In this paper we introduce a natural image prior that directly represents a Gaussian-smoothed version of the natural image distribution. We include our prior in a formulation of image restoration as a Bayes estimator that also allows us to solve noise-blind image restoration problems. We show that the gradient of our prior corresponds to the mean-shift vector on the natural image distribution. In addition, we learn the mean-shift vector field using denoising autoencoders, and use it in a gradient descent approach to perform Bayes risk minimization. We demonstrate competitive results for noise-blind deblurring, super-resolution, and demosaicing.
Kernel-blind deconvolution has seen the most effort recently, while we support the fully (noise and kernel) blind setting. Noise-blind deblurring is usually performed by first estimating the noise level and then restoration with the estimated noise. @cite_1 proposed a Bayes risk formulation that can perform deblurring by adaptively changing the regularization without the need of the noise variance estimate. @cite_16 @cite_35 explored a spatially-adaptive sparse prior and scale-space formulation to handle noise- or kernel-blind deconvolution. These methods, however, are tailored specifically for image deconvolution. Also, they only handle the noise- or kernel-blind case, but not fully blind.
@cite_35 @cite_16 @cite_1
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Blind deconvolution is to recover a sharp version of a given blurry image or signal when the blur kernel is unknown. Because this problem is ill-conditioned in nature, effectual criteria pertaining to both the sharp image and blur kernel are required to constrain the space of candidate solutions. While the problem has been extensively studied for long, it is still unclear how to regularize the blur kernel in an elegant, effective fashion. In this paper, we show that the blurry image itself actually encodes rich information about the blur kernel, and such information can indeed be found by exploring and utilizing a well-known phenomenon, that is, sharp images are often high pass, whereas blurry images are usually low pass. More precisely, we shall show that the blur kernel can be retrieved through analyzing and comparing how the spectrum of an image as a convolution operator changes before and after blurring. Subsequently, we establish a convex kernel regularizer, which depends only on the given blurry image. Interestingly, the minimizer of this regularizer guarantees to give a good estimate to the desired blur kernel if the original image is sharp enough. By combining this powerful regularizer with the prevalent nonblind devonvolution techniques, we show how we could significantly improve the deblurring results through simulations on synthetic images and experiments on realistic images. Blind motion deblurring methods are primarily responsible for recovering an accurate estimate of the blur kernel. Non-blind deblurring (NBD) methods, on the other hand, attempt to faithfully restore the original image, given the blur estimate. However, NBD is quite susceptible to errors in blur kernel. In this work, we present a convolutional neural network-based approach to handle kernel uncertainty in non-blind motion deblurring. We provide multiple latent image estimates corresponding to different prior strengths obtained from a given blurry observation in order to exploit the complementarity of these inputs for improved learning. To generalize the performance to tackle arbitrary kernel noise, we train our network with a large number of real and synthetic noisy blur kernels. Our network mitigates the effects of kernel noise so as to yield detail-preserving and artifact-free restoration. Our quantitative and qualitative evaluations on benchmark datasets demonstrate that the proposed method delivers state-of-the-art results. To further underscore the benefits that can be achieved from our network, we propose two adaptations of our method to improve kernel estimates, and image deblurring quality, respectively. Non-blind image deconvolution is an ill-posed problem. The presence of noise and band-limited blur kernels makes the solution of this problem non-unique. Existing deconvolution techniques produce a residual between the sharp image and the estimation that is highly correlated with the sharp image, the kernel, and the noise. In most cases, different restoration models must be constructed for different blur kernels and different levels of noise, resulting in low computational efficiency or highly redundant model parameters. Here we aim to develop a single model that handles different types of kernels and different levels of noise: general non-blind deconvolution. Specifically, we propose a very deep convolutional neural network that predicts the residual between a pre-deconvolved image and the sharp image rather than the sharp image. The residual learning strategy makes it easier to train a single model for different kernels and different levels of noise, encouraging high effectiveness and efficiency. Quantitative evaluations demonstrate the practical applicability of the proposed model for different blur kernels. The model also shows the state-of-the-art performance on synthesized blurry images. We present a novel approach to noise-blind deblurring, the problem of deblurring an image with known blur, but unknown noise level. We introduce an efficient and robust solution based on a Bayesian framework using a smooth generalization of the 0-1 loss. A novel bound allows the calculation of very high-dimensional integrals in closed form. It avoids the degeneracy of Maximum a-Posteriori (MAP) estimates and leads to an effective noise-adaptive scheme. Moreover, we drastically accelerate our algorithm by using Majorization Minimization (MM) without introducing any approximation or boundary artifacts. We further speed up convergence by turning our algorithm into a neural network termed GradNet, which is highly parallelizable and can be efficiently trained. We demonstrate that our noise-blind formulation can be integrated with different priors and significantly improves existing deblurring algorithms in the noise-blind and in the known-noise case. Furthermore, GradNet leads to state-of-the-art performance across different noise levels, while retaining high computational efficiency.