# e-book Ultrasound Imaging: Advances and Applications

Since b is not known b b is used in 21 instead of b. As it will be shown in the section of experimental results this approximation is valid. Let b i, j be the estimated value of b, computed from the pixels within the small window wi, j. The global value of b, once again, is obtained by averaging the estimated b i, j : 1 N,M bi, j.

First, the accuracy on the decompression parameters a, b estimation procedure is computed by using synthetic ultrasound data. The validity of the decompression method is also assessed by using real data. In addition, the adequacy and robustness of the ERF image retrieval method is investigated in the real case using two sets of experiments, including the application of the decompression method in 1 different BUS images acquired with fixed brightness and contrast parameters and 2 static BUS images acquired with variable operating parameters.

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Finally, GoF tests with Rayleigh and Gamma distributions are conducted in estimated ERF images which enables to support the hypothesis that most envelope RF data can be well modeled by these two distributions. The interpretation of the obtained results suggest the use of the simpler Rayleigh distribution to decompress that data.

The decompression method is initially tested in synthetic data by using Monte Carlo tests. Particularly, in this experiment it is intended to assess the estimation accuracy of the decompression parameters, a, b , for different images and amounts of noise. For each pair of decompression parameters 50 Monte Carlo runs were performed. In each run, two different types of synthetic images are used to revert the uniform and non uniform.

The non uniform image is the SheppLogan phantom also corrupted by the same three different amounts of noise used with the uniform phantoms. In both cases the noisy images are interpolated and log-compressed according to 6. Figure 3 presents the average and SD of the 50 estimated decompression obtained for each true pair a, b , by using the first phantom parameters, a, b , Fig.

## Ultrasound imaging from a single large sensor

Similar results are obtained in both cases which suggests that the decompression method has similar behavior for uniform and non-uniform images, and its performance is apparently independent on the severity of speckle noise contamination. The later conclusion is confirmed in Fig. In general, the estimation a is non biased and its SD increase mainly with a0 see Fig.

The variability of a tends to be less significant as b increases see Fig. The uncertainty associated with the decompression parameter b increases linearly with a. In fact, this behavior is similar to the one obtained for a, except for very small values of a, where the uncertainty about b increases with b see Fig. The method here proposed is able to invert the compression operations when synthetic images are given. Moreover, it is important to study the feasibility of the method when raw data is provided by the manufacturer.

Notice that the challenge of decompression from BUS images is only raised because raw data is generally not available in a clinical setting, thus limiting the application of algorithms which are based on statistical modeling of speckle or RF data. Performance is in simulated log compressed images of a noisy assessed by computing the mean and SD of a, b uniform image created with Rayleigh parameters a and noisy SheppLogan phantom b.

The RF image retrieval decompression method is applied to the BUS image, resulting in an estimate of the envelope data, image. As shown in Fig. This observation supports the adequacy of the proposed method to provide an estimate of the envelope RF data which resembles the original one.

## Medical Ultrasound Imaging Technology | Open Medscience

So far the decompression method was validated using an IVUS image from which the raw data was known. Moreover, it is also pertinent to investigate the robustness of the method according to different acquisition settings and scenarios. To this purpose, the RF image retrieval method is tested under two different conditions: first, by changing the probe position and keeping the operating parameters constant, and second by maintaining the probe steady and varying the contrast and brightness parameters.

Figure 5ac presents results of the application of the decompression method proposed in this chapter. For each set of RF estimated images, a homogeneous region was selected and its intensity histogram computed as shown in Fig. These results show that the statistical properties of the estimated RF images are comparable, suggesting that the decompression method is robust to small changes in image appearance.

### WE‐EF‐210‐00: Advances in Ultrasound Imaging Technology

The decompression parameters from each image set are depicted in Fig. The SDs for a and b are 3. Liver Fig. Right side Decompression parameters. As previously mentioned, the second experiment consisted in acquiring a series of BUS images by keeping the probe steady and varying the operating parameters. Results of the application of the decompression method in two different image sets are shown in Fig. In terms of gray-scale image appearance, the obtained ERF images present similar dynamic range and brightness.

Histogram analysis of data extracted from homogeneous regions in such images Fig. A comparison between the contrast and brightness parameters given by the US scanner with the estimated decompression parameters is given in Fig. Although a. Right side Decompression parameters estimated with proposed method vs. Considering the estimated parameters a these appear to change approximately in inverse proportion with respect to the original dynamic range settings a.

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Moreover, the estimated parameters b vary roughly in direct proportion according to the original linear gain settings b. These results support the ability of the proposed method to estimate the decompression parameters, evoking a similarity association between these values and the settings defined with the ultrasound equipment. Results aiming at assessing the adequacy and robustness of the proposed decompression method in the aforementioned real cases are detailed in Table 1. Besides the decompression parameters obtained for each image of the data set, it is also shown the KullbackLeibler distance [26] of each distribution with respect to the first distribution of each set.

Observations taken from Table 1 support, from a quantitative point of view, the robustness of the decompression method in estimating precisely the decompression parameters and the ERF images. It is relevant to investigate whether the assumptions made initially about the adequacy of the Rayleigh distribution to model the pixel intensities in ERF images. Thyroid cross-section a b dKL h1 , hID It is known that the assumption of fully developed speckle determines Rayleigh statistics for the amplitude of the envelope RF data, although the Gamma distribution seems to provide a better approximation [27, 28], mainly when interpolation is involved, which is the case.

Hence, the purpose of the study presented in Fig. Given this, the Maximum Likelihood ML estimates of the Rayleigh and Gamma distribution were computed locally for each image. This computation is done in 8 8 sliding blocks with 2 2 overlapping borders, throughout the images. Moreover, a correlation coefficient measure is computed to compare each distribution with the data histogram, given by:.

When the correlation coefficient, xy , is 1 it means the distribution under investigation either Rayleigh or Gamma perfectly models the local data. ML estimated Rayleigh distribution Fig.

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ML estimated Gamma distribution Fig. Gamma distribution Fig. In both cases, the Gamma distribution is able to better describe the data when compared to the Rayleigh distribution. An interesting observation is that the. The plaque contour is marked for ease of visualization. Rayleigh distribution provides a good description of the data in a very significant part of the images, essentially where strong scattering phenomena do not occur. Moreover, when the local comparison between the Gamma and Rayleigh distributions is carried out, it is observed that in most regions of the studied images, the Rayleigh distribution closely approaches the Gamma distribution.

The only exceptions occur in regions of substantial echogenicity, where the Gamma distribution is more suitable to describe the data. These results validate the adopted decision and does not include in the proposed decompression method the interpolation operation. This operation is the source of the Gamma distribution, but as it was confirmed in.

Carotid plaque Fig. GoF map associated with the local comparison between ML Rayleigh and Gamma local distributions right. This chapter proposes a statistical model for log-compressed BUS data which allows to parameterize the most significant operating settings of ultrasound equipments and revert the nonlinear compression, providing an estimate of ERF data. The estimated envelope intensity can be used by a variety of algorithms that rely on the statistics of the ultrasound signal. These include segmentation and speckle tracking algorithms, speckle reduction methods proposed in the next chapter , tissue classification methods, etc.

The method here presented relies on statistics of the compressed signal, which follows a double-exponential distribution and makes use of a realistic mapping function, designated as LCL, first proposed in [20] which is able to provide an estimate of the ERF image given that parameters related to dynamic range and linear gain are known. The decompression method makes use of this prior knowledge to accurately estimate such parameters and recover the ERF image.

Experiments performed in synthetic and real data show the accuracy of the estimates obtained for the decompression parameters. Moreover, this method is robust because it is able to provide similar outcomes for images acquired with different operating settings. On the other hand, similar decompression parameters were obtained for different images acquired with fixed operating settings. The Rayleigh distribution has shown to correctly describe the ERF estimated data which has important consequences in the assumptions made for designing the decompression method presented in this chapter.

Finally, a study recently presented in [29] compared the compression parameter estimation of the well-established method proposed in [7, 8] with the approach described in this chapter, observing that the later provides better results in terms of parameter estimation accuracy. As pointed out in [29] this could be explained as the decompression method proposed in this chapter is based on the statistics for the compressed signal, while the approach presented in [7, 8] uses statistics for the uncompressed signal, and attempts to match theoretically calculated normalized moments with those determined directly from the image.

The process of fitting the moments calculated in the image with theoretical moments of the exponential distribution cf. References 1. Phys Med Biol 48 14 2. Aysal T, Barner K Rayleigh-maximum-likelihood filtering for speckle reduction of ultrasound images.

Ultrasound Med Biol 33 1 4. Goodman JW Speckle phenomena in optics. Roberts and Company, Atlanta 5. Michailovich O, Tannenbaum A Despeckling of medical ultrasound images. Pattern Recogn Lett 24 45 9. Kim H, Varghese T Attenuation estimation using spectral cross-correlation.

Orfanidis SJ Optimum signal processing. An introduction.