METRIC. Ming-Te WU and Shiunn-Jang CHERN

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1 REDUCTION of ARTIFACT EFFECT by UING MULTI-CALE UBBAND FILTER BAED on ENERGY METRIC Ming-Te WU and hiunn-jang CHERN Department of Electrical Engineering, National un Yat-en University, Kaohsiung, 80 Taiwan. Fax:(+886) Abstract JPEG 000, based on the wavelet transform, is still one of the best image compression standards. In this paper, a new multi-scale subband wavelet decomposition approach with -scale, based on the energy metrics in spatial domain, is devised. Compared with the JPEG 000 and other recent developed scheme, the proposed scheme could be used not only reducing the artifact effects, such as blocing or blurring edge, but also improving the performance in terms of PNR. Experimental results with 0: compression ratio, for given adaptively energy threshold, are performed to verify that our proposed scheme yields improvement, in terms of PNR about 3.55db over the one with JPEG, around.50db better than the Kim s method [3], and about 0.8db over the one with JPEG 000 scheme. The computer results exemplify that with our proposed method it could reconstruct the compressed images to achieve desired performance subjectively and objectively. Key Words artifact effect, blocing, energy threshold, PNR, multi-scale subband filter, energy metric I. INTRODUCTION The problem of artifact effect reductions, viz., blocing or blurring edge, is very significant and has been studied, recently, in images processing and coding. To deal with this problem the conventional approach, such as post-processing for reducing or minimizing the blocing artifact, the filtering in the DCT domain has been investigated in [, 5, 9]. With the DCT transform approach an image is broen up into 8x8 sub-image blocs, after that each bloc is then transformed with the DCT. In consequence, the coefficients of DCT are quantized and encoded to perform image compression. However, with the DCT approaches, the blocing artifact would cause, even if they did efforts on reducing or minimizing the blocing artifact. To circumvent the drawbac described above, in [, 3,, 0], the wavelet transform domain technologies have been devised to reduce the edge blurring, but it did not reserve too much portion of high frequency coefficients, such that the impairment at bloc boundary was not considered. Although, based on a visual perception criterion [7] to reduce blocing effect in DCT-coded image has better improvement on subjective visibility, but less on objective measurement of the image quality. Moreover, in [5,6], to achieve low bit-rate and having performance improvement on deblocing or deringing, high frequency coefficients have many details in them were ignored, in these methods the blocing artifact have been treated as introduced by the high frequencies. Thus, to further improve the performance, in [8] one-dimensional or two-dimensional filtering schemes were suggested to remove the high frequencies. In this paper, a new multi-scale subband filtering approach, based on energy metrics in spatial domain, is proposed. The energy metrics and pre-selected energy threshold are used to properly preserve information of the high correlation on image texture or boundary, and ignore those with less correlation, to achieve desired bit rate as well as PNR, while to reducing the artifact effects, simultaneously. The detail procedure of the new multi-scale subband filtering approach will be discussed in what follows. II. MULTI-CALE UBBAND FILTERING UING ENERGY METRIC Let be denoted as an original image, with size M N, and (i, j) is the (i,j) element of the image, where i M, j N. In the JPEG 000 approach, after the first-level wavelet decomposition, is decomposed into new subband images,, =,, 3, and, where the size of is ( M N ). In which, and represent the low-low band and low-high band components of, and 3 and are designated as the high-low band and high-high band (or high frequencies) components of, respectively. For getting the high compression ratio of,, is often ignored, due to the fact that less significant information of image is reserved. In fact, this is not true; in high frequencies portion it still possesses much high correlation coefficients on image texture or boundary

2 information, and should not be ignored or completely removed. To circumvent this problem and improve the performance subjectively and objectively, in this paper, a new multistage wavelet decomposition, with -scales, is devised. The detail procedure of our new scheme will be addressed in what follows... DECOMPOITION WITH ENERGY METRIC For convenience to introduce the new multi-scale subband filter based on energy metrics in the spatial domain, it can be summarized as follows. First, we defined energy metric for subband image,, which was E( ) = ( i,j) () i= j= ( ) As described above, in conventional wavelet transform approach, only the relative low frequency coefficients were reserved depended on the compression ratio if high rate was required, the less relative high frequency information would be reserved. To properly reserve the high frequencies having correlation coefficients, we would compare the energy matrices with a pre-selected energy threshold, ETH, to reserve the significant portion of high frequency images. In which, the ETH is selected based on the statistics of the original image experimentally. That is, if E ( ) > ETH, () The nd-scale wavelet transform decomposition will be taen for, such that we would have new subimages, denoted as m, where and m =,,3,, with size of m being ( M N ). In addition, we set Level () = (3) which indicated that E( ) is coincided to equation (), and we have to perform the nd-scale decomposition to. We will use (3) to reconstruct the encoded image later. If equation () was not satisfied, and if E ( ) < ETH ) then we let level () = 0. We used a simple method to quantize and encode the image coefficients, i.e., if the absolute value of (i,j) was smaller than TH, which was a pre-selected quantized threshold value, and was determined, experimentally, based on the statistics of the processed image to remove small coefficients to reduce stored bits, then we set the absolute value of (i,j) was zero. Equivalently, if (i,j) < TH, then (i,j) = 0 (5) and we ignored these coefficients. On the other hand, we reserved the coefficients which (i,j) are larger than TH. In fact, the threshold value depended on bit-rate that demanded. If we want to get the satisfactory performance on image, we should continue analyze the high frequency energy of or m, even the subimages of m. Therefore, if we desired to decompose original image into second-level, the following steps have to be operated. tep : We defined the nd-scale energy metric, which was M N E( m ) = m(i,j) (6) ( ) i= j= imilar to step procedure, we get the nd-scale relation that gives us to judge if we need to reserve these coefficients or not. The judgement equation is: E( m ) > ETH (7) If equation (7) was satisfied, we did the 3rd-scale wavelet transform decomposition to m and m will be subband decomposed to subimages, which are denoted as mn,,m,n =,, 3 and, where the size of mn is ( M 8 N 8). In addition, we set Level (,m) = (8) which indicated that E( m ) is coincided to equation (7) and might do the 3rd-scale decomposition to m. We will use (8) to reconstruct encoded image later. If (7) was not satisfied, i.e. E ( m ) < ETH (9) we set level(,m) = 0. On the other hand, if m (i,j) < TH, then m (i,j) = 0 (0) that is, these coefficients are ignored. Meanwhile, we reserved the coefficients, in which the values of m (i,j) are larger than TH. With the similar idea, if we would lie to achieve specific desired performance, we may further decompose the original images described above into third-level, and can be describing in the following steps: tep 3: We defined the third level energy metric, which was M 8 N 8 E( mn ) = mn(i,j) () ( ) i= j= 8 8 imilar to step procedure, we got the 3rd-scale relation that gives us to judge if we need to reserve these coefficients or not. The judgement equation is: E( mn ) > ETH () If equation () is satisfied, we do the th-scale wavelet transform decomposition to mn and mn will be subband decomposed to subimages which denoted mnr,,m,n and r =,,3,, where the size of mnr is ( M 6 N 6). In addition, we set Level (,m,n) = (3) which indicated E( mn ) coincided equation () and might do the th-scale decomposition to mn. We will use (3) to reconstruct encoded image later. If () was not satisfied, i.e. E ( mn ) < ETH () we set level(,m,n) = 0. If mn (i,j) < TH, then mn (i,j) = 0 (5)

3 and we ignored these coefficients. imultaneously, we reserved the coefficients which mn (i,j) were larger than TH. upposed that r is the last level and then we do as follow: tep : If mnr (i,j) < TH, then mnr (i,j) = 0 and we ignored these coefficients. As mentioned above, we saved those coefficients that were larger than pre-selected threshold value and encoding those coefficients and then transport them to decoder end... RECONTRUCTION PROCEDURE To reconstruct the original image from the compressed image, the reverse process with two-dimension (-D) wavelet transform for every level has to be performed. The procedures are summarized as follows: tep : First, we synthesized the th-scale sub-images to 3rd-scale image. mn (i,j) = IWT( mn mn3 (i,j), (i,j), mn mn (i,j), (i,j)) (6) In equation (6), IWT indicate inverse wavelet transform. mnr(i,j) are the th-scale coefficients that we stored under satisfied equation (). On the other words, mnr(i,j) are those th-scale coefficients which larger than pre-selected threshold value. Here mn(i,j) is designated as the low-low band portion of mn (i,j). Also, mn ( i, j), mn3(i,j), and mn(i,j) represent the low-high band, high-low band, and the high-high band portions of (i,j), respectively. mn tep : Next, we would lie to synthesize the 3rd-scale sub-images from the nd-scale images. m (i,j) = IWT( m m m3 m (i,j) level(,m,), (i,j) level(,m,), (i,j) level(,m,3), (i,j) level(,m,)) (7) mn (i,j) are the 3rd-scale coefficients that obtained from equation (6), where m (i,j) represents the low-low band portion of ( i,j). imilarly, m (i,j), m3 (i,j), and m (i,j) are denoted as the low-high band, high -low band, and high-high band components of (i,j). m m tep 3: We synthesized the nd-scale sub-images to st-scale image. m (i,j) = IWT( 3 (i,j) level(,), (i,j) level(,), (i,j) level(,3), (i,j) level(,)) (8) (i,j) are the second-level coefficients that obtained from equation (7). (i,j) are the low-low band component of (i,j). (i,j) are the low-high band component of (i,j). 3 (i,j) are the high-low band component of (i,j). (i,j) are the high-high band component of (i,j). tep : Finally, we synthesized the st-scale sub-images to original size image. (i,j) = IWT( 3 (i,j) level(), (i,j) level(), (i,j) level(3), (i,j) level()) (9) Again, (i,j) denotes the st-scale coefficients obtained from equation (8), in which (i,j), (i,j), 3 (i,j), and (i,j) are designated as the corresponding low-low band, low-high band, high-low band, and high-high band components of (i,j), respectively. III. IMULATION AND REULT In this section, to evaluate the performance of artifact reduction, a simulation was performing for Lena gray level image. Four processing techniques, namely, JPEG, Kim s, JPEG 000 and the proposed techniques, were adopted. As an objective measure of image quality, the PNR was used. Table I are the PNR performances of JPEG, Kim s [3], JPEG 000 and our proposed methods. In this table, we used some pre-selected energy threshold values ETH and pre-selected quantized threshold values TH which are obtained from experiments. We may see that our proposed approach obtained better performance in visual effect and improvement about 3.55dB than JPEG method, about.50db than Kim s technique and about 0.8dB than JPEG 000 method with 0: compression ratio. From Fig., we may see that under using the same compression ratio, our proposed approach yield better

4 performance in visual effect than Kim s, JPEG and JPEG 000 methods. Table I The comparison of the proposed scheme with JPEG, Kim s algorithm, JPEG 000, in terms of PNR, for the Lena image using different compression ratio. Test image Lena Compression Ratio JPEG Kim PNR [db] JPEG 000 Proposed 30: : developed. Here, an energy threshold constraint was employed to verify that some high frequency coefficients are significant to for entire image reconstruction. From the tested images, we demonstrated that with the proposed scheme, the compressed image could be reconstructed with image performance improvement, not only texture but also edge. On deblocing part and visual perception, our proposed approach also achieved desired results, subjectively and objectively. REFERENCE [] Z. Xiong, M.T. Orchard, Y.Q. Zhang, A deblocing algorithm for JPEG compressed images using overcomplete wavelet representation, IEEE Trans. Circuits ystem Video Technol. volume 7, no., pp.33-37, April 997. (a) (b) (c) (d) Fig.. The PNR of Lena image using 0: compression ratio. (a) Original image, (b) Kim s method, (c) JPEG 000 method, (d) Proposed method. VI. CONCLUION In this paper, based on the energy metrics in spatial domain, a new multi-scale subband wavelet decomposition schemes, with -scale, has been []. O. Choy, Y.H. Chan, W.C. iu, Reduction of bloc-transform image coding artifacts by using local statistics of transform coefficients, IEEE ignal Process. Letter vol., no., pp. 5-7, January 997. [3] N. C. Kim, I.H. Jang, D.H. Kim, W.H. Hong, Reduction of blocing artifact in bloc-coded images using wavelet transform, IEEE Trans. Circuits ystem Video Technol. vol.8, no.3, pp , June 998.

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