Signal Processing: Image Communication 15 (2000) 869}877 Blocking e!ect reduction of compressed images using classi"cation-based constrained optimization  Tae Keun Kim, Joon Ki Paik*, Chee Sun Won, Yoonsik Choe, Jechang Jeong, Jae Yeal Nam Department of Electronic Engineering, Chung-Ang University, Seoul, South Korea Department of Electronic Engineering, Dongguk University, South Korea Department of Electrical Engineering, Yonsei University, South Korea Department of Electronic Communication Engineering, Hanyang University, South Korea Department of Computer Science, Keimyung University, South Korea Received 30 March 1998 Abstract In this paper we propose an adaptive image restoration algorithm using block-based edge-classi"cation for reducing block artifacts in compressed images. In order to e$ciently reduce block artifacts, edge direction of each block is classi"ed by using model-"tting criterion, and the constrained least-squares (CLS) "lter with corresponding direction is used for restoring the block. The proposed restoration "lter is derived based on the observation that the quantization operation in a series of coding processes is a nonlinear and many-to-one mapping operator. Then we propose an approximated version of a constrained optimization technique as a restoration process for removing the nonlinear and space-varying degradation operator. For real-time implementation, the proposed restoration "lter can be realized in the form of a truncated FIR "lter, which is suitable for postprocessing reconstructed images in digital TV, video conferencing systems, etc.  2000 Elsevier Science B.V. All rights reserved. Keywords: Image restoration; Constrained optimization; Blocking e!ect 1. Introduction As the demand for video communication has grown, many e$cient image compression methods have been developed and standardized. Especially, high quality image communication with low bit- rate is gaining growing interests in applications to video conferencing, videophone, interactive TV, etc. * Corresponding author.  This research was supported in part by Korea Science and Engineering Foundation Research Grant 96-0102-14-01-3. The block discrete cosine transform (BDCT) is the most widely used technique for the compression of both still and moving images. The main draw- back of the BDCT based compression techniques is, however, the block artifact which represents the arti"cial discontinuity between adjacent blocks, and results from the independent processing of the blocks without taking into account the between- block pixel correlations [1]. In order to reduce a block artifact without increasing the bit rate, the following approaches have been proposed; (i) lowpass "ltering on the 0923-5965/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 3 - 5 9 6 5 ( 9 9 ) 0 0 0 3 3 - 8