  In this paper we aim to tackle the problem of reconstructing a
high-resolution image from a single low-resolution input image, known as single
image super-resolution. In the literature, sparse representation has been used
to address this problem, where it is assumed that both low-resolution and
high-resolution images share the same sparse representation over a pair of
coupled jointly trained dictionaries. This assumption enables us to use the
compressed sensing theory to find the jointly sparse representation via the
low-resolution image and then use it to recover the high-resolution image.
However, sparse representation of a signal over a known dictionary is an
ill-posed, combinatorial optimization problem. Here we propose an algorithm
that adopts the smoothed $l_0$-norm (SL0) approach to find the jointly sparse
representation. Improved quality of the reconstructed image is obtained for
most images in terms of both peak signal-to-noise-ratio (PSNR) and structural
similarity (SSIM) measures.
