Extended smoothlets: An efficient multi-resolution adaptive transform

As a family of multiresolution adaptive transforms and a generalization of wedgelets, smoothlets are more efficient in representing images with various sharp edges than other “X-lets”. Smoothlets use a horizon function to model an edge and define transition in a fixed axis direction. Furthermore, the conventional elliptical smoothlets (ES) use half of an ellipse to model edges. Various sharp edges of images may not be expressed well by half of an ellipse with transition only in a fixed axis direction. In this paper, we propose extended smoothlets (ExSmoothlets) framework by using more general characteristic functions with adaptive transition directions. Specifically, two methods of ExSmoothlets, the elliptical ExSmoothlets (EES) and homocentric elliptical ExSmoothlets (HEES) are developed and evaluated in the experiments against the ES. The results show that the proposed EES and HEES can effectively improve the image quality in image approximation and denoising in terms of PSNR.