  Context. Most popular algorithms in use to remove the effects of a
telescope's point spread function (PSF) in radio astronomy are variants of the
CLEAN algorithm. Most of these algorithms model the sky brightness using the
delta-function basis, which results in undesired artefacts when used on image
extended emission. The adaptive scale pixel decomposition (Asp-Clean) algorithm
models the sky brightness on a scale-sensitive basis and thus gives a
significantly better imaging performance when imaging fields that contain both
resolved and unresolved emission.
  Aims. However, the runtime cost of Asp-Clean is higher than that of
scale-insensitive algorithms. In this paper, we identify the most expensive
step in the original Asp-Clean algorithm and present an efficient
implementation of it, which significantly reduces the computational cost while
keeping the imaging performance comparable to the original algorithm. The PSF
sidelobe levels of modern wide-band telescopes are significantly reduced,
allowing us to make approximations to reduce the computing cost, which in turn
allows for the deconvolution of larger images on reasonable timescales.
  Methods. As in the original algorithm, scales in the image are estimated
through function fitting. Here we introduce an analytical method to model
extended emission, and a modified method for estimating the initial values used
for the fitting procedure, which ultimately leads to a lower computational
cost.
  Results.The new implementation was tested with simulated EVLA data and the
imaging performance compared well with the original Asp-Clean algorithm. Tests
show that the current algorithm can recover features at different scales with
lower computational cost.
