• Place tissue in a transducer/tissue coupling medium (water in our case). Insonify with pulsed ultrasound.
• Collect sound scatter data at many angles
• Input data to a reconstruction algorithm based on a physics model. We describe the sound pressure field, p, by the Chernov Equation, in which tissue is modeled as a compressible fluid with a spatially varying density, , and compressibility, :
  
  • reconstruction with ultrasound data scattered at +/-90 degrees yields an image of
    
    
  • reconstruction with backscatter data yields an image of
    
    

The Need for Digital Signal Processing

• Ultrasound signals in general are quite weak, since the sound wave is reduced in magnitude ~44% by each cm of travel through tissue
• detected ultrasound signals include noise:
  • inherent in the electronics or due to vibrations
  • due to speckle that is created by sound scattered from many tiny regions within the tissue that are too small to be resolved by the imaging system
  • comparable in amplitude to that of the data

Wavelet Analysis for Digital Signal Processing of Data

Figure 5: Symmlet 4 wavelet [View Image]

• Wavelets are special mathematical functions localized in both time and frequency (or space and spatial frequency). An example of the Symmlet 4 mother wavelet is shown in Figure 5
• Ultrasound voltage signals can be expressed as a weighted sum of similar wavelets (a family). If one can design/find a wavelet family whose members have characteristics similar to those of the ultrasound pulses, the data can be denoised through the use of wavelet analysis

Denoising Method in Brief

• choose suitable wavelets (herein lies the art !)
• express the signal as the weighted sum of these wavelets (do the wavelet transform)
• set weights less than a particular value to zero
• retransform the remaining information to yield a denoised signal
• we are utilizing the algorithms of experts Donoho and Johnstone of Stanford University