A point target is imaged by a medical ultrasound imaging system to evaluate its image quality. The resulting image, referred to as a point spread function (PSF), can be used to characterize the imaging system in question. In order to observe the characteristics of the main and side lobes, we modeled and carried out computer simulations of an ultrasound focusing system where 64 channels were used on transmit and receive, the transmit focal depth was set to 30 mm, the transducer center frequency was 5 MHz, the element width was one wavelength, and the speed of sound was 1,500 m/s. We constructed an image of the point target at a depth of 40 mm and logarithmically compressed it over a dynamic range of 60 dB to be able to better observe the side lobes present in the image. In the center of Fig. 1, the brightest area, with a main lobe width of 1.2 mm, is the main lobe. The main lobe region is where the actual point target appears in the image, and the better the focusing performance, the smaller the main lobe region. The wingshaped bright area outside the main lobe region represents the side lobes and corresponds to noise. The side lobes arise due to the fact that the signal from scatterers outside the main lobe region is not completely canceled out in the focusing process. If a scatterer with small reflectivity, such that its echo is smaller than the magnitude of a side lobe signal, is present in an area where the side lobe appears, it appears as a small main lobe signal and cannot be observed in the image. Since the side lobe level is proportional to the main lobe level, large side lobes always appear around a strong scatterer. This makes it difficult to observe the inside of a low-reflectivity cyst.

Ultrasound echo signals reflected from the tissue of the human body are received as a superposition of signals from the main lobe region and clutter or side lobe signals from the other region. Therefore, dynamic receive focusing and various signal processing techniques are employed to reduce side lobes, thereby improving the image quality. However, since the magnitude of the side lobe signal in the ultrasound echo signal cannot be accurately estimated, the effect of the side lobe on the image cannot be precisely determined.

In order to solve this problem, we reported a method for separating the main and side lobe signals in the process of synthesizing ultrasound signals by computer simulation, and quantitatively calculated the magnitude of the side lobes in the image [13]. In a computer simulation, ultrasound echo signals from the human body are generated by modeling the body as consisting of a large number of scatterers with nonuniform reflection coefficients, which are distributed over a wide area. Since the position and reflectivity of the scatterers in a simulated human phantom are known in advance, the signal from each scatterer can be identified on receive, and, therefore, the main and the side lobe signal can be separated so that a side lobe-free image can be synthesized only from the main lobe without the side lobe. Since the side lobe-free image has the maximum possible resolution and contrast that an ultrasound imaging system can achieve under a given set of conditions, it can be used as a ground truth image in a simulation where ultrasound image signal processing is used to improve the image quality. The proposed method cannot be applied to actual human body data, but the effect of the side lobe on image quality can be theoretically explored by a computer simulation.

Multiplying each channel signal by a window function in the focusing process of the received ultrasound signal reduces the side lobe levels by suppressing the high spatial frequency components of the side lobe. This signal processing is called apodization. A general DAS beamformer performs dynamic receive beamforming that can be expressed as

where ch is the channel index, N is the total number of channels used, x_ch[n] is the received radiofrequency echo signal of the chth channel, n is the time index, ∆_m[n] is the dynamic receive focusing delay, w_ch[n] is the apodization weighting, and z[n] is the beamformer output. In this study, the Hamming function was used as an apodization window to reduce side lobe levels [2,3].

If the magnitude of the side lobe signal can be estimated in the focusing process of the ultrasonic signal, it can be used in the signal processing task for reducing the side lobe. The side lobe can be modeled as sinusoids of different spatial frequencies depending on the angle of incidence in the receive channels. Therefore, it is possible to estimate the magnitude of the side lobe by decomposing the received channel signal into spatial frequency components using the Fourier transform and separating out only the side lobe component [10]. A side lobe suppression filter using the magnitude of the side lobe estimated from an imaging point has been reported [12]; this is referred to as the side lobe EAR filter and is defined as follows:

where B_pixel is the brightness of an imaging point, B_filtered is the brightness of the filter output, QF is the side lobe level of a pixel, and γ is a scale factor (i.e., an experimentally determined parameter that controls the filter performance). The side lobe EAR filter first estimates and then subtracts the side lobes at an imaging point and operates to reduce the output brightness when the estimated side lobe levels are large.

MVB is a method of calculating and applying an optimized apodization window W[n] at all imaging points, which minimizes the variance of z[n] in Eq. (1), subject to the constraint that the gain in the desired beam direction equals unity. The apodization window can be found as

where R[n] is the spatial covariance matrix of the received channel data, and a is the steering vector. MVB has been applied to point-like images such as underwater sonar and radar, and recently has also been successfully used to improve the quality of medical ultrasound images [4,5-8].

A point target image can best represent the focusing performance of a medical ultrasound imaging system. In the point target image, the characteristics of the main lobe and the magnitude and distribution of the side lobe determine the resolution and contrast, respectively. The effect of side lobe suppression can be readily seen in the point target image because the main and the side lobe each occupy distinct different image regions. A computer simulation of the point target image was conducted to observe the effects of the side lobe, as well as side lobe suppression filtering.

The computer simulation conditions were the same as in the previous PSF computation. An array of nine-point targets were placed at intervals of 5 mm over a depth from 10 to 50 mm. The simulation program was written in MATLAB and executed on an IBM PC. Logarithmic compression was performed over a dynamic range of 60 dB to reveal the details of the side lobe in the image. Fig. 2A shows the PSF of conventional imaging, in which receive dynamic focusing was employed and the transmit focal depth was set to 30 mm. Fig. 2B and C are, respectively, the main and the side lobe image constructed by separately extracting the main and side lobe signals from Fig. 2A. Since the regions in which the main and side lobes are present do not overlap, the two lobes can be easily distinguished from each other. As a result of the logarithmic compression of the side lobe image alone in Fig. 2C, the side lobes appear over a large area because smaller side lobes are amplified. Fig. 2D shows the result of applying Hamming apodization to the receive focusing process to reduce the side lobe. The side lobe level is lower, but the width of the main lobe is greater, resulting in lower resolution. We applied signal processing methods such as side lobe EAR filtering and MVB. Fig. 2E shows the side lobe EAR-filtered image with a scale factor of 2. Fig. 2F shows the result of applying MVB with the spatial smoothing, temporal averaging, and diagonal loading factors of 64, 1, and 0.05, respectively. In side lobe suppression filtering, it can be seen that the side lobe could be reduced without degrading the main lobe characteristics. For the point target, the resolution and the degree of side lobe reduction turned out to be most pronounced for the MVB method. The main lobe image presented in Fig. 2B is not only useful from the standpoint of quantitative evaluation, but also can be used as a ground truth image for comparison with other images.

Fig. 3 compares the lateral field responses of the point target at a depth of 40 mm in the point target image. The solid line is the ultrasound field of the conventional image obtained using only DAS beamforming. The width of the main lobe is narrowest to achieve the best resolution, but the side lobe levels are high. The magnitude of the first side lobe is 15.9 dB lower than that of the main lobe when using a linear array transducer. As one of the most widely used signal processing methods for side lobe reduction, the Hamming apodization (dashed line) is effective in decreasing the side lobe levels below -52.8 dB, but increases the width of the main lobe. The side lobe EAR filtering (dotted line) and MVB (dash-dotted line) methods suppress the side lobe levels without increasing the width of the main lobe. Both methods require a large amount of computation, but produce better results than the apodization method. The lower side lobe levels indicate that the image contrast is increased and that lesions in the area with a smaller brightness difference can be better differentiated.

In ultrasound images, lesions such as tumors or cancers appear darker or brighter than the surrounding tissues. For a hypoechoic cyst in homogeneous soft tissue, the cyst boundary tends to look blurry and the contrast inside the cyst is lowered because side lobes infiltrate the cyst. Computer simulations of hypoechoic cyst images were performed to compare the image contrast. We randomly distributed a cloud of scatterers in the background so that the speckle pattern could be fully developed. Six cysts with a diameter of 4 mm were placed in the lateral direction at a depth of 35 mm with reflectivity of, from left to right, -30 dB, -24 dB, -18 dB, -12 dB, -6 dB, and +6 dB relative to that of the background. In addition, for the purposes of comparison, three point targets with reflectivity of 24 dB, 30 dB, and 36 dB higher than that of the background were placed in the axial direction at depths of 32 mm, 35 mm, and 38 mm on the left side of the leftmost cyst, respectively. In order to make the generated side lobe level slightly higher for comparison purposes, the transmission focusing depth was set to 50 mm, not 35 mm.

All the images shown in Fig. 4 are of size 10 mm (axial)×54 mm (lateral). Except for the rest, which used 60 dB, Fig. 4E was logarithmically compressed over a dynamic range of 70 dB to make smaller levels more observable. Fig. 4A is the conventional image. Fig. 4B and C are the main and side lobe images, respectively. Fig. 4D is the Hamming apodization image, Fig. 4E is the side lobe EAR-filtered image using a scale factor of 2, and Fig. 4F is the MVB image with spatial smoothing, temporal averaging, and diagonal loading factors of 32, 1, and 0.5, respectively. After side lobe EAR filtering, the brightness of the bright area associated with the main lobe was maintained, but that of the area associated with the side lobe became dark, with the result that the entire image became dark and that the speckle pattern tended to be different from that of the conventional image [4,9]. To cope with this phenomenon, the parameters of the side lobe EAR filter were adjusted so that the speckle pattern was similar to that of the conventional image. In addition, to make the brightness of all the images similar, the logarithmic compression was appropriately adjusted.

In the main lobe image, which is completely devoid of side lobe, the boundaries of the cysts are more pronounced, and the difference in contrast between the cysts is more conspicuous.

In the conventional image, the difference in speckle brightness inside the cysts is not large. This is because when the side lobe generated in the background of the cyst boundary is larger than the reflected signal from the inside of the cyst, the former masks the latter. When the reflectivity inside the cyst is small and the magnitude of the side lobe in the surrounding region is large, it is difficult to decide whether the cyst is present or not. For the cysts of reflectivity -30 dB, -24 dB, and -18 dB in Fig. 4A, the small difference in brightness between them can be attributed to the fact that in conventional DAS beamforming the side lobe level is 15.9 dB less than the main lobe peak level. When Hamming apodization is applied, the side lobe inside the cyst is suppressed. As the main lobe width increases, the lateral resolution decreases, and the cyst boundary appears to be shrunk toward the inside of the cyst.

In the side lobe EAR filter and MVB, the cyst boundary became more pronounced as a result of the side lobe being suppressed, and the difference in contrast between the cysts can be well identified.

To evaluate the speckle brightness contrast between the background and the cyst, we computed the contrast ratio (CR), which is defined as follows [15]:

where S_c is the average brightness inside the cyst and S_b is the average brightness in the background. For the -30 dB cyst, the two areas selected for the calculation are represented by the two dotted square boxes in Fig. 4A. The same windows were used for the remaining other cysts as well.

Table 1 compares the computed CR values of cysts. The CR difference between the cysts in the main lobe image is evident, but does not increase linearly because the logarithmic compression used in the image processing is a nonlinear operation. The logarithmic compression reduces the brightness contrast as the image becomes brighter. In conventional imaging, the CR does not decrease proportionally even if the reflectivity decreases because of the effect of the side lobe in the vicinity of the cyst. It can be seen that the contrast between the cysts increased in both examples of side lobe suppression filtering (i.e., side lobe EAR filtering and MVB). The Hamming apodized image has the best contrast, but there is still room for improvement compared with the CR value of the main lobe image. The MVB image performs best for point targets, but less so for speckle objects.

Fig. 5 compares the changes in speckle pattern due to the side lobe suppression filtering. We can see that both the conventional and main lobe images have the same speckle pattern. In the conventional image (Fig. 5A), since the magnitude of the side lobe is smaller than that of the main lobe by 15.9 dB, the side lobes are swamped by the main lobe signal in the speckle region comprised of random scatterers. In the speckle pattern of the side lobe image (Fig. 5C), the spatial frequency of the lateral side lobe is higher than in the main lobe image (Fig. 5B), and the side lobe signal corresponds to the fine pattern in the image. The Hamming apodization image (Fig. 5D) has a lower lateral resolution with a speckle pattern elongated in the lateral direction. For side lobe EAR filtering, the parameters were tuned such that the speckle pattern was similar to that of the conventional image. The speckle pattern of Fig. 5E turned out to be very different from that of the conventional image (Fig. 5A) when the parameters of the side lobe EAR filter were adjusted to increase the image resolution [12,13]. In particular, the MVB method with the spatial smoothing, temporal averaging, and diagonal loading factors of 64, 1, and 0.001, respectively, maintained nearly the same brightness of the bright area of Fig. 5F but rendered its dark area as much darker. It can be seen in Fig. 5 that speckle characteristics changed only slightly from one signal processing method to another and that the image quality degradation due to the side lobe can hardly be noticed. Moreover, it can be noted that the side lobe suppression methods cannot improve both resolution and contrast simultaneously in the speckle-only region.

In order to observe the effect of the side lobe in ultrasound images of the human body, pseudo-ultrasonic signals were synthesized using a computer. Since actual ultrasound data obtained from the human body cannot be used to synthesize a side lobe-free image, ultrasound images were synthesized from a distribution of scatterers, the reflectivity of which was obtained from converting the gray levels of an MR image of the human kidney [16]. We simulated a 64-channel system using a 3.5-MHz linear array transducer. The element pitch was one wavelength, and the transmit focal depth was at 80 mm. Starting from a depth of 40 mm, the image size was 117 mm (axial)×130 mm (lateral). The size of the kidney in the synthesized ultrasound image does not match that of the human kidney. Fig. 6A and B show an MR image of the human kidney and its gray level distribution converted into the ultrasonic reflectivity coefficient, respectively.

Fig. 7 shows computer-synthesized in vivo ultrasound B-mode images starting with the gray level MR image of the kidney, where Fig. 7A is the conventional image, Fig. 7B is the main lobe image, Fig. 7C is the side lobe image, Fig. 7D is the Hamming apodization image, Fig. 7E is the side lobe EAR-filtered image with a scale factor of 5, and Fig. 7F is the MVB image with the spatial smoothing, temporal averaging, and diagonal loading factors of 64, 1, and 0.01, respectively, and 90 dB of logarithmic compression to match the brightness of the other images with 60 dB of logarithmic compression. In order to check the image resolution, point targets were arranged at 5-mm intervals in the axial direction on the left side of the images. In the main lobe image (Fig. 7B), the fine tissue inside the kidney can be differentiated. In the side lobe image (Fig. 7C), the side lobe appears in the lateral direction at the boundary of the region with a large reflectivity. In the case of Hamming apodization (Fig. 7D), the resolution is lower, but the contrast is higher. Although the main lobe width is higher and thus the resolution is lower, suppression of the side lobes may well compensate for this disadvantage by providing an improved basis for making a diagnosis. In the side lobe EAR filtering (Fig. 7E) and MVB (Fig. 7F), the side lobe levels of the left array of point targets are lower, and the resolution is clearly better than that of the conventional image (Fig. 7A).

Fig. 8 zooms in on a part of the kidney to check the image resolution, where Fig. 8A is the conventional image, Fig. 8B is the main lobe image, Fig. 8C is the compound image, Fig. 8D is the Hamming apodization image, Fig. 8E is the side lobe EAR-filtered image, and Fig. 8F is the MVB image with spatial smoothing, temporal averaging, and diagonal loading factors of 64, 1, and 0.01, respectively. Ultrasound images that have not undergone postprocessing tend to have black spots. Since those specks appear coarse when zoomed in on, they were removed by median and lowpass filtering. Compared with the conventional image (Fig. 8A), the contrast of the kidney is highest in the main lobe image. Fig. 8D, E, and F have better resolution and contrast than Fig. 8A. The MVB image in Fig. 8F appears darker than other images since the brightness of the speckle regions is lower when both strong reflectors and speckle regions are present, so a logarithmic compression of 90 dB was applied to make the brightness similar to that of other images. The improvement of the MVB filtered image quality varies from one region to another depending on the anatomical structure. Accordingly, there is a need to adjust the parameters of MVB to suit the imaging characteristics of the region to be imaged for diagnosis.

In order to reduce image noise and improve resolution in ultrasound image signal processing, the compound imaging technique that averages images processed using different signal processing methods is widely used [17,18]. Fig. 8D, E, and F present the images obtained by applying different signal processing techniques to ultrasound data obtained from the human kidney. The compound image (Fig. 8C) obtained by superimposing Fig. 8D, E, and F is more similar to the main lobe image than any of Fig. 8D, E, and F in isolation.