Adaptive digital ridgelet transform and its application in image denoising

In this paper, we propose a new multiscale decomposition algorithm called adaptive digital ridgelet (ADR) transform. Differently from the traditional nonadaptive multiscale decompositions, this algorithm can adaptively deal with line and curve information in an image by considering its underlying structure. As the key part of the adaptive analysis, the curve parts of an image are detected accurately by a new curve part detection method. ADR transform is applied to image denoising experiment in this paper. Experimental results demonstrate its efficiency for reducing noises as PSNR values can be improved maximally 5 dB compared with other methods and MAE values are also considerably improved. A new comparison criterion is also proposed and using this criterion, it is shown that ADR transform can provide a better performance in image denoising.