Mar. 2006, Cupertino Picture quality requirements and NUT proposals for JPEG AIC Jae-Jeong Hwang, Young Huh, Dai-Gyoung Kim Kunsan National Univ., KERI, Hanyang Univ. hwang@kunsan.ac.kr
Contents 1. Picture quality requirements for JPEG AIC Should be superior to the previous standards In terms of Image quality metrics 2. NUT is able to meet the requirements NUFFT NUFCT Forward and Inverse transforms Smaller errors to reconstruct non-bandlimited signals Application to Medical image processing and Radar image processing 2
Picture quality of JPEG & JP2K JPEG JPEG2000 Compression ratio= 28:1 (67kbits) 3
Picture quality assessment Subjective Quality Assessment DSIS (Double Stimulus Impairment Scale DSQS (Double Stimulus Quality Scale) CS (Comparison Scale) SS (Single Stimulus) SSCQE (Single Stimulus Continuous Quality Evaluation) DSCQE (Double Stimulus Continuous Quality Evaluation) Objective Quality Assessment FR (Full-Reference) Metrics - MSE, PSNR, SSIM, Average Diff., Correlation quality, Max. Diff., Laplacian MSE, NAE, L p - norm. RR (Reduced-Reference) Metrics - Feature extraction (Edge, Spatial/Temporal feature etc) NR (No-Reference) Metrics - Blocking artifact, Blurring artifact, Ringing artifact, Contrast, Sharpness 4
Objective quality assessment MSE PSNR MSAD Blurring Blocking SSIM Original 0.0000 100.0000 0.0000 12.7931 10.3215 1.0000 JPEG 28.7004 33.5519 3.9835 12.5567 64.1014 0.8952 JPEG2000 10.4388 37.9443 2.3543 11.9047 8.9867 0.9554 *Expected values are derived by Normalized 1 st, or 2 nd order inference. => denotes almost same. AIC(expected) < 3.8 > 42.34 < 1.39 => 12.79 =>10.32 => 1 JPEG encoder produces a lot of blockiness, larger MSE/MSAD/PSNR and lower Similarity measure, while for JPEG2000-encoded images blurring is the main artifact. This is due to the compression algorithms (block-based DCT & Wavelets). The JPEG AIC should be developed by solving the artifacts and increasing picture quality. 5
Quality assessment references Ahmet M. Eskicioglu and Paul S. Fisher, Image quality measures and their performance, IEEE Transactions on Communications, Vol. 43, No. 12, Dec. 1995. A. Punchihewa, D.G. Bailey, R.M. Hodgson, A Survey of Coded Image and Video Quality Assessment, Proceedings of Image and Vision Computing New Zealand, Palmerston North, New Zealand, pp. 326-331, Nov. 26-28, 2003. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, In Proc. IEEE Tran. On Image Processing, Vol. 13, No. 4, pp. 600-612, Apr. 2004. F. Ebrahimi, M. Chamik, S. Winkler, "JPEG vs. JPEG2000: An objective comparison of image encoding quality," In Proc. SPIE Applications of Digital Image Processing, Vol. 5558, pp. 300-308, Denver, CO, Aug. 2-6, 2004. G. A. D. Punchihewa, D.G. Bailey, and R.M. Hodgson, "Objective evaluation of edge blur and ringing artefacts: application to JPEG and JPEG2000 image codecs", Image and Vision Computing New Zealand, Dunedin, New Zealand, pp. 61-66, Nov. 28-29, 2005. 6
NUT implementation issues Uniform sampled Image t Nonuniform Adaptive Re-sampling t n Nonuniform transform/ Quantizer w k Entropy Coding Compressed Bitstream Recon. Image ' t Nonuniform Adaptive Interpolation ' t n Nonuniform Inverse transform/ Dequantizer w k Entropy Decoding 7
NUT implementation issues Nonuniform resampling Based on edge information, region-selective. 8
Resampling references M. D. Rawn, On Nonuniform Sampling Expansions Using Entire Interpolating Functions, and On the Stability of Bessel-Type Sampling Expansions, IEEE Trans. on Inform. Theory, Vol. 35, No. 3, pp. 549-557, May 1989. P. J. S. G. Ferreira, Nonuniform Sampling of Nonbandlimited Signals, IEEE Sig. Proc. Letters, Vol. 2, No. 5, pp. 89-91, May 1995. F. Marvasti, Nonuniform sampling theorems for bandpass signals at or below the Nyquist density, IEEE Trans. On Sig. Proc., Vol. 44, No. 3, pp. 572-576, Mar. 1996. G. Wolberg, Nonuniform Image Reconstruction Using Multilevel Surface Interpolation, IEEE Int. Conf. on Image Proc., pp. 909-912, Oct. 1997. S. Azizi, D. Cochran, and J. N. McDonald, A sampling approach to region-selective image compression, IEEE Conf. on Signals, Systems and Computers, pp. 1063-1067, Oct. 2000. K. L. Hung and C. C. Chang, New irregular sampling coding method for transmitting images progressively, IEE Proc.-Vis. Image Signal Process., vol. 150, no. 1, pp. 44-50, Feb. 2003. G. Ramponi and S. Carrato, An adaptive irregular sampling algorithm and its application to image coding, Image and Vision Computing, vol. 19, pp. 451-460, 2001. M. Bartkowiak, High Compression Of Colour Images With Nonuniform Sampling, Proceedings of ISCE'2002, Erfurt, Germany, Sept. 23-26, 2002. 9
NUT via interpolation & UT Representation of nonuniform samples by interpolating uniform samples Apply the uniform transform Increase complexity Fast algorithm required 10
Fast algorithms of NUT F. J. Beutler, Error free recovery of signals from irregularly spaced samples, SIAM Review, vol. 8, no. 3, pp. 328-335, July 1966. A. Dutt and V. Rokhlin, Fast Fourier Transforms for Nonequispaced Data, SIAM J. Sci. Comput., vol. 14, no. 6, pp. 1368-1393, Nov. 1993. G. Beylkin, On the fast Fourier transform of functions with singularities, Applied and Computational Harmonic Analysis, vol. 2, pp. 363-382, 1995. Q. H. Liu and N. Nguyen, An accurate algorithm for nonuniform fast Fourier transforms (NUFFT's), IEEE Microwave and Guided Wave Letters, Vol. 8, no. 1, pp. 18 20, Jan. 1998. J. A. Fessler and B. P. Sutton, Nonuniform fast Fourier transforms using min-max interpolation, IEEE Transactions on Signal Processing Vol. 51, no. 2, pp. 560 574, Feb. 2003. 11
Fast algorithms of NUT B. Tian and Q. H. Liu, Nonuniform fast cosine transform and the Chebyshev PSTD algorithm, IEEE International Symposium on Antennas and Propagation, Vol. 4, pp. 2184 2187, July 1999. A. A. Aydiner, W. C. Chew, J. Song, and T. J. Cui, A sparse data fast Fourier transform (SDFFT), IEEE Transactions on Antennas and Propagation, Vol. 51, no. 11, pp. 3161 3170, Nov. 2003. 12
Recon Error reduction by NUT G.-X. Fan, and Q. H. Liu, Fast Fourier transform for discontinuous functions, IEEE Trans. Antennas Propagat., vol. 52, no. 2, pp. 461-465, Feb. 2004. 13
NUT applications in Medical imaging B. P. Sutton, D. C. Noll, and J. A. Fessler, Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities, IEEE Transactions on Medical Imaging, Vol. 22, no. 2, pp. 178 188, Feb. 2003. Summary: In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. M. Bronstein, A. Bronstein, and M. Zibulevsky, Iterative reconstruction in diffraction tomography using nonuniform fast Fourier transform, IEEE International Symposium on Biomedical Imaging, pp. 633 636, July 2002. 14
MRI Reconstruction example Time(s) NRMSE b) Exact conjugate phase 4.07 0.19 c) Exact iterative (10 iter) 128.16 0.04 d) No correction 0.06 0.22 e) Fast conjugate phase 0.33 0.19 f) Fast iterative (10 iter) 2.20 0.04 15
NUT applications in SAR imaging B. Subiza, E. Gimeno-Nieves, J. M. Lopez-Sanchez, and J. Fortuny-Guasch, An approach to SAR imaging by means of non-uniform FFTs, IEEE International Geoscience and Remote Sensing Symposium (IGARSS '03), Vol. 6, pp. 4089 4091, July 2003. 16
Conclusions Quality requirement for JPEG AIC should be defined based on JPEG->JP2K->AIC transition. Fast algorithms should be developed such as NUFFT->SDFFT->NUFCT for real data transform. Applications like medical imaging, high quality imaging can be found out. 17