Image compression using variable blocksize vector quantization based on rate-distortion decomposition

In this paper, we propose an optimal quadtree segmentation of an image for variable blocksize vector quantization (VBVQ) such that the total distortion of the reconstructed image is minimal and the total required bits don´t exceed the bit budget. The above constraint problem is converted into an equivalent unconstrained problem by using Lagrange multiplier. We prune the full quadtree by comparing the Lagrangian costs of the parent and four child nodes. If the adjacent subblocks merge into a larger block reducing the Lagrangian cost, these subblocks will be merged. Otherwise, these subblocks will be vector quantized. From our simulation results, we see that the reconstructed image of our proposed algorithm has 1-3 db higher PSNR than the fixed blocksize VQ and conventional VBVQ algorithms