Restoration of chopped and nodded images by framelets

In infrared astronomy, an observed image from a chop-and-nod process can be considered as the result of passing the original image through a high-pass filter. Here we propose a restoration algorithm which builds up a tight framelet system that has the high-pass filter as one of the framelet filters. Our approach reduces the solution of restoration problem to that of recovering the missing coefficients of the original image in the tight framelet decomposition. The framelet approach provides a natural setting to apply various sophisticated framelet denoising schemes to remove the noise without reducing the intensity of major stars in the image. A proof of the convergence of the algorithm based on convex analysis is also provided. Simulated and real images are tested to illustrate the efficiency of our method over the projected Landweber method.