Variational-distance-dependent image restoration

There is a need to restore color images that suffer from distance-dependent degradation during acquisition. This occurs, for example, when imaging through scattering media. There, signal attenuation worsens with the distance of an object from the camera. A 'naive' restoration may attempt to restore the image by amplifying the signal in each pixel according to the distance of its corresponding object. This, however, would amplify the noise in a nonuniform manner Moreover, standard space-invariant denoising over-blurs close by objects (which have low noise), or insufficiently smoothes distant objects (which are very noisy). We present a variational method to overcome this problem. It uses a regularization operator which is distance dependent, in addition to being edge-preserving and color-channel coupled. Minimizing this functional results in a scheme of reconstruction-while-denoising. It preserves important features, such as the texture of close by objects and edges of distant ones. A restoration algorithm is presented for reconstructing color images taken through haze. The algorithm also restores the path radiance, which is equivalent to the distance map. We demonstrate the approach experimentally.