to learn and restore the structure of the data. However, DIP is notorious for its vulnerability to overfitting due to the overparameterization of the network. Building upon insights into the impact of the DIP input and drawing inspiration from the gradual denoising process in cutting-edge diffusion models, we introduce Autoencoding Sequential DIP (aSeqDIP) for image reconstruction. This method progressively denoises and reconstructs the image through a sequential optimization of network weights. This is achieved using an input-adaptive DIP objective, combined with an autoencoding regularization term. Compared to diffusion models, our method does not require training data and outperforms other DIP-based methods in mitigating noise overfitting while maintaining a similar number of parameter updates as Vanilla DIP. Through extensive experiments, we validate the effectiveness of our method in various image reconstruction tasks, such as MRI and CT reconstruction, as well as in image restoration tasks like image denoising, inpainting, and non-linear deblurring. 

In this work, we study the deep image prior (DIP) for reconstruction problems in magnetic resonance imaging (MRI). DIP has become a popular approach for image reconstruction, where it recovers the clear image by fitting an overparameterized convolutional neural network (CNN) to the corrupted/undersampled measurements. To improve the performance of DIP, recent work shows that using a reference image as an input often leads to improved reconstruction results compared to vanilla DIP with random input. However, obtaining the reference input image often requires supervision and hence is difficult in practice. In this work, we propose a self-guided reconstruction scheme that uses no training data other than the set of undersampled measurements to simultaneously estimate the network weights and input (reference). We introduce a new regularization that aids the joint estimation by requiring the CNN to act as a powerful denoiser. The proposed self-guided method gives significantly improved image reconstructions for MRI with limited measurements compared to the conventional DIP and the reference-guided method while eliminating the need for any additional data.