This study aims to reduce blocking artifacts in compressed images coded by the block discrete cosine transform (BDCT). The theory of projection onto convex sets (POCS) is applied. Two adaptive constraints are used. The first constraint corresponds to a model that simulates an image before compression using a Delaunay triangular mesh. The mesh is constructed by dividing each block into a set of triangles. The number of triangles in a block is determined by the local block activity. The second constraint is a narrow quantization constraint, where the bound of a BDCT coefficient is also determined by the local block activity. The block activity is measured by the ac components of the BDCT coefficients by incorporating the human visual system model. Our technique produces significantly improved results after a single iteration, and compares favorably with existing methods.