Postprocessing for vector-quantized images based on projection onto hypercubes

In this paper, in order to reduce blocking artifacts in vector-quantized images, we propose a new postprocessing algorithm, based on the projection onto a subset of quantization constraint set (QCS). The notion behind the projection onto QCS is to prevent the postprocessed data from diverging from QCS, i.e., blurring, which is usually caused by a low-pass filtering operation. First, we theoretically analyze the projection onto QCS, and show that the projection onto a subset of QCS could yield a better performance than the projection onto QCS case. Since the quantizer regions in the vector quantizer (VQ) are arbitrarily shaped unless the VQ has a structural codebook, it is not easy to implement a projector for QCS. In order to simplify the projection, we introduce hypercubes for a subset of QCS, where the hypercubes are the elements of the subset. Hence, the proposed postprocessing algorithm has two steps: linear space-invariant low-pass filtering (or projecting onto smoothness constraint sets) and then projecting onto hypercubes. Simulation results show that the proposed algorithm can reduce blocking artifacts without blurring the edge components, and achieve a 0.5-2.0-dB gain. Furthermore, the contouring effect can also be removed by iteratively applying the proposed postprocessing algorithm, based on the constrained minimization problem.