Fast and simple super-resolution with single images

We present a fast and simple algorithm for super-resolution with single images. It is based on penalized least squares regression and exploits the tensor structure of two-dimensional convolution. A ridge penalty and a difference penalty are combined; the former removes singularities, while the latter eliminates ringing. We exploit the conjugate gradient algorithm to avoid explicit matrix inversion. Large images are handled with ease: zooming a 100 by 100 pixel image to 800 by 800 pixels takes less than a second on an average PC. Several examples, from applications in wide-field fluorescence microscopy, illustrate performance.