Image approximation and smoothing by support vector regression

A new image representation by support vector regression (SVR) is introduced. After a grey level image is approximated as a continuous function using SVR, which maps a 2D pixel coordinate input into a 1D pixel grey level output, the image can then be expressed in terms of the extracted support vectors and their corresponding Lagrange multipliers. The image is reconstructed by a linear combination of kernels with weights equal to the values of Lagrange multipliers. With support vector representation, we can observed that: 1) it is able to remove noise from image, the denoising effect of SVR representation is implicit during image encoding, and it can be controlled by the SVR training parameters; 2) if a Gaussian RBF kernel is used in SVR representation, Gaussian smoothing can be easily implemented by increasing the variance of kernel during image reconstruction and sharpening can be done by reducing the variance