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Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2-D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this paper, we overview recent graph spectral techniques in GSP specifically for image/video processing. The topics covered include image compression, image restoration, image filtering, and image segmentation. [ABSTRACT FROM AUTHOR]

Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning. [ABSTRACT FROM AUTHOR]

In this paper, we address the total variation (TV)-based nonlinear image restoration problems. In nonlinear image restoration problems, an original image is corrupted by a spatiallyinvariant blur, the build-in nonlinearity in imaging system, and the additive Gaussian white noise. We study the objective function consisting of the nonlinear least squares data-fitting term and the TV regularization term of the restored image. By making use of the structure of the objective function, an efficient alternating direction method of multipliers can be developed for solving the proposed model. The convergence of the numerical scheme is also studied. Numerical examples, including nonlinear image restoration and high-dynamic range imaging are reported to demonstrate the effectiveness of the proposed model and the efficiency of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

The JPEG compression method is among the most successful compression schemes since it readily provides good compressed results at a rather high compression ratio. However, the decompressed result of the standard JPEG decompression scheme usually contains some visible artifacts, such as blocking artifacts and Gibbs artifacts (ringing), especially when the compression ratio is rather high. In this paper, a novel artifact reducing approach for the JPEG decompression is proposed via sparse and redundant representations over a learned dictionary. Indeed, an effective two-step algorithm is developed. The first step involves dictionary learning and the second step involves the total variation regularization for decompressed images. Numerical experiments are performed to demonstrate that the proposed method outperforms the total variation and weighted total variation decompression methods in the measure of peak of signal to noise ratio, and structural similarity. [ABSTRACT FROM AUTHOR]

Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant \theta for using nonconvex nonsmooth regularization, and show that the difference between each pixel and its four adjacent neighbors is either 0 or larger than \theta in the recovered image. Moreover, we give an explicit form of \theta for the box-constrained image restoration model with the non-Lipschitz nonconvex \ellp-norm (0

Multiplicative noise removal is a challenging image processing problem, and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems. Sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, in this paper, we propose to learn a dictionary from the logarithmic transformed image, and then to use it in a variational model built for noise removal. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio, and mean absolute deviation error, the proposed algorithm outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel supervised nonnegative matrix factorization-based framework for both image classification and annotation. The framework consists of two phases: training and prediction. In the training phase, two supervised nonnegative matrix factorizations for image descriptors and annotation terms are combined to identify the latent image bases, and to represent the training images in the bases space. These latent bases can capture the representation of the images in terms of both descriptors and annotation terms. Based on the new representation of training images, classifiers can be learnt and built. In the prediction phase, a test image is first represented by the latent bases via solving a linear least squares problem, and then its class label and annotation can be predicted via the trained classifiers and the proposed annotation mapping model. In the algorithm, we develop a three-block proximal alternating nonnegative least squares algorithm to determine the latent image bases, and show its convergent property. Extensive experiments on real-world image data sets suggest that the proposed framework is able to predict the label and annotation for testing images successfully. Experimental results have also shown that our algorithm is computationally efficient and effective for image classification and annotation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of segmentation of large collections of images. We propose a semisupervised optimization model that determines an efficient segmentation of many input images. The advantages of the model are twofold. First, the segmentation is highly controllable by the user so that the user can easily specify what he/she wants. This is done by allowing the user to provide, either offline or interactively, some (fully or partially) labeled pixels in images as strong priors for the model. Second, the model requires only minimal tuning of model parameters during the initial stage. Once initial tuning is done, the setup can be used to automatically segment a large collection of images that are distinct but share similar features. We will show the mathematical properties of the model such as existence and uniqueness of solution and establish a maximum/minimum principle for the solution of the model. Extensive experiments on various collections of biological images suggest that the proposed model is effective for segmentation and is computationally efficient. [ABSTRACT FROM AUTHOR]

In this paper, we propose and present an algorithm for total variation (TV)-based blind deconvolution. Both the unknown image and blur can be estimated within an alternating minimization framework. With the generalized cross-validation (GCV) method, the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps. Experimental results confirm that the performance of the proposed algorithm is better than variational Bayesian blind deconvolution algorithms with Student's-t priors or a total variation prior. [ABSTRACT FROM AUTHOR]

The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l¹-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance. [ABSTRACT FROM AUTHOR]

Comments on an article about matrix formulation arising from the constrained optimization of the least squares restoration of multichannel images. Equation for the degradation of multichannel images.