Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

BLADE: Filter Learning for General Purpose Computational Photography

The Rapid and Accurate Image Super Resolution (RAISR) method of Romano, Isidoro, and Milanfar is a computationally efficient image upscaling method using a trained set of filters. We describe a generalization of RAISR, which we name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable edge-adaptive filtering framework that is general, simple, computationally efficient, and useful for a wide range of problems in computational photography. We show applications to operations which may appear in a camera pipeline including denoising, demosaicing, and stylization

Image reconstruction from incomplete information

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Truncated decompositions and filtering methods with Reflective/Anti-Reflective boundary conditions: a comparison

The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C. Tang, A fast algorithm for deblurring models with Neumann boundary conditions, SIAM J. Sci. Comput., 21 (1999), no. 3, pp.851-866] and Anti-Reflective [S. Serra Capizzano, A note on anti-reflective boundary conditions and fast deblurring models, SIAM J. Sci. Comput., 25-3 (2003), pp. 1307-1325] boundary conditions. We give numerical evidence to the fact that spectral decompositions (SDs) provide a good image restoration quality and this is true in particular for the Anti-Reflective SD, despite the loss of orthogonality in the associated transform. The related computational cost is comparable with previously known spectral decompositions, and results substantially lower than the singular value decomposition. The model extension to the cross-channel blurring phenomenon of color images is also considered and the related spectral filtering methods are suitably adapted.Comment: 22 pages, 10 figure

Data-Driven Image Restoration

Every day many images are taken by digital cameras, and people are demanding visually accurate and pleasing result. Noise and blur degrade images captured by modern cameras, and high-level vision tasks (such as segmentation, recognition, and tracking) require high-quality images. Therefore, image restoration specifically, image deblurring and image denoising is a critical preprocessing step. A fundamental problem in image deblurring is to recover reliably distinct spatial frequencies that have been suppressed by the blur kernel. Existing image deblurring techniques often rely on generic image priors that only help recover part of the frequency spectrum, such as the frequencies near the high-end. To this end, we pose the following specific questions: (i) Does class-specific information offer an advantage over existing generic priors for image quality restoration? (ii) If a class-specific prior exists, how should it be encoded into a deblurring framework to recover attenuated image frequencies? Throughout this work, we devise a class-specific prior based on the band-pass filter responses and incorporate it into a deblurring strategy. Specifically, we show that the subspace of band-pass filtered images and their intensity distributions serve as useful priors for recovering image frequencies. Next, we present a novel image denoising algorithm that uses external, category specific image database. In contrast to existing noisy image restoration algorithms, our method selects clean image “support patches” similar to the noisy patch from an external database. We employ a content adaptive distribution model for each patch where we derive the parameters of the distribution from the support patches. Our objective function composed of a Gaussian fidelity term that imposes category specific information, and a low-rank term that encourages the similarity between the noisy and the support patches in a robust manner. Finally, we propose to learn a fully-convolutional network model that consists of a Chain of Identity Mapping Modules (CIMM) for image denoising. The CIMM structure possesses two distinctive features that are important for the noise removal task. Firstly, each residual unit employs identity mappings as the skip connections and receives pre-activated input to preserve the gradient magnitude propagated in both the forward and backward directions. Secondly, by utilizing dilated kernels for the convolution layers in the residual branch, each neuron in the last convolution layer of each module can observe the full receptive field of the first layer

On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Lojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications