Despeckling Of Ultrasound Images Ronen Tur

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

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

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

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

1D

– transmitted pulse – reflectivity coefficient at x – received signal

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

2D Complex problem Sum over different

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

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

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

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

Example

Noise In Ultrasound Major disadvantage of ULS imaging 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

Homomorphic Denoising Original After Denoising

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

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

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

Power Spectral Densities Model:

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

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

Correlation Visualization

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

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

Decorrelation Example

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

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 )

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

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

Log Transformed Speckles Noise statistics – no consensus Fully developed speckle Rayleigh distribution Partially developed speckle Various non-Rayleigh distributions

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

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

Examples Of Distributions

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

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

Block Diagram

In Silico Results

In Vivo Results

Thank you… Any questions?

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

Optional: Quantitative Assesment NMSE SNR Beta Alpha