Energy-based adaptive transform scheme in the DPRT domain and its application to image denoising

In this paper, an energy-based adaptive transform scheme in the discrete periodic Radon transform domain is proposed for an efficient representation of linear singularities in images. Experimental results using non-linear approximation show that it possesses the superior property of energy concentration compared with the discrete wavelet transform and finite ridgelet transform. Furthermore, we have applied the scheme to the denoising problem and proposed a novel threshold selection method. Results of our experimental work, carried out on images containing strong linear singularities and texture components with varying levels of additive white Gaussian noise, show that our approach achieves a substantial improvement in terms of both signal-to-noise ratio and in visual quality as compared with that of the discrete wavelet transform and finite ridgelet transform.