A method constructs an image with improved peak signal-to-noise ratio (PSNR) from a scattered pixel set. The method generates an approximation function that is a linear combination of a plurality of Many-Knot (MK) spline basis functions, and constructs the image with improved PSNR by conducting a least squares treatment on the approximation function to minimize a residual of each pixel value in the scattered pixel set from the approximation function.