High-quality image interpolation via nonlinear image decomposition

This paper presents a new image-interpolation approach where one can adjust edge sharpness and texture intensity according to one’s taste. This approach is composed of the three stages. At the first stage, with the BV-G image-decomposition variational model, an image is represented as a product of its two components so that its separated structural component may correspond to a cartoon image-approximation and its separated texture components may collect almost all oscillatory variations representing textures, and the texture co mponent can be amplified or attenuated according to user’s taste. At the second stage, each separated component is interpolated with an interpolation method suitable to it. Since the structural component keeps sharp edges, its proper interpolation method is a TV-regularization super-resolution interpolation method that can restore frequency components higher than the Nyquist frequency and remove sample-hold blurs without producing ringing artifacts near edges. The texture component is an oscillatory function, and its proper interpolation method is a smoothne ss-regularization super-resolution interpolation method that can restore continuous variations and remove the blurs. At the final stage, the two interpolated components are combined. The approach enlarges images without not only blurring edges but also destroying textures, and removes blurs caused by the sample-hold and/or the optical low-pass filter without producing ringing artifacts. Keywords: Image decomposition, variational problem, interpolation, deblurring, super-resolution