We propose to leverage denoising autoencoder networks as priors to address image restoration problems. We build on the key observation that the output of an optimal denoising autoencoder is a local mean of the true data density, and the autoencoder error (the difference between the output and input of the trained autoencoder) is a mean shift vector. We use the magnitude of this mean shift vector, that is, the distance to the local mean, as the negative log likelihood of our natural image prior. For image restoration, we maximize the likelihood using gradient descent by backpropagating the autoencoder error. A key advantage of our approach is that we do not need to train separate networks for different image restoration tasks, such as non-blind deconvolution with different kernels, or super-resolution at different magnification factors. We demonstrate state of the art results for non-blind deconvolution and super-resolution using the same autoencoding prior.
A denoising autoencoder @cite_13 is an autoencoder trained to reconstruct data that was corrupted with noise. Previously, Alain and Bengio @cite_2 and @cite_42 used DAEs to construct generative models. We are inspired by the insight of Alain and Bengio that the output of an optimal DAE is a local mean of the true data density. Hence, the autoencoder error (the difference between its output and input) is a mean shift vector @cite_25 . This motivates using the magnitude of the autoencoder error as our prior.
@cite_42 @cite_13 @cite_25 @cite_2
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We propose to leverage denoising autoencoder networks as priors to address image restoration problems. We build on the key observation that the output of an optimal denoising autoencoder is a local mean of the true data density, and the autoencoder error (the difference between the output and input of the trained autoencoder) is a mean shift vector. We use the magnitude of this mean shift vector, that is, the distance to the local mean, as the negative log likelihood of our natural image prior. For image restoration, we maximize the likelihood using gradient descent by backpropagating the autoencoder error. A key advantage of our approach is that we do not need to train separate networks for different image restoration tasks, such as non-blind deconvolution with different kernels, or super-resolution at different magnification factors. We demonstrate state of the art results for non-blind deconvolution and super-resolution using the same autoencoding prior. Denoising auto-encoders (DAEs) have been successfully used to learn new representations for a wide range of machine learning tasks. During training, DAEs make many passes over the training dataset and reconstruct it from partial corruption generated from a pre-specified corrupting distribution. This process learns robust representation, though at the expense of requiring many training epochs, in which the data is explicitly corrupted. In this paper we present the marginalized Denoising Auto-encoder (mDAE), which (approximately) marginalizes out the corruption during training. Effectively, the mDAE takes into account infinitely many corrupted copies of the training data in every epoch, and therefore is able to match or outperform the DAE with much fewer training epochs. We analyze our proposed algorithm and show that it can be understood as a classic auto-encoder with a special form of regularization. In empirical evaluations we show that it attains 1-2 order-of-magnitude speedup in training time over other competing approaches. The work explores the use of denoising autoencoders (DAEs) for brain lesion detection, segmentation, and false-positive reduction. Stacked denoising autoencoders (SDAEs) were pretrained using a large number of unlabeled patient volumes and fine-tuned with patches drawn from a limited number of patients (n=20, 40, 65). The results show negligible loss in performance even when SDAE was fine-tuned using 20 labeled patients. Low grade glioma (LGG) segmentation was achieved using a transfer learning approach in which a network pretrained with high grade glioma data was fine-tuned using LGG image patches. The networks were also shown to generalize well and provide good segmentation on unseen BraTS 2013 and BraTS 2015 test data. The manuscript also includes the use of a single layer DAE, referred to as novelty detector (ND). ND was trained to accurately reconstruct nonlesion patches. The reconstruction error maps of test data were used to localize lesions. The error maps were shown to assign unique error distributions to various constituents of the glioma, enabling localization. The ND learns the nonlesion brain accurately as it was also shown to provide good segmentation performance on ischemic brain lesions in images from a different database. Denoising autoencoders have been previously shown to be competitive alternatives to restricted Boltzmann machines for unsupervised pretraining of each layer of a deep architecture. We show that a simple denoising autoencoder training criterion is equivalent to matching the score (with respect to the data) of a specific energy-based model to that of a nonparametric Parzen density estimator of the data. This yields several useful insights. It defines a proper probabilistic model for the denoising autoencoder technique, which makes it in principle possible to sample from them or rank examples by their energy. It suggests a different way to apply score matching that is related to learning to denoise and does not require computing second derivatives. It justifies the use of tied weights between the encoder and decoder and suggests ways to extend the success of denoising autoencoders to a larger family of energy-based models.