University of Illinois at Urbana-Champaign The University of Illinois at Urbana-ChampaignThe Beckman Institute at the University of Illinois at Urbana-Champaign

Insana Lab: Ultrasonic Imaging - The University of Illinois at Urbana-Champaign

Project 5: Efficient Ultrasonic Beamforming Strategies: Spatial Filtering
Kang-Sik Kim []

 Fig 1. Focusing (or beamforming) is one of the most important factors in determining the image quality of ultrasound B-mode images [1-8]. Currently, most ultrasound systems employ different focusing methods on transmit and receive. On transmit, the focal length is often fixed, and therefore the best spatial/contrast resolution is near the transmit focal length. Lateral resolution is degraded in the near-field and far-field. On the other hand, delaying and summing echo samples from receive channels dynamically allows us to focus receive echo signals at every depth; the method is called dynamic receive focusing (DRF) [2-7]. Overall B-mode image quality and resolution are affected by both transmit and receive focusing whose performance is represented by beam patterns as in Fig 1.

As shown in left panel of Fig. 1, conventional dynamic focusing (CDF) provides the best pulse-echo spatial resolution near the transmit focal depth. Therefore to further improve the resolution of current ultrasound imaging, it is necessary to overcome the limitation of the fixed transmit focusing. The goal of this research project is to develop efficient 2-way dynamic focusing methods.

 Fig 2 shows lateral beam patterns at the focal depth  and in the far field for continuous-wave transmission. The beam width is just the Fourier transform of the aperture function  provided we can eliminate the quadratic phase term, , which degrades resolution. Focusing eliminates this quadratic phase term, such that the rectangular aperture of a linear array is expressed by sinc(x) function. The goal of focusing (bamforming) is to eliminate the quadratic phase term.

 Fig 3 illustrates pulse echo beam patterns from conventional dynamic focusing methods. In the near or far field, the beam pattern has high side lobe levels that reduce image contrast. Near the transmit focal length, the pulse echo beam pattern attains the diffraction limit on spatial resolution, limited by the frequency of the sound waves and aperture size. Mathematically, the narrowest-possible linear array beam pattern is given by sinc2 function, but this occurs only in the narrow range known as the depth of focus. The goal is to implement diffraction limited beam patterns at all image depths.

 Fig 4 describes the spatial matched filter (SMF) beamformer mathematically and graphically. Spatial matched filters focusing the beam instead without the use of the conventional delay-and-sum operation. Applying SMF to echoes from unfocused beams allows us to approximate diffraction-limited imaging conditions at all depths, with some loss of axial resolution. SMF beamforming can be considered as an alternative to CDF.

 Fig 5. To implement the SMF beamformer, we transmit ultrasound waves using a large transmit aperture with a fixed focal length. RF images are formed from each receive channels. The transmit and receive beam patterns are expressed as shown in Fig. 5 where x1 represents the lateral location of each receive element.

 Fig 6. Next, a spatial matched filter is applied to each RF image and summed. Filtering aligns the individual channel images so that delay circuits are unnecessary. This method can provide two-way focused beam pattern at all imaging depths regardless of transmit focal depth.

 Fig 7 is a block diagram of the proposed SMF method using impulse-response results to show the effects at each stage.

 Fig 8. Continuous-wave (CW) beam patterns from simulations of linear array fields via Field II are shown to illustrate SMF method and compare it with CDF method. We used a 10 MHz array with 96 transmit and receive channels. The fixed transmit focal length was 40 mm. No apodization was applied. The label "Focus" indicates diffraction limited pulse-echo beam patterns, the gold standard for comparisons. The label "CDF" indicates conventional dynamic focusing was applied. The label "SMF" indicates the spatial matched filter beamformer was applied. It shows nearly the same beam pattern as Focus at all imaging depth regardless of the transmit focal depth. SMF improves the lateral resolution as compared with DRF.

 Fig 9 shows the point spread function (PSF) for each of the three methods using a pulsed transducer excitation. The bandwidth of the pulse is 70% of the center frequency. SMF method provides almost the same PSF as Focus at 40 mm and 60 mm. However the PSF of SMF is slightly inferior to Focus because 2-D spatial matched filters were used for constructing 2-D images while 1-D spatial matched filters were used in the previous CW case. Despite of this difference, SMF provides improved resolution in the near-field and far-field compared with CDF.

 Fig 10 displays computer simulated cyst phantom images using the three beamforming methods. SMF provides comparable images to Focus (gold standard) at 40 mm (transmit focal length) and 60 mm (far field). However, in the near field, like the PSF result of Fig 9, the spatial resolution and contrast to noise ratio (CNR) of SMF image is slightly degraded compared with Focus. Compared with CDF, SMF image quality is significantly improved in the near and far fields.

Fig 11. Other simulations were performed to compare the performance between CDF and SMF in the presence of a planar phase aberrator. All images are of a cyst positioned in the transmit-aperture near field. Images on the left were constructed w/o phase aberration, while those on the right were constructed w/ phase aberration. The rms aberration amplitude is 34 ns and the spatial correlation length along the lateral dimension is 3.6mm. These are typical values for breast tissue. With phase aberration, image resolution is degraded significantly with both CDF and SMF methods, but the image quality of the SMF image is superior to CDF. Both methods are equally sensitive to phase aberration.

Fig 12. We images the point spread functions from a 10 MHz, f/1.5, 60% BW, 45 mm diameter, annular array (8 rings) to verify performance experimentally. PSF in the near field (25 mm), at the transmit focal depth (45 mm), and in the far field (65 mm) are shown. The target was a wire phantom in water.

Fig 13 compares the SMF method applied to individual channels (before BF) versus that applied to beamformed RF echo signals (after BF). Although the latter method is simpler and faster, filtering individual channels generates superior image quality because of lower side lobes. Using apodization to reduce the side lobe level is effect at the cost of main lobe width (spatial resolution).

Fig 14. SMF is well suited to high frequency imaging with array, where delay circuits for dynamic focusing are difficult to implement. To evaluate the performance of spatial filtering method on beamformed data for high frequency application, PSF simulations were generated. We assumed a circular aperture, 70 MHz transducer with 45% BW, 4.66 mm diameter and 7 mm focal depth (f/1.5). The figure displays the PSFs from a fixed geometric focus and SMF method six depths. SMF provides a more improved beam except at the 7 mm focal length.


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[9] J. A. Jensen, "Field: A program for simulating ultrasound systems," Med. Biol. Eng. Comp., vol. 4, no. Suppl. 1, pt. 1, pp. 351353, 1996.

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