Humans perceive their surroundings in great detail even though most of our visual field is reduced to low-fidelity color-deprived (e.g. dichromatic) input by the retina. In contrast, most deep learning architectures are computationally wasteful in that they consider every part of the input when performing an image processing task. Yet, the human visual system is able to perform visual reasoning despite having only a small fovea of high visual acuity. With this in mind, we wish to understand the extent to which connectionist architectures are able to learn from and reason with low acuity, distorted inputs. Specifically, we train autoencoders to generate full-detail images from low-detail "foveations" of those images and then measure their ability to reconstruct the full-detail images from the foveated versions. By varying the type of foveation, we can study how well the architectures can cope with various types of distortion. We find that the autoencoder compensates for lower detail by learning increasingly global feature functions. In many cases, the learnt features are suitable for reconstructing the original full-detail image. For example, we find that the networks accurately perceive color in the periphery, even when 75 of the input is achromatic.
Image deconvolution is the ill-posed problem of recovering a sharp image, given a blurry one generated by a convolution. In this work, we deal with space-invariant non-blind deconvolution. Currently, the most successful methods involve a regularized inversion of the blur in Fourier domain as a first step. This step amplifies and colors the noise, and corrupts the image information. In a second (and arguably more difficult) step, one then needs to remove the colored noise, typically using a cleverly engineered algorithm. However, the methods based on this two-step approach do not properly address the fact that the image information has been corrupted. In this work, we also rely on a two-step procedure, but learn the second step on a large dataset of natural images, using a neural network. We will show that this approach outperforms the current state-of-the-art on a large dataset of artificially blurred images. We demonstrate the practical applicability of our method in a real-world example with photographic out-of-focus blur. We present a novel approach to low-level vision problems that combines sparse coding and deep networks pre-trained with denoising auto-encoder (DA). We propose an alternative training scheme that successfully adapts DA, originally designed for unsupervised feature learning, to the tasks of image denoising and blind inpainting. Our method's performance in the image denoising task is comparable to that of KSVD which is a widely used sparse coding technique. More importantly, in blind image inpainting task, the proposed method provides solutions to some complex problems that have not been tackled before. Specifically, we can automatically remove complex patterns like superimposed text from an image, rather than simple patterns like pixels missing at random. Moreover, the proposed method does not need the information regarding the region that requires inpainting to be given a priori. Experimental results demonstrate the effectiveness of the proposed method in the tasks of image denoising and blind inpainting. We also show that our new training scheme for DA is more effective and can improve the performance of unsupervised feature learning. We present an approach to low-level vision that combines two main ideas: the use of convolutional networks as an image processing architecture and an unsupervised learning procedure that synthesizes training samples from specific noise models. We demonstrate this approach on the challenging problem of natural image denoising. Using a test set with a hundred natural images, we find that convolutional networks provide comparable and in some cases superior performance to state of the art wavelet and Markov random field (MRF) methods. Moreover, we find that a convolutional network offers similar performance in the blind de-noising setting as compared to other techniques in the non-blind setting. We also show how convolutional networks are mathematically related to MRF approaches by presenting a mean field theory for an MRF specially designed for image denoising. Although these approaches are related, convolutional networks avoid computational difficulties in MRF approaches that arise from probabilistic learning and inference. This makes it possible to learn image processing architectures that have a high degree of representational power (we train models with over 15,000 parameters), but whose computational expense is significantly less than that associated with inference in MRF approaches with even hundreds of parameters.