Shapelets and related techniques in radio-astronomical imaging

We present the use of orthonormal basis functions, in particular, shapelets and prolate spheroidal wave functions, in radio astronomical imaging. By using such methods, it is possible to overcome some limitations of traditional pixel based image deconvolution. Therefore, such techniques will enable us to increase the achievable imaging dynamic range thus paving the way for novel scientific results. We give an overview of the current state of the art of such methods and provide examples of its use.