Downsampling based image compression scheme achieves better quality at low bit rates. This paper presents a new scheme in such a paradigm based on adaptive sparse representations with respect to two trained overcomplete dictionaries. The original image is downsampled at the encoder side and an upscaling technique is employed to restore the downsampled image to its original resolution at the decoder side. Due to the downsampling, the high frequency details are removed; therefore, the bit budget of low frequency information is increased, leading to better coding performance at the low bitrates. In order to further improve the coding efficiency, we also propose to encode the residual image as side information. This residual image is obtained by difference between the original image and upscaled image. The low resolution image and the residual image are represented over two dictionaries trained by a bilevel dictionary learning algorithm. Furthermore, the visual salient information is considered into the rate allocation process to improve the rate-distortion performance. The enhanced scheme achieves improvement of the quality at a variety of bitrates at the expense of increasing the system complexity, when compared to the conventional codecs.