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Image super resolution (SR) aims at recovering the missing high frequency details from single image or multiple images. Existing SR methods can be divided into three categories: interpolation-based, reconstructionbased and example learning-based. Our paper focuses on the third category. Example learning-based SRmethods [6] utilize the LR-HR image pair to infer the missing high-frequency details in the LR image and achieve state-of-the-art performance.Recently, in the field of example learningbased SR, more and more researchers resort to learn the LR-HR relationship directly, i.e. y = f (x), where x is the input LR image feature, y is the targeted HR image and f is the mapping function that transforms the LR feature into HR image. Instead of commonly used parametric models, non-parametric methods [3], especially gaussian process regression (GPR)-related methods [2, 4, 5] begin to emerge in the SR field. However, previous GPR-based SR methods simply learn all the GPR models independently and ignore the correlation between them. On the other hand, each pixel prediction can be treated as a task, so that inferring a HR patch can be regarded as a multi-task problem. In this paper, we focus on the multi-task gaussian process (MTGP) regression and apply it to superresolution problem. We first give a brief overview of MTGP proposed in [1]. Then we study how SR problem corresponds to MTGP and propose the multi-task gaussian process super-resolution (MTGPSR) framework. MTGP tries to solve the following problem: Given N distinct inputs x1, ...,xN we define the complete set of responses for M tasks as y = (y11, ...,yN1, ...,y12, ...,yN2, ...,y1M , ...,yNM) , where yi j is the response for the jth task on the ith input xi. We also denote the N ×M matrix Y such that y = vecY . Given a set of observations yo, which is a subset of y, we wish to predict the unobserved values of yu of some input points for some tasks. MTGP wishes to learn M related latent functions { fl} by placing a GP prior over { fl} and directly induce correlations between tasks. Assuming that the GPs have zero mean we define ⟨ fl(x) fk(x ′) ⟩ = K f lkk x(x,x′) (1)

Multi-task Gaussian Process Regression-based Image Super Resolution