A non-aliasing Pyramidal transform

namely NAP transform

is presented to avoid the frequency aliasing of Contourlet transform.NAP transform consists of non-aliasing pyramidal filter banks (NPFB) and DFB.In this paper

we firstly represent the definition and specific parameter setting of NPFB in the frequency domain.NPFB decomposes image into an approximation subband and several detail subbands with different resolutions;whilst DFB decomposes the detail subbands into directional subbands.Not only has the basis function of NAP transform a variety of characteristics such as multi-resolution

multi-direction

localization to meet demands of anisotropy scale relations

but also are their regularity and localization better than those of Contourlet transform in the spatial domain.Results from the experiments of image denoising show that NAP transform can represent image more sparsely and has a significant improvement from the aspect of image denoising

compared with Contourlet transform.