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Fusion of Brushlet and Wavelet Denoising Methods for Nuclear Images

Explore the fusion of brushlet and wavelet denoising methods in nuclear images, improving image quality and reducing noise. This approach combines brushlet analysis for texture-based denoising and 3D wavelet modulus analysis for edge-based denoising in PET and SPECT images. The advantages of brushlet analysis include compact representation of textures, adaptive tiling, directional selectivity, fast implementation, and orthogonal basis. De-noising with brushlet basis functions involves isolating oriented textures via thresholding, spatial adaptivity, and minimizing threshold levels based on noise variance estimation. The technique enhances image quality by reducing directional and textural noise, preserving structure edges, and providing effective signal recovery from noise-dominated multi-scale expansions.

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Fusion of Brushlet and Wavelet Denoising Methods for Nuclear Images

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  1. FUSION OF BRUSHLET AND WAVELET DENOISING METHODS FOR NUCLEAR IMAGES Elsa Angelini1, Yinpeng Jin1, Peter Esser2, R. Van Heertum2, Andrew Laine1 1 Department of Biomedical Engineering 2 Department of Radiology Columbia University, New York, NY, USA ISBI 2004 Washington, DC April 17, 2004

  2. Sample PET and SPECT Images SPECT Liver PET Brain

  3. Previous Work on Multi-Scale Processing of PET and SPECT • Local reconstruction to improve spatial resolution within a region of interest • T. Olson and J. De Stefano, "Wavelet Localization of the Radon Transform." IEEE Trans. Image Processing, vol. 42, pp. 2055-2067, 1994. • F. Rashid-Farrokhi, K. Liu, C. Berenstein, and D. Walnut, "Wavelet-based Multiresolution Local Tomography." IEEE Trans. Image Processing, vol. 22, pp. 1412-1430, 1997. • S. Zhao, G. Wang, and J. Hsieh, "Wavelet Sampling and Localization Schemes for the Radon Transform in Two Dimensions." SIAM Journal on Applied Mathematics, vol. 57, pp. 1749-1762, 1997. • M. Bottema, B. Morean, and S. Suorova, "An Application of Wavelets in Tomography." Digital Signal Processing, vol. 8, pp. 244-254, 1998. • W. Maldych, "Tomography, Approximate Reconstructions, and Continuous Wavelet Transforms." Journal of Applied Computation and Harmonic Analysis, vol. 7, pp. 54-100, 1999. • Accelerating implementation of the traditional FBP algorithm • A. Delaney and Y. Bresler, "Multi-resolution Tomographic Reconstruction Using Wavelets." IEEE Trans. Image Processing, vol. 4, pp. 799-813, 1995. • L. Blanc-Feraud, P. Charbonnier, P. Lobel, and M. Barlaud, "A Fast Tomographic Reconstruction Algorithm in the 2-D Wavelet Transform Domain." IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 305-308, 1994. • Post-filtering or regularization/constraints in tomographic reconstruction • E. Kolaczyk, "A Wavelet Shrinkage Approach to Tomographic Image Reconstruction." Journal of American Statistics Association, vol. 91, pp. 1079-1090, 1996. • N. Lee and B. Lucier, "Wavelet Methods for Inverting the Radon Transform with Noisy Data." IEEE Trans. Image Processing, vol. 10 (1), pp. 79-94, 2001. • J. Lin, A. Laine, and S. Bergmann, "Improving PET-based Methods Using the Wavelet Transform for Positron Emission Tomography." IEEE Trans. Biomedical Engineering, vol. 48, pp. 202-212, 2001. • J. Kalifa, A. Laine, and P. Esser, "Regularization in Tomographic Reconstruction Using Thresholding Estimators." IEEE Trans. Medical Imaging, vol. 22 (3), pp. 351-359, 2003.

  4. Image De-Noising in PET and SPECT Texture-Based De-noising (Brushlet Analysis) Image Fusion Edge-Based De-noising (3D Wavelet Modulus Analysis) • Directional and Textural Noise SPECT PET • Over-Smooth • Structure Edges

  5. Image De-Noising in PET and SPECT Texture-Based De-noising (Brushlet Analysis) Image Fusion Edge-Based De-noising (3D Wavelet Modulus Analysis) • Directional and Textural Noise SPECT PET • Over-Smoothed • Structure Edges

  6. 2D Analysis Function Fourier Tiling to construct expansion basis Brushlet and Textural Analysis Brushlets Basis Functions Expansion Reconstruction

  7. Brushlet and Textural Analysis Advantages of Brushlets Analysis • Compact representation of textured signals. • Adaptive tiling of frequency plane. • Adaptive directional selectivity. • Fast implementation with folding operators and FFT. • Orthogonal basis.

  8. De-noising with Brushlet Basis Functions(ISBI 02) Data Mean Regions Variance Map frequency Noise s Brushlet and Textural Analysis Isolate oriented textures via thresholding • Minimax threshold level based on noise variance, estimated in the background. • Spatial adaptivity of thresholding for 3 types of regions: texture, smooth, edges [Vetterli]. • De-noising via hard thresholding of low frequency coefficients.

  9. Examples of Brushlet De-Noising: SPECT Brain Data Brushlet and Textural Analysis Original Denoised

  10. Image De-Noising in PET and SPECT Texture-Based De-noising (Brushlet Analysis) Image Fusion Edge-Based De-noising. (3D Wavelet Modulus Analysis) • Directional and Textural Noise SPECT PET • Over-Smoothed • Structure Edges

  11. Edge-Based De-noising Wavelet and Edge De-noising • 3D Dyadic Wavelet Thresholding. • Feature selection based on spatial orientation of contours in three dimensions. • Cross-Scale Regularization(MICCAI’ 03) • Explore correlations of signal features across spatial-frequency scales. • Effective signal recovering from noise-dominated multi-scale expansions.

  12. 3D Dyadic Wavelets and Wavelet Modulus DC m,1 m,2 m,3 Input Data Wavelet Coefficients 3D: N,1 N,2 N,3 Wavelet Modulus in 3D: Wavelet Edge De-noising

  13. Traditional* Dyadic Wavelet Thresholding (3D) Wavelet Decomposition Wavelet Reconstruction Threshold Threshold Threshold Input Image Enhanced (Denoised) Image Threshold Threshold Threshold DC Wavelet Edge De-noising * [Mallat 92]

  14. Dyadic Wavelet Modulus Thresholding (3D) Wavelet Decomposition Wavelet Reconstruction Modulus Thresholding Enhanced (Denoised) Image Modulus Thresholding DC Wavelet Voxel De-noising Input Image

  15. Cross-scale Regularization (CSR) Wavelet Edge De-noising Wavelet Modulus at Expansion Levels 1 and 2 - “Pre-processing” of higher level sub-bands: • De-correlation of noise in spatial-frequency expansion Level 1 Level 2 Input Image + x - “Windowed” Normalization - Avoid attenuation of weak edges - 50% Max rule (brain, liver data) - 70% Max rule (bone data) N “Regularization Map”

  16. Comparison: CSR vs. Soft Threshold Wavelet Edge De-noising Input Data CSR De-noising Soft Thresholding

  17. Image De-Noising in PET and SPECT Texture-Based De-noising (Brushlet Analysis) Edge-Based De-noising. (3D Wavelet Modulus Analysis) • Directional and Textural Noise. SPECT PET Image Fusion • Over-Smoothed Structure Edges.

  18. Multi-Scale Image Fusion • Fusion:To combine different or incomplete representations into a unified form with integrated information. • Motivation of fusion in the context of denoising: • Brushlet analysis provides better enhancement of “harmonic textures”, representing physiological activities inside target organs. • Wavelet modulus thresholding provides better enhancement of “anatomicaledges”, or delineation of anatomical structures of clinical interest. • Both types of information are important for accurate diagnostic decisions and image interpretation.

  19. Multi-Scale Image Fusion Fusion Process A B Wavelet Expansion Wavelet Expansion A1 A2 A3 B1 B2 B3 Fusion Rule: Fi(x,y,z) = Max(Ai(x,y,z), Bi(x,y,z)) F1 F2 F3 Wavelet Reconstruction F De-noised Data Sets Both [A] and [B] expanded and reconstructed with 3D Dyadic Transform

  20. Multi-Scale Image Fusion Example: Fusion of coefficient features at the most detailed expansion level. Wavelet Modulus De-Noising Brushlet De-Noising Fused Image Features

  21. Multi-Scale Image Fusion Brushlet De-Noising Input Data Image Fusion Result Wavelet Modulus De-Noising Example Cases: Fusion of denoised images

  22. Multi-Scale Image Fusion Brushlet De-Noising For comparison: Reconstructed Using OSEM Wavelet Modulus De-Noising Example: Fusion of denoised images Input Data: Clinical PET Brain Reconstructed Using FBP Image Fusion Result

  23. Multi-Scale Image Fusion Preliminary Clinical Evaluation • Brushlet de-noising: • Beneficial for enhancing “harmonic activity”, e.g. anatomical or physiological variations within the target organs. • Wavelet modulus analysis with cross-scale regularization: • Beneficial for enhancing “anatomical edges”, with a better definition and delineation of the organ contours. • Fused images: • Effectively combined important features from both processed images, without introducing artifacts. • When compared to OSEM reconstructions, provided significantly improved image quality in terms of both lower noise level and improved contrast for key anatomical and physiological features.

  24. Conclusion • Multi-scale fusion of two expansions • Selected predominant wavelet coefficient modulus from distinct de-noising expansions. • Effective integration of de-noising methods for enhancement of anatomical and physiological features. • Potential improvements of the method • Preservation of the linearity of the nuclear measures. • Refinement of fusion rule. • Further evaluation studies • Clinical phantom data. • Clinical data with pathological ground truth.

  25. References • Y. Jin, E. Angelini, P. Esser, and A. Laine, "De-noising SPECT/PET images using cross-scale regularization," MICCAI, pp. 32-40, Montreal, Canada, 2003. • F. Meyer and R. R. Coifman, "Brushlets: A tool for directional image analysis and image compression," Applied and Computational Harmonic Analysis, vol. 4, No. 1, pp. 147-187, 1997. • E. D. Angelini, J. Kalifa, and A. F. Laine, "Harmonic multiresolution estimators for denoising and regularization of SPECT-PET data," International Symposium on Biomedical Imaging, pp. 697-700, Washington, D.C., USA, 2002. • S. Mallat and S. Zhong, "Signal characterization from multiscale edges," 10th International Conference on Pattern Recognition, pp. 891-896, Atlantic City, NJ, USA, 1990. • E. Angelini, A. Laine, S. Takuma, J. Holmes, and S. Homma, "LV volume quantification via spatio-temporal analysis of real-time 3D echocardiography," IEEE Transactions on Medical Imaging, vol. 20, No. 6, pp. 457-469, 2001. • S. G. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE International Conference on Image Processing, pp. 535 -539, Chicago, IL, USA, 1998. • S. G. Nikolov, D. R. Bull, C. N. Canagarajah, M. Halliwell, and P. N. T. Wells, "Fusion of 2-D images using their multiscale edges," IEEE International Conference on Pattern Recognition, pp. 41-44, Barcelona, Spain, 2000. • I. Koren, A. Laine, and F. Taylor, "Image fusion using steerable dyadic wavelet transform," IEEE International Conference on Image Processing, pp. 232-235, Washington, D.C., USA, 1995.

  26. Acknowledgements This study was supported in part by Siemens Medical Solutions, Inc.

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