Abstract: Single image superresolution is a classic and active image processing problem, which aims to generate a high-resolution (HR) image from a low-resolution input image. Due to the severely under-determined nature of this problem, an effective image prior is necessary to make the problem solvable, and to improve the quality of generated images. In this paper, a novel image superresolution algorithm is proposed based on gradient profile sharpness (GPS). GPS is an edge sharpness metric, which is extracted from two gradient description models, i.e., a triangle model and a Gaussian mixture model for the description of different kinds of gradient profiles. Then, the transformation relationship of GPSs in different image resolutions is studied statistically, and the parameter of the relationship is estimated automatically. Based on the estimated GPS transformation relationship, two gradient profile transformation models are proposed for two profile description models, which can keep profile shape and profile gradient magnitude sum consistent during profile transformation. Finally, the target gradient field of HR image is generated from the transformed gradient profiles, which is added as the image prior in HR image reconstruction model. Extensive experiments are conducted to evaluate the proposed algorithm in subjective visual effect, objective quality, and computation time. The experimental results demonstrate that the proposed approach can generate superior HR images with better visual quality, lower reconstruction error, and acceptable computation efficiency as compared with state-of-the-art works.

Abstract: Natural images exhibit geometric structures that are informative of the properties of the underlying scene. Modern image processing algorithms respect such characteristics by employing regularizers that capture the statistics of natural images. For instance, total variation (TV) respects the highly kurtotic distribution of the pointwise gradient by allowing for large magnitude outlayers. However, the gradient magnitude alone does not capture the directionality and scale of local structures in natural images. The structure tensor provides a more meaningful description of gradient information as it describes both the size and orientation of the image gradients in a neighborhood of each point. Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor. Our method alternates two minimization steps: 1) robust estimation of the structure tensor as a semidefinite program and 2) reconstruction of the image with an adaptive regularizer defined from this tensor. This two-step procedure allows us to extend anisotropic diffusion into the convex setting and develop robust, efficient, and easy-to-code algorithms for image denoising, deblurring, and compressed sensing. Our method extends naturally to nonlocal regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV and diffusion operators. Our experiments show a consistent accuracy improvement over classic regularization.

Abstract: 1337 wileyonlinelibrary.com C O M M U N IC A IO N anisotropic arrangement and shape of the scatterers. Light transport in the scales thus has evolved to increment the scattering strength along the out-of-plane direction, leading to a pronounced total refl ectance, i.e., its brightness. This led, as a trade-off, to a decrease of the in-plane scattering strength, which in any case does not contribute to the brightness. In this respect, our results identify the degree of anisotropy as a key microscopic structural feature in determining a bright white refl ectance for thin, low-refractive-index optical coatings. Such discovery can be successfully applied in developing new lightweight, thin optical materials with immediate technological impact in applications ranging from coatings to displays and light-emitting diodes (LEDs)/illumination. The structure responsible of the extraordinary bright whiteness of the Cyphochilus beetle is shown in Figure 1 . The body of the beetle is covered by white scales (Figure 1 b), which are about 100 μm wide and 250 μm long. Analysis on scanning electron microscope (SEM) images of 80 different scales of the same beetle, gently dissected with a razor blade, reveals an average thickness of 7 μm with a standard deviation of σ = 1.5 μm ( Figure 2 a). The bright whiteness of the Cyphochilus beetle scales angle results from multiple scattering of light by the microstructure present inside the scales (Figure 1 d), [ 9 ] which is characterized by a cuticular random network of interconnected chitin rods, typically shorter than 1 μm and with a diameter of approximately 250 nm. [ 7 ] SEM images and analy sis reported in literature reveal a very high fi lling fraction of the chitin network with respect to the volume of the scale (f ≈ 60%). [ 7,9 ] As discussed in our previous work, [ 9 ] the particular morphology of the internal structure allows a high density of scatterers (which intuitively increases the scattering intensity and, consequently, the brightness) yet reducing the optical crowding effect (which instead tends to lower the overall scattering strength). [ 10 ] A high fi lling fraction usually leads to pronounced structural correlations due to the physical size of the scattering elements, [ 11,12 ] which in turn leads to a modulated spectral response, i.e., a coloration. [ 13–16 ] This is the case, for example, of the blue and green appearance of certain species of birds, [ 17–19 ]

Abstract: Multiplicative noise removal is a challenging task in image processing. Inspired by the impressive performance of nonlinear diffusion models in additive noise removal, we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods. We develop a nonlinear diffusion filter denoising framework, which considers not only the information of the gradient of the image, but also the information of gray levels of the image. Furthermore, under this framework, we propose a doubly degenerate diffusion model for multiplicative noise removal, which is analyzed with respect to some of its properties and behavior in denoising process. In numerical aspects, we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model. Finally, the experimental results illustrate effectiveness and efficiency of the proposed model.

Abstract: This paper presents two novel contributions on the recently introduced Mixed High-Order (MHO) methods [`Arbitrary order mixed methods for heterogeneous anisotropic diffusion on general meshes', preprint (2013)]. We first address the hybridization of the MHO method for a scalar diffusion problem and obtain the corresponding primal formulation. Based on the hybridized MHO method, we then design a novel, arbitrary order method for the Stokes problem on general meshes. A full convergence analysis is carried out showing that, when independent polynomials of degree k are used as unknowns (at elements for the pressure and at faces for each velocity component), the energy-norm of the velocity and the L2-norm of the pressure converge with order (k + 1), while the L2-norm of the velocity (super-)converges with order (k + 2). The latter property is not shared by other methods based on a similar choice of unknowns. The theoretical results are numerically validated in two space dimensions on both standard and polygonal meshes.

Abstract: In this paper, we present an adaptive anisotropic diffusion (AD) method for the speckle filtering of polarimetric synthetic aperture radar (PolSAR) images. One of the main innovations of our work is that we employ a likelihood-ratio test method to measure the equality of two polarimetric covariance matrices to control the diffusivity, and thus consider the full polarimetric information and the statistical traits of PolSAR data in the diffusion process. Meanwhile, to overcome the drawback of the conventional AD methods, we integrate the local homogeneity information into the diffusion model to adaptively control the generosity of the filtering. Experiments were conducted on a simulated image and two airborne PolSAR images to illustrate the filtering performance, and the results show that the proposed method effectively reduces speckle, retains edges, and targets, and preserves the polarimetric scattering mechanisms.

Abstract: Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an advection-diffusion equation augmenting the equations of magnetohydrodynamics. We introduce a new method for solving the anisotropic diffusion equation using an implicit finite-volume method with adaptive mesh refinement and adaptive time-stepping in the RAMSES code. We apply this numerical solver to the diffusion of cosmic ray energy, and diffusion of heat carried by electrons, which couple to the ion temperature. We test this new implementation against several numerical experiments and apply it to a simple supernova explosion with a uniform magnetic field.

Abstract: This article provides an overview of the origin, computation, properties, and applications of the diffusion tensor model. It details how the diffusion tensor formalism was initially introduced to quantify anisotropic diffusion of water molecules in the brain and to model diffusion-weighted measurements from magnetic resonance imaging experiments. It outlines the various computational options to reliably estimate the diffusion tensor. It finally describes the mathematical properties of the tensor model, how they relate to tissue microstructure, and how they can be used for neuroscience and clinical applications.

Abstract: Anisotropy and compositional and structural heterogeneity in clays are causes of considerable deviations from homogeneous diffusion, in particular in terms of direction-dependent transport rates and preferred transport zones. Conventional diffusion experiments, in which the sample is treated as a homogeneous black box in a concentration gradient, are interminable and insensitive to spatial effects. In contrast, tomographic imaging methods are capable of both reducing the amount of observation time required and revealing space-dependent features of the diffusion process. In the present study, positron-emission-tomography (PET) was applied as the most sensitive quantitative spatiotemporal tomographic modality for direct observation of positron-emitting radiotracers in opaque media at reasonable resolution (1 mm) on a laboratory scale (100 mm). Geoscientific applications of PET, or GeoPET, have revealed anisotropic and heterogeneous effects in diffusion experiments that have been conducted on Opalinus clay samples of different sizes, as well as on other rock types. Applying the Comsol Optimization Module to 2D-image sections of the PET tomograms, effective parameter values were derived, thereby quantifying the anisotropic diffusion.

Abstract: A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle. It is shown that the direct application of the M-matrix theory to the stiffness matrix of the weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh dihedral angles to be strictly acute (a constant-order away from 90 degrees). To avoid this difficulty, a reduced system is considered and shown to satisfy the discrete maximum principle under weaker mesh conditions. The discrete maximum principle is then established for the full weak Galerkin approximation using the relations between the degrees of freedom located on elements and edges. Sufficient mesh conditions for both piecewise constant and general anisotropic diffusion matrices are obtained. These conditions provide a guideline for practical mesh generation for preservation of the maximum principle. Numerical examples are presented.

Abstract: This study is concerned with the problem of shadow detection and removal from single images of natural scenes In this work, the authors propose a shadow detection method with a surface descriptor, termed colour-shade, which allows them to include the physical considerations derived from the image formation model capturing gradual colour surface variations The authors incorporate a colour-shade descriptor into the condition random field model to find same illumination pairs and to obtain coherent shadow regions The authors propose a shadow removal method using an improved local colour constancy computation, which uses anisotropic diffusion to estimate the illuminant locally for each image pixel in shadow The authors evaluate their method on two shadow detection databases The experimental results demonstrate that their shadow detection and removal method is state of the art

Abstract: Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods.

Abstract: This work is devoted to the comparison of numerical schemes to approximate anisotropic diffusion problems arising in tokamak plasma physics. We focus on the spatial approximation by using finite volume method and on the time discretization. This latter point is delicate since the use of explicit integrators leads to a severe restriction on the time step. Then, implicit and semi-implicit schemes are coupled to finite volumes space discretization and are compared for some classical problems relevant for magnetically confined plasmas. It appears that the semi-implicit approaches (using ARK methods or directional splitting) turn out to be the most efficient on the numerical results, especially when nonlinear problems are studied on refined meshes, using high order methods in space.

Abstract: In this work, the authors have proposed a multi-frame super-resolution method that is based on the diffusion-driven regularization functional. The new regularizer contains a variable exponent that adaptively regulates its diffusion mechanism depending upon the local image features. In smooth regions, the method favors linear isotropic diffusion, which removes noise more effectively and avoids unwanted artifacts (blocking and staircasing). Near edges and contours, diffusion adaptively and significantly diminishes, and since noise is hardly visible in these regions, an image becomes sharper and resolute—with noise being largely reduced in flat regions. Empirical results from both simulated and real experiments demonstrate that our method outperforms some of the state-of-the-art classical methods based on the total variation framework.

Abstract: This study presents a new Perona–Malik (PM) model which is based on new non-local means (NLM) theory for an image denoising. In the proposed model, the intensity, space position and gradient information are introduced into NLM model, which weakens the staircasing effect and preserves edge in a processed image. The new PM model enhances the denoising capability, and decreases fine characteristics to be over-smoothed. Comparative experiments show that the denoising capability of the proposed model is superior to the other three existing models.

Abstract: This paper presents the despeckling applications of 48 filters for B-mode echocardiographic images. The filters are grouped into eight types, namely, local statistics, fuzzy, Fourier, multiscale, nonlinear iterative, total variation, nonlocal mean, and hybrid. The thrust areas of analyses are noise suppression, edge, and structure preservation evaluated in terms of image quality metrics, visual quality assessment, and clinical validation. The comparative analysis reveals that filters based on generalized likelihood ratio, local statistics (mean and variance), detail preserving anisotropic diffusion, fast bilateral, sparse representation based beta process factor analysis, and patch-based locally optimal Wiener and probabilistic nonlocal means stand out among the techniques being considered for comparison.

Abstract: This paper introduces a computer aided diagnosis (CAD) technique for segmentation of mass in breast ultrasound (BUS) images followed by an efficient classification of the image into benign or malignant one. The presence of speckle noise, low contrast and blurred boundary of mass in a BUS image makes it challenging to determine the mass, which is the region of interest (ROI) in the current work. Detecting an accurate ROI in turn results in efficient feature extraction and classification. In current work, image enhancement and speckle noise reduction are implemented for preprocessing in a simple but efficient way through filtering techniques. The results of the preprocessing stage are as effective as those obtained using traditional speckle reduction anisotropic diffusion (SRAD) algorithm. ROI is then accurately determined on preprocessed image by employing local region based active contour method. BUS images are classified through textural, morphological and histogram oriented feature metrics in this work. The obtained features are dimensionally reduced using principal component analysis (PCA) and classified through support vector machine (SVM) method. The proposed method is tested on several images and found to be very effective having an accuracy of 95.7% with very high specificity and positive predictive value (PPV).

Abstract: One of the inherent characteristics of radar images is the presence of speckle noise. Speckle appears as a grainy texture in the image and highly reduces the image quality. Therefore, it is desirable to reduce speckle, prior to any image interpretation. With regard to the importance of synthetic aperture radar (SAR) images, a lot of efforts have already been made to remove speckle noise from radar images, and accordingly famous filters have been introduced, each with their special advantages and disadvantages. In this paper, we examine five methods like the ones in the field of space and frequency domain. we will compare five different approaches: Wavelet Thresholding methods, anisotropic diffusion and speckle reducing anisotropic diffusion, also we suggest a method for reducing speckle of synthetic aperture radar images which is in fact a combination of hybrid mean-median filter and the method of speckle reducing anisotropic diffusion. The results indicate that the performance of our proposed method, based on criteria such as PSNR, improving SNR, standard protect the edge (β), in almost all cases is better the other compared methods; and it also offers more desirable results from the point of visual quality.

Abstract: Many denoising approaches extend image processing to a hyperspectral cube structure, but do not take into account a sensor model nor the format of the recording. We propose a denoising framework for hyperspectral images that uses sensor data to convert an acquisition to a representation facilitating the noise-estimation, namely the photon-corrected image. This photon corrected image format accounts for the most common noise contributions and is spatially proportional to spectral radiance values. The subsequent denoising is based on an extended variational denoising model, which is suited for a Poisson distributed noise. A spatially and spectrally adaptive total variation regularisation term accounts the structural proposition of a hyperspectral image cube. We evaluate the approach on a synthetic dataset that guarantees a noise-free ground truth, and the best results are achieved when the dark current is taken into account.

Abstract: Existing approaches for diffusion on graphs, e.g., for label propagation, are mainly focused on isotropic diffusion, which is induced by the commonly-used graph Laplacian regularizer. Inspired by the success of diffusivity tensors for anisotropic diffusion in image processing, we presents anisotropic diffusion on graphs and the corresponding label propagation algorithm. We develop positive definite diffusivity operators on the vector bundles of Riemannian manifolds, and discretize them to diffusivity operators on graphs. This enables us to easily define new robust diffusivity operators which significantly improve semi-supervised learning performance over existing diffusion algorithms.