A multiscale antidiffusion approach for Gaussian blurred images

Antidiffusion is a process running the diffusion equation into minus time. Though extremely important for the scale space image representation and restoration of Gaussian blur, it is a horribly ill-posed problem, since minor noise leads to very erroneous result. To solve this ill-posed problem stably, we first apply a multiscale representation method to decompose an image into components of various scales. We then show that the ill-posedness is introduced by antidiffusing such components with scales smaller than the antidiffusion time t. This implies that, for a component with scale larger than the antidiffusion time t, we can do antidiffusion stably. On the other hand, for a component with smaller scale, if an attempt were made on antidiffusing it, the ill-posedness would result; conversely, if we leave it unchanged, the ill-posedness will no longer exist. Our algorithm is computationally efficient and is robust to noise because it is mainly performed by an integration computation (convolution), contrasting with the differential computation required by direct antidiffusion. Experimental results show its effectiveness in restoring Gaussian blurred images