Image denoising is a fundamental and important task in image processing and computer vision fields. There are many methods are proposed to reconstruct clean images from noisy versions. These methods differ in both methodology and performance. On one hand, denoising methods can be classified into local and non-local methods. On the other hand, they can be marked as spatial and frequency domain methods. Sparse coding and low-rank are two popular techniques for denoising recently. This paper summarizes existing techniques and provides several promising directions for further studying in the future.

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables models. We derive the asymptotic normality for estimators of the slope parameter and the nonparametric component in the case of known error variance with NA(negatively associated) random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finite sample behavior of the estimators is investigated via simulations too.

Data has been collected for analysis purposes by governments, companies, and institutions.  Data analytics is used to discover precious knowledge from huge amount of data. Spatial analysis is one of the main components of GIS tools. Spatial analysis is the process of manipulating of spatial data to reach knowledge. Spatial interpolation methods are employed to build prediction models for unmeasured points. Spatial interpolation methods play a crucial role for many engineering and financial disciplines. Trend Surface Analysis (TSA) is one of the most applied and dependable spatial interpolation methods. TSA, basically, searches the best fitted polynomial expression for the given data set. Such calculations may require so much time, computing and storage capacity. In recent years, there is a new trend to transfer these kinds of burdens to cloud servers which are dedicated to give computing and storage services. However, data is one of the most valuable assets of institutions. Therefore, privacy of each party becomes more critical. Data owners try to hide their data from both clients and cloud servers. The clients want to get a prediction value without disclosing the coordinates where it may invest its money and time. Our study proposes a secure solution in this framework. We examine our solution thoroughly in terms of accuracy and security.