Image recovery via geometrically structured approximation

In recent years, the ℓ1ℓ1 norm based regularization has been one promising technique for solving many ill-posed inverse problems in image recovery. As the performance gain of these methods over linear methods comes from the separate process for smooth image regions and image discontinuities, their performance largely depends on how accurate such separation is. However, there is a lot of ambiguities between smooth image regions and image discontinuities when only degraded images are available. This paper aims at developing new wavelet frame based image regularization to resolve such ambiguities by exploiting geometrical regularities of image discontinuities. Based on the geometrical connectivity constraint on image discontinuities, an alternating iteration scheme is proposed which is simple in implementation and efficient in computation. The experiments show that the results from the proposed regularization method are compared favorably against that from several existing ℓ1ℓ1 norm or ℓ0ℓ0 norm based image regularizations.