IMAGE DEBLOCKING IN WAVELET DOMAIN BASED ON LOCAL LAPLACE PRIOR

Transcription

1 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 IMAGE DEBLOCKIG I WAVELET DOMAI BASED O LOCAL LAPLACE PRIOR Vijay Kumar ath and Deepika Hazarika Department of Electronics and Communication Engineering, School of Engineering, Tezpur Uniersity (A Central Uniersity), apaam, Tezpur, Assam, India. knath@tezu.ernet.in and deepika@tezu.ernet.in ABSTRACT This paper presents a efficient non iteratie waelet based image deblocking method which employs a maximum a posteriori (MAP) estimator that uses the Laplace probability density function with local ariance to smooth out the blocking artifacts in block discrete cosine transform (DCT) compressed images. We hae shown that the noise standard deiation has a strong relationship with the aerage of first 3x3 alues from the quantization table. The method is adaptie to different block DCT compressed images that are compressed at arious bit rates. The proposed method outperforms seeral well known waelet and non waelet based methods both in terms of isual quality and peak signal to noise ratio (PSR). KEYWORDS Block DCT, Waelet transform, Laplace probability density function, Quantization, Blocking artifacts, MAP estimator, Image deblocking. 1. ITRODUCTIO The block DCT [1] is a ery important component in seeral image and ideo compression schemes such as JPEG, MPEG1, MPEG and H.61 []. At high compression ratios, the block DCT based methods often exhibits blocking artifacts. Blocking artifacts are the artificial block boundaries which are isually annoying particularly in still images. The main challenge in the image deblocking methods is to effectiely smooth out the blocking artifacts while presering the true edges and other important details. Many waelet and non waelet based methods hae been proposed to reduce the blocking artifacts in block DCT compressed images. Reee and Lim [3] reduced the blocking artifacts using a 3x3 Gaussian filter at the block boundaries. The main problem with this simple method is that the true edges at the block boundaries may also get blurred. Minami and akhor [4] proposed to reduce the blocking artifacts by minimizing a criterion called mean squared difference of slope (MSDS). The projection onto conex sets (POCS) algorithms [5,6,7,8] hae shown good results but the main problem with the POCS method is its iteratie nature and the high computational complexity. Xu et al. [9] proposed to reduce the blocking artifacts in discrete hadamard transform (DHT) domain. They calculate the block actiities in the DHT domain to classify the smooth and coarse regions and according to the block actiities the blocking artifacts were adaptiely filtered. Wu et al. [10] proposed a waelet based postprocessing technique to remoe the blocking artifacts based on soft thresholding. The techniques discussed in [11,1] use an oercomplete waelet representation to reduce the blocking artifacts. Aerbuch et al. [13] proposed to apply weighted sums on pixel quartets which are symmetrically aligned to the block boundaries to suppress the blocking artifacts. The image deblocking scheme based on pointwise shape adaptie DCT (SA-DCT) [14] hae shown excellent state of the art results which is able to remoe both DOI : /ijma

2 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 the blocking and ringing artifacts. hai et al. [15] proposed an image deblocking scheme through post filtering in shifted windows of image blocks for JPEG compressed images. hang et al. [16] proposed an image deblocking scheme based on adaptie bilateral filter where texture regions and block boundary discontinuities are first detected and based on that the bilateral filter parameters are selected. ath et al. [17] proposed an image deblocking technique based on adaptie bilateral filter where the bilateral filter parameters were selected based on empirical study. The bilateral filter parameters were made adaptie to the quantization tables. In this paper, we propose a non iteratie, spatially adaptie, waelet based image deblocking method which is based on modelling the waelet coefficients in each subbands using a Laplace pdf with local ariance. The noise standard deiation is made adaptie to the quantization tables used in the compression process. This paper is organized as follows. The proposed waelet domain image deblocking technique is described in Section. The experimental results are presented in Section 3. Finally, the conclusions are gien in Section 4.. PROPOSED WAVELET DOMAI IMAGE DEBLOCKIG METHOD We model the degradation due to the quantization noise as some additie noise. We use the following obseration model d = z + n (1) where z is the original uncompressed image, d is the obsered block DCT compressed image and n is the degradation due to quantization process. The waelet coefficients of the image d is gien by D( k) = ( k) + ( k) () where ( k) represents the waelet coefficients of the uncompressed image. We use a MAP estimator to estimate ( k) from the noisy obseration D( k) which is gien by [18,19] ( k) = arg max P ( ( k) D( k)) (3) The aboe equation can also be written as ( k ) ( k ) D( k ) ( k) = arg max P ( D( k) ( k) ) P ( ( k) ) ( k ) ( k ) (4) We assume the noise to be zero mean Gaussian with ariance σ for the similar reasons described in [0] 1 ( k) P ( ( k) ) = exp (5) πσ σ Substituting Equation (5) in (4), we hae ( D( k) ( k) ) ( k) = arg max + f ( ( k)) (6) ( k ) σ where f ( ( k)) = log( P ( k )( ( k))). Hence, the MAP estimate of ( k) is computed by setting the deriatie with respect to ( k) equals to zero D( k) ( k) + f ( ( k)) = 0 (7) σ We model the waelet coefficients using Laplace pdf with local ariance [18,19], hence 1 ( k) P ( k ) ( ( k)) = exp (8) σ ( ) ( k) k σ 40

3 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 Soling the aboe equations, we can write as [18,19] σ ( k) = sign( D( k) ) D( k) σ ( k) From the aboe, ( a ) + can be defined as 0, a < 0 ( a) + = (10) a, otherwise If the SOFTWA operator [18] is defined as SOFTWA( p, η) = sign( p)( p η ) + (11) Equation (9) can be written as σ ( k) = SOFTWA D( k), (1) σ ( k) For each noisy waelet coefficient, an estimate of σ ( k ) is formed based on its local neighbourhood B( k ). Here, we use a square window B( k) centred at D( k ). The estimate for σ ( k ) is gien by [18,19] σ 1 where M is the number of coefficients in B( k ). ( k) = max 0, D ( j) σ M j B( k ) + (9) (13) To use the Equation (1) to find an estimate of ( k ), we need to find a suitable alue of σ. It is to be noted that the σ is not an estimate of the standard deiation of the difference between the original and the block DCT compressed image - σ is just the assumed alue of standard deiation of n in our obseration model (1). It is assumed that σ is the standard deiation of the noise when added to the original image z would require, for remoal, the same amount of adaptie smoothing necessary to reduce the blocking artifacts produced by the block DCT based compression scheme with the quantization table Q. Much larger alues of σ may result in oersmoothing and much smaller alues may result in insufficient remoal of blocking artifacts. Figure 1. Scatter plot of σ ersus Q (3 3) and cure fitting using linear polynomial a x 41

4 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 Motiated by the strategy as discussed in [14], we performed experiments on a large number of test images in which we first plot the best alues of σ (found experimentally) which gies lowest mean square error for different compression ratios (different compression ratios means different alues of Q (3 3) ). a x Q 3 1 = Q (14) a(3x3) i, j 9 i,j=1 Qa (3x3) is the aerage of first 3x3 alues from the quantization matrix ( i, j Q ). The data when fitted with a linear polynomial, gies σ as σ = a1. Qa + a (15) where a 1=0.09 and a =.. The experimental results show that the results are not ery sensitie to the fitting errors and the fitted cure can be considered for a wide range of test images and quantization tables. The σ alues are larger for higher compression ratios and smaller for lower compression ratios. Finally the DCT quantization constraint and the range constraint is imposed onto the filtered output (output image after the inerse D DWT). The experimental results to be presented in next section will show that this technique reduce the blocking artifacts ery efficiently while presering edges and textures..1. Quantization Constraint and Range Constraint In the POCS based deblocking schemes, the final deblocked image is constrained with the quantization constraint set. The quantization constraint found from the quantization table restricts the alue of the DCT coefficients to be within the quantization interal. The deblocked image should satisfy the quantization constraint, to be consistent with the original image. The output image after the inerse D DWT (say b % ) generally do not satisfy the quantization constraint, so it is projected onto the quantization constraint set to obtain a deblocked image which is consistent with the original image. Let m represents the set of DCT coefficients of image b %. The (u, th DCT coefficient at block position (x,y) is modified as follows C ( ) max u,, if mx, y ( u, Cmax ( u, ( ) min x, y ( ) min ( ) m x, y ( u,, otherwise > mxy ( u, = C u,, if m u, < C u, (16) where ( x y ) ( ) ( x y ) ( ) ( ) ( ) C u, = q u, u, max, ( ) ( ) C u, = q u, 0.5 u, min, For u =0, 7, =0,..7, x =0, (row/8)-1, y =0,..(col/8)-1.The quantized coefficients ( q ) that is aailable at the decoder input is gien by ma, b ( u, qx, y ( u, round ( u, where m is the original image DCT coefficients and ( u, = (17) represents the quantization interal of the (u, th DCT coefficient. A narrow quantization constraint set discussed in [1], produces 4

5 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 better results in terms of mean square error. For narrow quantization constraint set, the C u is gien by Cmax ( u, and min (, ) ( x y ς ) ( ) ( x y ς ) ( ) ( ) ( ) C u, = q u, + u, max, 1 ( ) ( ) C u, = q u, u, (18) min, where 0 < ς1, ς 0.5. We use ς 1=0.3 and ς =0.3 for the experiments. The inerse block DCT with the modified coefficients is performed to obtain the deblocked image. Finally the range constraint is applied on this image. Since the 8 bit original images used in the experiments hae alues in the range of (0-55), the deblocked image must also satisfy this range. Any alue outside the range of (0-55) is projected into this gien range. 3. EXPERIMETAL RESULTS The proposed method has been tested on a large number of arious test images compressed by the JPEG standard and the quantization tables Q1, Q and Q3 [10,1] which are commonly used in literature for simulating arious types of block DCT compression. In this paper, we report our results only for Lena, Barbara and Peppers image. The baseline IJG JPEG implementation [] is used for the simulation of all JPEG experiments presented in this paper. We used a waelet transform with Daubechies-8 waelet and four leels of decomposition. Center square shaped window of size 5x5 is used in the waelet domain to estimate the ariances. Table 1. PSR comparison between the proposed method and best results reported in [13] for restoration from JPEG compression with different Quality factors. In Table 1, the PSR results of the proposed method is compared with the best PSR results obtained by any of the methods [5,13,3,4,5,6] as reported in [13]. The results show that for Lena, Barbara and Peppers images the proposed method outperforms the best results reported in [13]. In Table, the PSR results of the proposed method is compared with the results of seeral well known decimated and non-decimated waelet based image deblocking schemes [10,11,1,7]. The results show that the proposed scheme consistently outperforms all the methods gien in Table. This suggests that the fitted cure in Fig. 1 may be considered for deblocking purpose for a wide range of quantization tables that include both JPEG and non-jpeg tables. Fig. shows the isual results comparison between the proposed deblocking scheme and a well known method discussed in Ref. [1] which is based on oercomplete waelet representation. The isual results show that our method can efficiently reduce the blocking artifacts while presering true edges and textural information. 43

6 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 Table. PSR comparison between [10,11,1,7] and proposed method for restoration from block DCT Quantization for three different Quantization tables. Q Lena (51x51) Table Test Image [11] [7] [10] [1] Proposed Q Q Q Barbara (51x51) Test Image [11] [7] [10] [1] Proposed Q Q Q Peppers(51x51) Test Image [11] [7] [10] [1] Proposed Q Q Q (a) (b) (c) Figure. Deblocking results for Barbara image (a) Original (b) Block DCT compressed with Q (PSR=5.59 db) (c) Processed with Liew and Yan s [1] algorithm (PSR=6.04 db) (d) Processed with proposed method (PSR=6.14 db) (d) 44

7 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February COCLUSIO We hae proposed an efficient spatially adaptie waelet transform domain image deblocking method which employs a MAP estimator that uses a Laplace pdf with local ariance to reduce the blocking artifacts. The noise standard deiation is made adaptie to the quantization table used in the compression process and is calculated using an empirical expression. The local ariance estimate of each coefficient is estimated from the local obseration of the signal. The proposed method can suppress the blocking artifacts ery efficiently while presering the image details and object edges. REFERECES [1]. Ahmad, T. atarajan, and K. Rao, Discrete Cosine Transform, IEEE transactions on Computers, ol. C-3, no. 1, pp , [] V. Bhaskaran and K. Konstantinides, Image and ideo compression standards - Algorithms and architectures, Kluwer Academic Publishers [3] H. Reee and J. Lim, Reduction of blocking effects in image coding, Opt. Eng., ol. 3, no. 1, pp , [4] S. Minami and A. akhor, An optimization approach for remoing blocking artifacts in transform coding, IEEE Transactions on Circuit and Systems for Video Technology. Vol. 5, pp. 74-8, [5] Y. Yang,. P. Galatsanos and A. K. Katsaggelos, Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images, IEEE Transactions on Circuits and Systems for Video Technology. Vol.3, pp , [6] Y. Yang,. P. Galatsanos, and A. K. Katsaggelos, Projection based spatially adaptie reconstruction of block-transform compressed images, IEEE Trans. Image Processing, ol. 4, no. 7, pp , [7] Y. Yang and. P. Galatsanos, Remoal of compression artifacts using projections onto conex sets and line process modeling, IEEE Transactions on Image Processing, Vol. 6, pp , [8] H. Paek, R. C. Kim and S. U. Lee, On the POCS based postprocessing technique to reduce the blocking artifacts in transform coded images, IEEE Transactions on Image Processing, Vol. 8, pp , [9] J. Xu, S. heng and X. Yang, Adaptie ideo blocking artifact remoal in Discrete Hadamard Transform domain, Optical Engineering, Vol. 45, 006. [10] S. Wu, H. Yan and. Tan, An Efficient Waelet-Based Deblocking Algorithm for Highly Compressed Images, IEEE Transactions on Circuits and Systems for Video Technology, ol.11, pp , 001. [11]. Xiong, M. T. Orchard and Y. hang, A deblocking algorithm for JPEG compressed images using oercomplete waelet representation, IEEE Transactions on Circuits and Systems for Video Technology, ol. 77, pp , [1] A. W. C. Liew and H. Yan, Blocking artifacts suppression in block coded images using oercomplete waelet representation, IEEE Transactions on Circuits and Systems for Video Technology, ol.14, pp , 004. [13] A.. Aerbuch, A. Schclar and D. L. Donoho, Deblocking of block transform compressed images using weighted sums of symmetrically aligned pixels, IEEE Transactions on Circuits and Systems for Video Technology, ol. 14, pp. 00-1,

8 The International Journal of Multimedia & Its Applications (IJMA) Vol.4, o.1, February 01 [14] A. Foi, V. Katkonik and K. Egiazarian, Pointwise shape adaptie DCT for high quality denoising and deblocking of grayscale and color images, IEEE Transactions on Image Processing, ol.16,no.5, pp , 007. [15] G. hai, W. hang, X. Yang, W. Lin and Y. Xu, Efficient image deblocking based on postfiltering in shifted windows, IEEE Transactions on Circuits and Systems for Video Technology, ol.18, pp.1-16,008. [16] M. hang and G. K. Bahadir, Compression Artifact Reduction with Adaptie Bilateral Filtering, in Proc. Visual Communications and Image Processing. Vol. 757, 009. [17] V. K. ath, D. Hazarika and A. Mahanta, Blocking Artifacts Reduction Using Adaptie Bilateral Filtering, in Proc. International Conference on Signal Processing and Communications, ol.6, pp , 010. [18] V. K. ath, A. Mahanta, Image denoising based on Laplace distribution with local parameters in Lapped transform domain, International Conference on Signal Processing and Multimedia Applications, Seille, Spain, July 011. [19] H. Rabbani and M. Vafadust, Image / ideo denosing based on a mixture of Laplace distributions with local parameters in multidimensional complex waelet domain," Signal Processing, ol. 88, no. 11, pp , 008. [0] R. A. Gopinath, Waelet-based post-processing of low bit rate transform coded images, in IEEE International Conference on Image Processing, 1994, pp [1] S. H. Park and D. S. Kim, Theory of projection onto the narrow Quantization constraint set and its application, IEEE Transactions on Image Processing, ol. 8, pp , [] I. J. Group. [Online]. Aailable: [3] T. Chen, H. R. Wu and B. Qiu, Adaptie postfiltering of transform coefficients for the reduction of blocking artifacts, IEEE Transactions on Circuits and Systems for Video Technology. ol. 11, pp , 001. [4] R. Castagno, S. Marsi and G. Ramponi, A simple algorithm for the reduction of blocking artifacts in images and its implementation, IEEE Transactions on Consumer Electronics, ol.44, [5] MPEG-4 ideo erification model ersion 18.0 (VM-18), ISO/IEC JTC1/SC9/WG11Std., 001. [6] R. Rosenholts and A. akhor, Iteratie procedures for reduction of blocking artifacts in transform domain image coding, IEEE Transactions on Circuits and Systems for Video Technology, ol., pp , 199. [7] T. C. Hsung and D. P. K. Lun, Application of singularity detection for the deblocking of JPEG decoded images, IEEE Transactions on Circuits Systems II, ol.45, pp ,