Abstract—For compressed images, a major drawback is that those images will exhibit severe blocking artifacts at very low bit rates due to adopting Block-based Discrete Cosine Transform (BDCT). In this paper, a novel deblocking scheme using sparse representation is proposed. A new transform called All Phase Biorthogonal Transform (APBT) was proposed in recent years. APBT has the similar energy compaction property with Discrete Cosine Transform (DCT). It has very good column properties, high frequency attenuation characteristics, low frequency energy aggregation, and so on. In this paper, we use it to generate the over-completed dictionary for sparse coding. For Orthogonal Matching Pursuit (OMP), we select an adaptive residual threshold by combining blind image blocking assessment. Experimental results show that this new scheme is effective in image deblocking and can avoid over-blurring of edges and textures. We can obtain deblocked images in the receiver.