1. Despeckling Of Ultrasound Images Ronen Tur

2. Outline Ultrasound Imaging What Is Speckle Noise? Standard Denoising Methods Modified Homomorphic Despeckling

3. Papers Michailovich O. & Tannenbaum A., “Despeckling of Medical Ultrasound Images”, IEEE transactions on ultrasonics, ferroelectrics and frequency control, vol. 53, no.1, january 2006 Quistgaard J., “Signal Acquisition and Processing in Medical Diagnostic Ultrasound”, IEEE Sig. Proc., jan. 1997

4. ULS Imaging - Motivation Non-invasive Non-ionizing radiation (CT) Cheap (vs. expensive MRI) Real-time imaging Tracking Monitoring during treatment Portable platforms

5. ULS Physics Acoustic impedance Different tissue  Different impedance Reflection Desired picture: reflectivity function Denote it by " וכל העם רואים את הקולות..." ( פרשת השבוע )

6. ULS Physics cannot be measured directly Pulse-echo imaging 4 steps: Transmission Reflection Reception Estimation

7. 1D

8. – transmitted pulse – reflectivity coefficient at x – received signal

9. 1D – transmitted pulse – reflectivity coefficient at x – received signal Estimation: For the case,

10. 2D Complex problem Sum over different

11. 2D - Beamforming Array of N elements - ith signal received Problem: Given Estimate

12. 2D - Beamforming Approximation of inverse scattering solution - round trip to the ith element Result called RF-image t

13. Envelope Detection Carrier freq. ~5MHz Information in the envelope Demodulation Take the absolute value

14. PSF – Point Spread Function Defined for any imaging system PSF - the impulse response of the system Ideal: Delta function Realistic: Has a blurring effect

15. Example

16. Noise In Ultrasound Major disadvantage of ULS imaging Where does the noise come from?

17. Speckle Noise Coherent imaging 1960 – Operation of the first laser Objects viewed by coherent light have granular appearance Unrelated to macroscopic structure What drives this phenomena? " היהפוך כושי עורו, נמר חברבורותיו..." ( ירמיה י " ג / כ " ג )

18. Speckle Noise – Cont. 1977 – Goodman’s paper on speckle Roughness on the order of a wavelength Many independent scatterers Interference occurs

19. Visualization

20. Speckle Noise – Cont. 1977 – Goodman’s paper on speckle Roughness on the order of a wavelength Many independent scatterers Interference occurs Signal dependent noise

21. Denoising Speckles Old methods Linear filtering Median filtering Image is smoothed as well The giant leap… Speckle noise is multiplicative! Denoise the log of the image instead

22. Homomorphic Denoising Original After Denoising

23. Noise Statistics Standard denoising assume WGN This is not the case Proposed method: 1. Preprocess input a. “Flatten” the noise (White) b. Gaussianize the noise (Gaussian) 2. Use usual denoising schemes (WGN) Reflectivity func. remains unchanged

24. Mathematical Model Assuming LSI Convolution with PSF Model: - the axial and lateral indices, resp. - the RF-image - the tissue reflectivity function - Point Spread Function (PSF) - additive noise

25. LSI Assumption Linearity usually holds, but… The system is NOT shift invariant!!! e.g. Radial – freq. dependent attenuation Solution: segmentation Deal with one segment at a time Each small segment is LSI w.l.o.g. we shall deal with one segment

26. Power Spectral Densities Model:

27. Power Spectral Densities Assuming lack of correlation between: Image samples (variance ) Noise samples (variance )

28. Power Spectral Densities Assuming lack of correlation between: Image samples (variance ) Noise samples (variance ) PSD of reconstructed image isn’t white! Defined by the PSF Has non-negligible support

29. Correlation Visualization

30. Preproc. 1 st Step - Decorrelation Speckle noise is not white Either take correlation into account, or.. Perform decorrelation Apply the linear filter: “Flattens” the PSD of the image

31. Preproc. 1 st Step - Decorrelation Speckle noise is not white Either take correlation into account, or.. Perform decorrelation Apply the linear filter: “Flattens” the PSD of the image Chosen empirically

32. Decorrelation Example

34. PSF Estimation PSF required for filter Blind deconvolution methods Based on smoothness properties of PSF w.r.t. the reflectivity function

35. Generalized Model Model for speckled images Additive term may be neglected Thus we have:

36. Good Old Additive Noise Taking the log: Subscript denotes the log Problem: rejection of additive noise But what are the noise statistics?

37. Log Transformed Speckles Noise statistics – no consensus Many scatterers per resolution cell Rayleigh distribution Many scatterers per resolution cell Various non-Rayleigh distributions Rician, K, Nakagami…

38. Generalized Gamma dist. Contains several relevant distributions Fasten your seat-belts…

39. Generalized Gamma dist. Contains several relevant distributions Fasten your seat-belts…

40. Examples Of Distributions

41. Preproc. 2 nd Step - Shrinkage Noise resembles Gaussian, with few outliers Proposition: Perform outlier-shrinkage Afterwards, deal with noise as WGN

42. Outlier-Shrinkage Apply median filter, diff. denoted Calculate residuals: Final result of shrinkage: That’s it Standard WGN denoising should work now

43. Block Diagram

44. In Silico Results

46. In Vivo Results

48. Thank you… Any questions?

49. Discussion Is speckle noise multiplicative? Only under specific conditions Model it better… Real-time applicability Differentiate between Real reflectors And speckle scattering Using sparsity constraints

51. Optional: Quantitative Assesment In silico: NMSE – Normalized MSE Speckle SNR – ration of mean to std. Beta – measure of preservation of sharp details In vivo: Speckle SNR – ration of mean to std. Alpha – evaluate resolution

52. Exploring Speckles רעש חברבורות Coherent imaging Rough object Roughness on the order of a wavelength Many scatterers within resolution cell Pattern determined by imaging system! Signal dependent noise " היהפוך כושי עורו, נמר חברבורותיו..." ( ירמיה י " ג / כ " ג )