1 FUSION OF BRUSHLET AND WAVELET DENOISING METHODS FOR NUCLEAR IMAGES Elsa Angelini 1, Yinpeng Jin 1, Peter Esser 2, R. Van Heertum 2, Andrew Laine 1 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 interestLocal 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 , –F. Rashid-Farrokhi, K. Liu, C. Berenstein, and D. Walnut, "Wavelet-based Multiresolution Local Tomography." IEEE Trans. Image Processing, vol. 22, pp , –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 , –M. Bottema, B. Morean, and S. Suorova, "An Application of Wavelets in Tomography." Digital Signal Processing, vol. 8, pp , –W. Maldych, "Tomography, Approximate Reconstructions, and Continuous Wavelet Transforms." Journal of Applied Computation and Harmonic Analysis, vol. 7, pp , Accelerating implementation of the traditional FBP algorithmAccelerating implementation of the traditional FBP algorithm –A. Delaney and Y. Bresler, "Multi-resolution Tomographic Reconstruction Using Wavelets." IEEE Trans. Image Processing, vol. 4, pp , –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 , Post-filtering or regularization/constraints in tomographic reconstructionPost-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 , –N. Lee and B. Lucier, "Wavelet Methods for Inverting the Radon Transform with Noisy Data." IEEE Trans. Image Processing, vol. 10 (1), pp , –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 , –J. Kalifa, A. Laine, and P. Esser, "Regularization in Tomographic Reconstruction Using Thresholding Estimators." IEEE Trans. Medical Imaging, vol. 22 (3), pp , 2003.

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

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

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

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

8 De-noising with Brushlet Basis Functions (ISBI 02) Isolate oriented textures via thresholding frequency Brushlet and Textural Analysis - 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. Data Mean Regions Map Variance Noise 

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

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

11 Edge-Based 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. Wavelet and Edge De-noising

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

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

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

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

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

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

18 Multi-Scale Image Fusion To combine different or incomplete representations into a unified form with integrated information.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 “anatomical edges”, or delineation of anatomical structures of clinical interest. –Both types of information are important for accurate diagnostic decisions and image interpretation.

19 Fusion Process F1F1 F2F2 F3F3 A1A1 A2A2 A3A3 Wavelet Expansion AB B1B1 B3B3 B2B2 F Wavelet Reconstruction Fusion Rule: F i (x,y,z) = Max(A i (x,y,z), B i (x,y,z)) Multi-Scale Image Fusion Both [A] and [B] expanded and reconstructed with 3D Dyadic Transform De-noised Data Sets

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

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

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

23 Brushlet de-noising: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:Wavelet modulus analysis with cross-scale regularization: –Beneficial for enhancing “anatomical edges”, with a better definition and delineation of the organ contours. Fused images: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. Preliminary Clinical Evaluation Multi-Scale Image Fusion

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 , Montreal, Canada, 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 , 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 , Washington, D.C., USA, S. Mallat and S. Zhong, "Signal characterization from multiscale edges," 10th International Conference on Pattern Recognition, pp , Atlantic City, NJ, USA, 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 , 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 , Chicago, IL, USA, 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 , Barcelona, Spain, I. Koren, A. Laine, and F. Taylor, "Image fusion using steerable dyadic wavelet transform," IEEE International Conference on Image Processing, pp , Washington, D.C., USA, 1995.

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