High Quality Image Interpolation via Local Autoregressive and Nonlocal 3-D Sparse Regularization

In this paper, we propose a novel image interpolation algorithm, which is formulated via combining both the local autoregressive (AR) model and the nonlocal adaptive 3-D sparse model as regularized constraints under the regularization framework. Estimating the high-resolution image by the local AR regularization is different from these conventional AR models, which weighted calculates the interpolation coefficients without considering the rough structural similarity between the low-resolution (LR) and high-resolution (HR) images. Then the nonlocal adaptive 3-D sparse model is formulated to regularize the interpolated HR image, which provides a way to modify these pixels with the problem of numerical stability caused by AR model. In addition, a new Split-Bregman based iterative algorithm is developed to solve the above optimization problem iteratively. Experiment results demonstrate that the proposed algorithm achieves significant performance improvements over the traditional algorithms in terms of both objective quality and visual perceptionComment: 4 pages, 5 figures, 2 tables, to be published at IEEE Visual Communications and Image Processing (VCIP) 201

Forecasting seasonality in prices of potatoes and onions: challenge between geostatistical models, neuro fuzzy approach and Winter method

This paper, we studied the ability of geostatistical models (ordinary kriging (OK) and Inverse distance weighting (IDW)), adaptive neuro-fuzzy inference system (ANFIS) and Winter method for prediction of seasonality in prices of potatoes and onions in Iran over the seasonal period 1986_2001. Results show that the best estimators in order are winter method, ANFIS and geostatistical methods. The results indicate that Winter and ANFIS had powerful results for prediction the prices while geostatistical models were not useful in this respect.Price; Geostatistical model; Kiriging; Inverse distance weighting; Winter’s method; Adaptive neuro fuzzy inference system; Potatoes; Onions; Iran

Forecasting seasonality in prices of potatoes and onions: challenge between geostatistical models, neuro fuzzy approach and Winter method

Price, Geostatistical model, Kiriging, Inverse distance weighting, Winter’s method, Adaptive neuro fuzzy inference system, Potatoes, Onions, Iran, Crop Production/Industries, Demand and Price Analysis,

Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a pre-collected dataset of example image patches, and then for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image non-local self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI

Daily minimum and maximum temperature simulation over complex terrain

Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult to produce due to terrain driven nonstationarity. We develop a bivariate stochastic model for the spatiotemporal field of minimum and maximum temperature. The proposed framework splits the bivariate field into two components of "local climate" and "weather." The local climate component is a linear model with spatially varying process coefficients capturing the annual cycle and yielding local climate estimates at all locations, not only those within the observation network. The weather component spatially correlates the bivariate simulations, whose matrix-valued covariance function we estimate using a nonparametric kernel smoother that retains nonnegative definiteness and allows for substantial nonstationarity across the simulation domain. The statistical model is augmented with a spatially varying nugget effect to allow for locally varying small scale variability. Our model is applied to a daily temperature data set covering the complex terrain of Colorado, USA, and successfully accommodates substantial temporally varying nonstationarity in both the direct-covariance and cross-covariance functions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS602 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page