  Sparse representation of images under certain transform domain has been
playing a fundamental role in image restoration tasks. One such representative
method is the widely used wavelet tight frame systems. Instead of adopting
fixed filters for constructing a tight frame to sparsely model any input image,
a data-driven tight frame was proposed for the sparse representation of images,
and shown to be very efficient for image denoising very recently. However, in
this method the number of framelet filters used for constructing a tight frame
is the same as the length of filters. In fact, through further investigation it
is found that part of these filters are unnecessary and even harmful to the
recovery effect due to the influence of noise. Therefore, an improved
data-driven sparse representation systems constructed with much less number of
filters are proposed. Numerical results on denoising experiments demonstrate
that the proposed algorithm overall outperforms the original data-driven tight
frame construction scheme on both the recovery quality and computational time.
