The challenging inverse problem of blind deblurring has been investigated thoroughly for natural images. Existing algorithms exploit edge-type structures, or similarity to smaller patches within the image, to estimate the correct blurring kernel. However, these methods do not perform well enough on natural stochastic textures (NST), which are mostly random and in general are not characterized by distinct edges and contours. In NST even small kernels cause severe degradation to images. Restoration poses therefore an outstanding challenge. In this work, we refine an existing method by implementing an anisotropic fractal model to estimate the blur kernel's power spectral density. The final kernel is then estimated via an adaptation of a phase retrieval algorithm, originally proposed for sparse signals. We further incorporate additional constraints that are specific to blur filters, to yield even better results. The latter are compared with results obtained by recently published blind deblurring methods.

Embedding textured images in manifolds reveals latent information regarding texture structure and allows useful analysis of these high dimensional images in a low dimensional space. We present a framework for analysis and synthesis of natural stochastic textures (NST) which constitute an important subset of textures that are modelled as realizations of random processes. The randomness of NST differentiates them from other types of images and requires a dedicated method for analysis and synthesis. We demonstrate several applications of this framework. The first is synthesis of new types of NST. The second is NST analysis, reaffirming our previous findings regarding the fundamental properties of NST, and showing that they emerge naturally in the latent parameter space. Finally, we show the advantage of producing a manifold representation with intrinsic geometry.

Natural stochastic textures (NSTs), characterized by their fine details, are prone to corruption by artifacts, introduced during the image acquisition process by the combined effect of blur and noise. While many successful algorithms exist for image restoration and enhancement, the restoration of natural textures and textured images based on suitable statistical models has yet to be further improved. We examine the statistical properties of NST using three image databases. We show that the Gaussian distribution is suitable for many NST, while other natural textures can be properly represented by a model that separates the image into two layers; one of these layers contains the structural elements of smooth areas and edges, while the other contains the statistically Gaussian textural details. Based on these statistical properties, an algorithm for the denoising of natural images containing NST is proposed, using patch-based fractional Brownian motion model and regularization by means of anisotropic diffusion. It is illustrated that this algorithm successfully recovers both missing textural details and structural attributes that characterize natural images. The algorithm is compared with classical as well as the state-of-the-art denoising algorithms.

Denoising of Natural Stochastic Colored-Textures (color NST) is of special interest in image processing. Existing algorithms produce over-smoothed images with sharp edges, and do not restore the fine textural color details. We analyze the structure of color NST images and propose a simple model. This model is Gaussian and has a low number of parameters that can be estimated efficiently. A maximum-a-posteriori (MAP) scheme is proposed for patch-wise denoising of color NST. The denoised images exhibit better restored textural details compared to existing algorithms. A boosting algorithm is proposed for denoising of complex images containing both cartoon-type and textural image components.

Statistics of natural images has become an important subject of research in recent years. The highly kurtotic, non-Gaussian, statistics known to be characteristic of many natural images are exploited in various image processing tasks. In this paper, we focus on natural stochastic textures (NST) and substantiate our finding that NST have Gaussian statistics. Using the well-known statistical self-similarity property of natural images, exhibited even more profoundly in NST, we exploit a Gaussian self-similar process known as the fractional Brownian motion, to derive a fBm-PDE-based singleimage superresolution scheme for textured images. Using the same process as a prior, we also apply it in denoising of NST.

Enhancement of Natural Stochastic Textures (NST) is of special interest in image processing. These textures are considered to be realizations of random processes, and exhibit different statistical properties than those characteristic of cartoontype natural images or of structured textures. NSTs are interesting due to their fine details, which pose a challenge to enhancement algorithms. Existing algorithms, based on models of natural images, do not produce satisfactory results on NST. The long-range dependence (LRD) property of NST is explored and substantiated in this paper. An optimization scheme, implemented in the frequency domain, is then proposed. This scheme exploits the LRD as a property of the frequency magnitude, while a desired phase, extracted from the degraded image, is imposed. The scheme is general and can be further used in other image processing tasks. Zero-phase filters are of special interest in this context.

Texture enhancement presents an ongoing challenge, in spite of the considerable progress made in recent years. Whereas most of the effort has been devoted so far to enhancement of regular textures, stochastic textures that are encountered in most natural images, still pose an outstanding problem. The purpose of enhancement of stochastic textures is to recover details, which were lost during the acquisition of the image. In this paper, a texture model, based on fractional Brownian motion (fBm), is proposed. The model is global and does not entail using image patches. The fBm is a self-similar stochastic process. Self-similarity is known to characterize a large class of natural textures. The fBm-based model is evaluated and a single-image regularized superresolution algorithm is derived. The proposed algorithm is useful for enhancement of a wide range of textures. Its performance is compared with single-image superresolution methods and its advantages are highlighted.

Single-image superresolution has become a widely-studied subject in image processing in recent years. Although considerable effort has been devoted in this context to contour enhancement, much less has been done to improve the textures of a degraded image. In this study, we present a novel algorithm which utilizes the power-law spectra of approximated 1/f processes, fitting a model of degraded natural textures to recover the information lost by blurring. A mosaic of realizations of the approximated 1/f processes is first imposed on the degraded texture, and a deblurring process is then applied. The entire process is iterated until convergence. This algorithm exploits the self-similarity, characteristic of textures of natural images, and recovers the missing high-resolution information without using prior information of any specific image.

A key-value store (KVS) offers functions for storing and retrieving values associated with unique keys. KVSs have become the most popular way to access Internet-scale “cloud” storage systems. We present an efficient wait-free algorithm that emulates multi-reader multi-writer storage from a set of potentially faulty KVS replicas in an asynchronous environment. Our implementation serves an unbounded number of clients that use the storage concurrently. It tolerates crashes of a minority of the KVSs and crashes of any number of clients. Our algorithm minimizes the space overhead at the KVSs and comes in two variants providing regular and atomic semantics, respectively. Compared with prior solutions, it is inherently scalable and allows clients to write concurrently. Because of the limited interface of a KVS, textbook-style solutions for reliable storage either do not work or incur a prohibitively large storage overhead. Our algorithm maintains two copies of the stored value per KVS in the common case, and we show that this is indeed necessary. If there are concurrent write operations, the maximum space complexity of the algorithm grows in proportion to the point contention. A series of simulations explore the behavior of the algorithm, and benchmarks obtained with KVS cloud-storage providers demonstrate its practicality.