In the present work, a relatively novel method called attractor image coding (commonly known as fractal image coding) for lossy image compression is investigated. Roughly speaking, the original image is partitioned into several disjoint range blocks. For each range block, an affine transformation is constructed to approximate the range block by another part of the same image. Compression is obtained by compactly storing only the descriptions of these transformations. The decoded image is obtained by iteratively applying these transformations on any initial image. However, the attractor coding, being a block-based algorithm, suffers from the usual blocking artifacts which is highly disturbing to human visual system (HVS). The blockiness is mainly due to the independent processing of each block in encoding. Discontinuities may occur across the block boundaries in the decoded image that are smooth in the original image. The problem is more prominent when the bit rate is reduced. In this t...