Image interpolation is a basic problem of image processing

in order to get a more reasonable weight function

the paper studies the application of gradients in one-dimensional signal interpolation

and generalizes it to the interpolation of image

then obtains a method for image interpolation based on gradients.In linear interpolation model

the weighted function is only dependent on the distance of the pixels

but not on the gradient

which often leads to the blurring of the image.Since image is a piecewise continual function

the gray value of an unknown pixel is closer to the pixel with smaller gradient than the pixel with bigger gradient

so a decreased weighted function of gradient is constructed in this method to interpolate the unknown pixels.It also discusses the selection of the related parameter in the model

and obtains a reasonable parameter based on the distribution of the gradient.The algorithm is tested on two images

all results show that the new method has higher peak signal to noise ratio and better intensity of image than known methods

and that it suits to simple image especially.