Abstract: Current image reconstruction models using block compressed sensing (block CS), where data acquisition is conducted in a block-by-block manner through the same measurement matrix, overcomes the difficulties encountered in traditional CS technology of the random measurement ensembles being numerically unwieldy. However, a lot of block artifacts occur in reconstructed images due to the block-by-block manner lack a consideration of global sparsity. This paper analyses three main reasons resulting in block artifacts when image blocks is recovered independently which include nonuniform distribution of block sparsity, spectrum leakage and restricted block size. To resolve them, a new image global model is proposed based on global sparsity. At the encoder, it incoherently measures image block by block using Gaussian random matrix. At the decoder, it introduces reordering operator and reassembles measurement matrix which is not only fit for global reconstruction but also suits CS observed value obtained by measuring image block-by-block. This measurement matrix is still incoherent with sparsity matrix of images, so it can fully utilize global sparsity of images to recovery images by CS algorithms. Experimental results show that the proposed model not only has effectively removed block artifacts, but also has a strong robustness to variable block size.