Spectral-based quantitative ultrasound imaging-processing RF vs IQ data

Abstract

Quantitative ultrasound (QUS) is an imaging technique which includes spectral-based parameterization. Typical spectral-based parameters include the backscatter coefficient (BSC) and attenuation coefficient slope (ACS). Traditionally, spectral-based QUS relies on the radio frequency (RF) signal to calculate the spectral-based parameters. Many clinical and research scanners only provide the in-phase and quadrature (IQ) signal. To acquire the RF data, the common approach is to convert IQ signal back into RF signal via mixing with a carrier frequency. In this study, we hypothesize that the performance, i.e., accuracy and precision, of spectral-based parameters calculated directly from IQ data is as good as or better than using converted RF data. To test this hypothesis, estimation of the BSC and ACS using RF and IQ data from software and physical phantoms were analyzed and compared. The results indicated that there were only small differences in estimates of the BSC between when using the original RF, the IQ derived from the original RF and the RF reconverted from the IQ, i.e., root mean square errors (RMSEs) were less than 0.04. Furthermore, the structural similarity index measure (SSIM) was calculated for ACS maps with a value greater than 0.96 for maps created using the original RF, IQ data and reconverted RF. On the other hand, the processing time using the IQ data compared to RF data were substantially less, i.e., reduced by more than a factor of two. Therefore, this study confirms two things: 1) there is no need to convert IQ data back to RF data for conducting spectral-based QUS analysis, because the conversion from IQ back into RF data can introduce artifacts. 2) For the implementation of real-time QUS, there is an advantage to convert the original RF data into IQ data to conduct spectral-based QUS analysis because IQ data-based QUS can improve processing speed.

Introduction

Quantitative ultrasound (QUS) is an imaging technique which includes spectral-based parameterization, elastography, shear wave imaging, flow estimation and envelope statistics (1). Many studies have demonstrated that QUS is useful in tissue characterization with liver disease (2–5), breast cancer (6–8), thermal treatment (9) and thyroid cancer (10). In terms of spectral-based QUS, the backscatter coefficient (BSC) and attenuation coefficient slope (ACS) are frequently utilized because they can be system-independent parameters and are fundamental properties of tissues.

The BSC is a quantitative ultrasound parameter that describes internal scattering structures in a medium (11). The BSC is typically estimated versus frequency and is related to normalized power spectrum from the backscattered signal. The normalized power spectrum is estimated through the calibration of the system with a reference signal, which can be acquired through several means, e.g., planar reflector method (12), reference phantom method (13), or an in situ calibration target (14, 15). These methods account for system-related signals and settings. To estimate the normalized power spectrum requires access to time domain signals.

The ACS is another QUS parameter that depends on estimation of the power spectrum from the backscattered signals. Many previous studies have investigated the effect of ACS maps for breast tissue characterization with backscatterd signal (16, 17). There are three typical spectral-based methods to calculate the attenuation: spectral difference method (18, 19), spectral log difference (SLD) (20) and hybrid method (21). The spectral difference method uses multiple time-gated windows, and estimate the ACS by comparing the spectrum from all these windows versus depth. Compared to spectral difference method, the SLD uses the power spectra from only two windows in a data block, and takes the logarithm of the spectra to do the estimation. The hybrid method is similar to spectral difference method, which uses all the time-gated windows, and it makes a prior assumption that the local attenuation and the cumulative attenuation from the surface of the transducer to the depth increase linearly with frequency (20). All these three methods highly depend on the reference phantom to make the estimation. The requirement of a well-calibrated reference phantom is a limitation of these methods, but many studies have shown that SLD could generate an accurate attenuation image for breast because it could make a better estimation of attenuation for heterogeneous tissues within these three methods.

Unlike these reference-phantom-based algorithms, there is also a reference frequency method (phantom free method). The method only depends on the adjacent frequencies to estimate the ACS (2, 22), which means it cancels system-dependent effects using spectral normalization in adjacent frequencies. The technique has limitations such as a requirement for a large computing window and the requirement for the useful frequency range to estimate the ACS, which will lead to a low-resolution attenuation image. As with the BSC, the ACS is calculated with the spectral information derived from the backscattered signal.

Traditionally, the radio frequency (RF) signals have been used to calculate BSC and ACS. However, in practical scenarios many imaging machines will not provide raw RF data, but instead only provide the IQ data. The reason for this is that the IQ data takes much less storage space than storing the RF data (23, 24). To estimate the BSC or ACS, traditionally the IQ data is converted back into RF data first, and then the QUS parameters are estimated from the RF (25, 26). However, because the power spectrum from the IQ data and RF data are similar to each other, and QUS is a spectral-based method, it is reasonable that the IQ data could be used to calculate QUS parameters without a loss in information. Furthermore, every time the RF data is converted to IQ or IQ converted back to RF, the introduction of artifacts to the signal can occur leading to biases in QUS estimates or increases in QUS estimate variance. In this study, we assess the performance of spectral-based QUS when using the original RF data, the IQ converted data and the RF data reconverted from the IQ data and compare the results of QUS using each data signal format from the same datasets. We also assess the computational requirements for processing data using either original RF, IQ, or reconvereted RF data. The remaining part of the paper is organized as follows. Section II introduces the process of converting RF data into IQ data, and vice versa. It also introduces the image quality metrics and the methods used for calculation of two QUS parameters, the BSC and the ACS. Section III presents the results for when using RF data or IQ data to calculate the BSC and the ACS. Section IV discusses the processing speed performance associated with both RF data and IQ data, and the filter’s impact on QUS calculation during the conversion process, followed by Section V on conclusions.

Methods

RF data to IQ data

IQ demodulation mainly consists of three steps: the down-mixing, low pass filtering and decimation (27–29). The general pipeline is shown in Fig. 1.

Figure 1.

Pipeline of converting RF data into IQ data

First, the real valued RF-signal is mixed with a complex sinusoid signal:

$$x_{IQ}\left(t\right)=x_{RF}\left(t\right)\mathrm{*}{e}^{-j2\pi t\mathrm{*}{f}_{\mathit{Demod}}}.$$ (1)

Second, a low-pass filter is applied to remove the negative frequency spectrum and noise outside the desired bandwidth of the complex signal, and it serves as the anti-aliasing filter for the following decimation process. Finally, the complex signal is decimated. Because IQ demodulation preserves the information content in the band-pass signal, there is no information loss during this process. However, some artifacts due to the imperfect design of filter can be introduced. In this study, the decimation factor for the calculation of BSC and ACS for the phantom case was 4, and the decimation factor for the calculation of ACS for the simulation case was 8. For the low-pass filtering, a simple butterworth filter with fifth order was used during the process of converting from RF into IQ.

IQ data to RF data

The reconstruction of RF data from IQ data is the reversal of the complex demodulation. The pipeline of this process is shown in Fig. 2. The decimation is replaced with interpolation, and the down-mixing is replaced with up-mixing.

Figure 2.

Pipeline of converting IQ data into RF data

The first step is the interpolation of IQ data. This involves two parts: zero-padding and low-pass filtering. Zero-padding is used to increase sampling rate. After inserting zeros, a low-pass filter is applied to remove components out of the base-band signal. In this paper, a cascade of three interpolation filters with a stopband attenuation of 60 dB and a passband ripple of 0.1 dB was used for reconverting from IQ into RF, the interpolation factor was the same as the decimation factor that was used during the RF2IQ process.

Next, the interpolated IQ signal is up mixed with the carrier frequency. This will shift the frequency spectrum from the base-band back to its original band. It is achieved by multiplying the interpolated IQ signal by the inverse of the complex exponential for down-mixing:

$$I{Q}_{up-mix}\left(r\right)=IQ\left(r\right)\mathrm{*}{e}^{j2\pi t\left(r\right)\mathrm{*}{f}_{\mathit{Demod}}}.$$ (2)

Finally, By taking the real part of the up-mixed IQ-signal, the reconstructed RF data is acquired.

Image quality metrics

To quantify the similarities and differences with different QUS images when processed using RF (original and reconvereted) and IQ data, two metrics were chosen. The first metric is structural similarity index measure (SSIM) (30), and is defined as:

$$\mathit{SSIM}(x,y)=\frac{\left(2{\mu }_x{\mu }_y+C_1\right)\left(2{\sigma }_{xy}+C_2\right)}{\left({\mu }_x^2+{\mu }_y^2+C_1\right)\left({\sigma }_x^2+{\sigma }_y^2+C_2\right)}.$$ (3)

where ${\mu }_x,{\mu }_y,{\sigma }_x,{\sigma }_y$ and ${\sigma }_{xy}$ are the local means, standard deviations, and cross-covariance for images x, y. $C_1$ and $C_2$ are two regularization constants. SSIM results in a value between 0 to 1. The closer to 1, the higher the similarity between two images, and the higher the image quality.

The second metric used to quantify performance is the root-mean-square error (RMSE). The RMSE is defined as:

$$E=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left|A_i-F_i\right|}^2}.$$ (4)

where F is the forecast array and A is the actual array made up of n observations. The lower the RMSE, the closer the forecast array is to the actual array.

Backscatter Coefficient Estimation

The BSC is a common spectral-based quantitative ultrasound parameter. For our experiments, we used the reference phantom method. The reference phantom was a custom built CIRS phantom (Sun Nuclear Corp, Norfolk, VA) with sound speed of 1537 m/s and attenuation of 0.67 dB/cm/MHz. We constructed a test phantom made with agar and glass beads randomly distributed spatially throughout to make a uniform phantom. We used the insertion loss method (31) to estimate the speed of sound and attenuation of the test phantom. The details of the phantom are listed in Table 1.

Table 1.

Details of the phantom

	Water[ml]	Agar[g]	Glass beads[g]
Phantom	50	1.5	6
T/R: 5MHz	SOS [m/s]	AC [dB/cm/MHz]	Freq range [MHz]
Phantom	1502	0.39	2.3-6.2

Because the system effects and diffraction effects could be compensated with the help of a reference phantom, the BSC from the sample was estimated according to:

$$\sigma \left(f\right)={\sigma }_{ref}\left(f\right)\frac{S(f,F)}{S_{ref}(f,F)}\frac{A_{ref}(f,F)}{A(f,F)}$$ (5)

where $S(f,F)$ and $S_{ref}(f,F)$ are the averaged power spectra from data blocks located at the same depth in the sample and the reference phantom, respectively. ${\sigma }_{\mathit{ref}}\left(f\right)$ is the known BSC of the reference phantom, and $A_{\mathit{ref}}(f,F)$ and $A(f,F)$ are the attenuation of the sample and reference phantom.

We used a Verasonics L9-4 probe to scan both the sample and reference phantom. The center frequency of L9-4 was 5 MHz. To calculate the BSC, we chose an analysis frequency range of 3 to 6 MHz and used phantom scan data from a depth of 3.5 cm with a window of 1.25 mm in length. The Verasonics provided raw RF signals. With demodulation and decimation, we obtained the IQ data from the raw RF data, i.e., RF2IQ. With modulation and interpolation of the IQ data, we could reacquire the RF data, i.e., RF2IQ2RF.

Attenuation Coefficient Slope Estimation

Attenuation imaging is another important parameter for quantitative ultrasound imaging. A common method for spectral-based estimation of ACS is to use the SLD method to reconstruct attenuation images, and it is based on the RF data spectrum. In Fig. 3, the schematic of the segmentation of the RF data with SLD method is shown.

Figure 3.

Schematic of the segmentation of the RF data and the composition of one data block. The data blocks have some overlap both in the axial and lateral direction.

We can model the spectrum of the proximal and distal window as follows:

$$S_s\left(f,z_p\right)=T\left(f,z_0\right)D_s\left(f,z_p\right)BS{C}_S\left(f,z_p\right)e^{\left(-4{\alpha }_s\left(f\right)\left(z_p-z_0\right)\right)}$$ (6)

$$S_s\left(f,z_d\right)=T\left(f,z_0\right)D_s\left(f,z_d\right)BS{C}_S\left(f,z_d\right)e^{\left(-4{\alpha }_s\left(f\right)\left(z_d-z_0\right)\right)}$$ (7)

where $T\left(f,z_0\right)=P\left(f\right)A_s\left(f,z_0\right),P\left(f\right)$ denotes the scanner transfer function, $A_s\left(f,z_0\right)$ is the total ultrasound attenuation from the transducer to the beginning of the data block. For the same imaging system, $T\left(f,z_0\right)$ is the same with two windows. Dividing (6)/(7), and taking the logarithm of both sides, we obtain:

$$\mathit{ln}\left(\frac{S_s\left(f,z_p\right)}{S_s\left(f,z_d\right)}\right)-\mathit{ln}\left(\frac{D_s\left(f,z_p\right)}{D_s\left(f,z_d\right)}\right)=4\left(z_d-z_p\right){\alpha }_s\left(f\right)+\mathit{ln}\left(\frac{BS{C}_S\left(f,z_p\right)}{BS{C}_S\left(f,z_d\right)}\right).$$ (8)

Because $\mathit{ln}\left(\frac{S_s\left(f,z_p\right)}{S_s\left(f,z_d\right)}\right)$ could be estimated from the backscattered RF data and $\mathit{ln}\left(\frac{D_s\left(f,z_p\right)}{D_s\left(f,z_d\right)}\right)$ could be estimated through the reference phantom method (see the Appendix), the left side of Eq. (8) is known. $z_d-z_p$ is the distance between the center of the two windows, and is a selected and known parameter. For soft tissues, the attenuation coefficient is approximated to have a linear dependence with frequency, i.e., ${\alpha }_s\left(f\right)=\beta f$. As a result, by choosing a finite frequency range for analysis, Eq. 8 is an inverse problem.

Because the SLD uses the RF data spectrum information to calculate the attenuation value, we could also use the IQ data spectrum to do the calculation. We tested two cases of attenuation imaging. The first case consisted of simulations of a cylindrical phantom with a concentric cylinder inclusion and the second case was from a physical, homogeneous phantom. The frequency range, the wavelength, and the block size used to estimate the attenuation values are listed in Table 2.

Table 2.

Frequency range, wavelength and blocksize of two datasets to estimate attenuation coefficient

Dataset	Freq. range (MHz)	Wavelength (mm)	Blocksize (mm)
Simulation	2.5-5.5	0.38	15.2
Phantom	4-7	0.3	9

Simulations

The simulations were constructed and run with the k-wave (32) toolbox in Matlab. For the construction of the simulation, a homogeneous phantom with two concentric circles was created. The background density of the phantom was 1007 kg/m³ and the speed of sound was a constant 1540 m/s. We created two attenuation values inside the phantom region. One is a circular region R1 with 0.4 dB/cm/MHz, and the other one is the background region R2 with 0.25 dB/cm/MHz. The center frequency of the simulated ultrasound array was set to 3.6 MHz, the pitch was 0.4 mm, and the grid size was 0.1 mm×0.1 mm×1 mm. We also generated a homogeneous phantom with the ACS of 0.2 dB/cm/MHz using the same imaging settings to acquire the diffraction effects of the transducer with the reference phantom method. In attenuation imaging with the SLD method, full angular spatial compounding is a technique that can reduce the variance of the resulting image by compounding over different angular views. In our simulation, we also used full angular spatial compounding with sixty angles of view to optimize the attenuation images.

With the k-wave simulations, we obtain the raw RF data. With demodulation, we then acquire the IQ data from the raw RF data, i.e., RF2IQ. Then with modulation, we obtain the RF data once again from the IQ data, i.e., RF2IQ2RF. As a result, we started from raw RF data, demodulated it into IQ data, and modulated it again into RF data. We calculated the mean and variance values of attenuation in two regions R1 and R2, estimated the time required to process QUS parameters from the different data formats (RF-based, RF2IQ, RF2IQ2RF) and calculated the SSIM. Also, in order to test whether the data were statistically different, a simple one way analysis of variance was done for three different cases.

Physical Phantom Experiments

We also used the Verasonics system to scan the physical phantom that was used in BSC experiments for estimating the ACS. We used a regularization technique that was described in the previous work (33) to provide maps of the ACS. Assuming the RF-based data to be the reference, we calculated structural similarity index measure (SSIM) of the reference ACS image with the RF2IQ image and the RF2IQ2RF image. The bias and variance of the ACS estimates from the phantoms were also tabulated when processed from each data format.

Results

Backscatter Coefficient

The power spectra estimated from data acquired from the physical phantom using the three data modes (raw RF, IQ (RF2IQ), RF reconverted from IQ (RF2IQ2RF)) are plotted in Fig. 4a. In addition, three BSC curves constructed with the original RF data, RF2IQ data and RF2IQ2RF data are also plotted in Fig. 4b. The RMSE values were calculated by comparing the BSC estimated from the original RF data and between the RF2IQ data and RF2IQ2RF data. These values are listed in Table 3.

Figure 4.

(a) The power spectrum of RF, RF2IQ and RF2IQ2RF; (b) The BSC result of different methods

Table 3.

RMSE of BSC

BSC	RF	RF2IQ	RF2IQ2RF
RMSE	Ref	0.043	0.047

From Fig. 4 and Table 3, the power spectra and BSC curves consructed using the three sets of data were visibly similar to each other and a low RMSE was obtained. The small RMSE between the RF and RF2IQ and RF2IQ2RF indicates that the BSC estimates did not depend on the type of data format. Therefore, the conversion between the RF to IQ and then the IQ back to RF, resulted in only negligible changes to the BSC estimate.

Attenuation Coefficient Slope Estimation

The results from the k-wave simulation are shown in Fig. 5 There are minor observable differences with the three cases, as demonstrated in Table 4. In general, the attenuation imaging with the three cases appears similar to each other with only small differences. From the quantitative result, both the average values and the variances of two regions were close to each other, i.e., all estimates were within 0.02 dB/MHz/cm of the ground truth. Because the number of samples making up the IQ data was much smaller than the RF data, the amount of time to process the IQ data was lower. Table 4 lists the estimated attenuation values for the attenuation maps estimated using the different RF versus RF2IQ versus reconverted RF2IQ2RF as well as the processing time and SSIM values. A plot of a lateral cross section of the attenuation map at a depth of 2.5 cm is shown in Fig. 5(e). The three profiles are similar to each other, with a RMSE of 0.026 between RF and RF2IQ, and a RMSE of 0.031 between RF and RF2IQ2RF, and the profile of the raw RF is the closest to the ground truth. The results of one way analysis of variance (ANOVA) is plotted in Fig. 5(h), and it shows that the distribution of values with three cases are similar to each other. The p-value of the F test was 0.5874, which suggests that differences between different cases were not statistically significant. On the other hand, the reduced value of SSIM from RF2IQ (0.92) to RF2IQRF (0.90) suggests that additional time-data conversions will lead to reduced image similarity.

Figure 5.

(a)-(f) The ACS result of different methods with the simulation case; (g) The attenuation lateral profile of different cases; (h) The box plot of the value of the three different cases

Table 4.

Quantitative result of simulation case

Simulation	R1	R2	Time[s]	SSIM
RF-based	0.26 +/− 0.02	0.40 +/− 0.03	236.47	Ref
RF2IQ	0.27 +/− 0.02	0.40 +/− 0.04	96.09	0.92
RF2IQ2RF	0.27 +/− 0.03	0.41 +/− 0.05	515.04	0.90
Ground-truth	0.25	0.40	-	-

As shown in the Fig. 6, the attenuation images constructed from the physical phantom using the different data formats were visually similar. Table 5 provides results of the attenuation estimates, SSIM values, and processing time for each method. The estimated attenuation values were close to the ground truth values using all data formats and the variance of the estimates were similar between all data formats. As quantified by the SSIM, the attenuation maps were similar to each other, i.e., the SSIM between RF2IQ image and RF-based was 0.98, and the SSIM between RF2IQ2RF image and RF-based was 0.96. These results indicate that the RF2IQ2RF resulted in a slightly worse image similarity relative to the reference image compared to the RF2IQ image. In addition, the processing time required for the different data formats were varied, with the IQ format resulting in the shortest processing time.

Figure 6.

The ACS result of different methods with the phantom case

Table 5.

Quantitative result of phantom case

Phantom case	Value	Time[s]	SSIM
RF-based	0.35 +/− 0.03	4.68	Ref
RF2IQ	0.36 +/− 0.04	2.90	0.98
RF2IQ2RF	0.36 +/− 0.03	5.26	0.96
Ground-truth	0.39	-	-

Discussion

Not all ultrasound scanner systems provide the raw RF data for conducting spectral analysis but instead provide the demodulated IQ data. The process of converting the RF data to IQ data involves demodulation to baseband, filtering, and decimation. Estimation of the BSC and ACS rely on calculating the power spectra from backscattered ultrasound. Calculation of the power spectrum from the raw RF backscattered ultrasound and the IQ converted data result in similar spectra but shifted in the frequency axis. Knowledge of the frequency, i.e., the carrier frequency, used to demodulate the RF data allows shifting the baseband IQ spectrum to match the RF spectrum. However, the conversion from raw RF to IQ can result in minor differences between spectra calculated from the RF and IQ.

A common practice is to take the IQ data and reconvert it back to RF data, Which we call RF2IQ2RF, in order to conduct spectral-based QUS analysis. In this process, interpolation and filtering along with a remodulation using the carrier frequency is required to reconstitute the RF data. In so doing, additional perturbations to the signal can occur. Estimation of the power spectrum from RF2IQ2RF data results in spectral shapes that are similar to spectra calculated from both the IQ and original RF data. However, additional perturbations to the signal occur during the conversion process, which can result in slight modifications to the calculated power spectra.

However, in comparing the estimation of the power spectrum from RF, RF2IQ, and RF2IQ2RF, only minor differences were observed. Therefore, when estimating the BSC, the RMSE values between the power spectra estimated from the RF, RF2IQ, and RF2IQ2RF were low. However, the RMSE did increase with increasing data conversion, i.e., when going from RF to RF2IQ to RF2IQ2RF. This is likely due to the nonlinear processes involved with converting the data from original RF to the IQ data format and back to RF again.

In a similar fashion, when creating maps of the ACS, similar images were observed when using the original RF data, IQ data and RF reconverted from the IQ data. Ths SSIM was used to compare the similarity of ACS images created using the different data formats. A high similarity was observed between the different created ACS maps with values close to unity for each case. However, the RF2IQ ACS images had a larger SSIM value (0.98) than the RF2IQ2RF ACS images (0.96) suggesting that every time the data is converted to another data format, perturbations to the data occur resulting in reduced similarity.

Ideally, access to the original RF data provides the best fidelity signal to use for conducting spectral-based QUS analysis. However, only small changes in spectral estimates occur when converting the raw RF to IQ and converting the IQ back to RF. Such data format conversions result in additional biases to spectral-based estimates, but these changes were not statistically significant. Therefore, spectral-based QUS can utilize any of these data formats (RF, RF2IQ, RF2IQ2RF) without concern.

In the process of converting from RF to IQ and from IQ to RF, it both contains low-pass filtering. It is worth studying and discussing the effect of these low-pass filters on the accuracy of QUS parameters. In this paper, a butterworth filter with fifth order was used during the process of converting from RF into IQ, and a cascade of three interpolation filters with a stopband attenuation of 60 dB and a passband ripple of 0.1 dB was used for reconverting from IQ into RF. In order to test the differences using different filters, we tried three different filters both with the process of converting from RF into IQ and reconverting from IQ into RF, and they were denoted as Filter1, Filter2 and Filter3, respectively. A butterworth filter with fifth order, with thirtieth order and a low-pass filter with a passband ripple of 1 dB and a stopband attenuation of 60 dB were tested for the process of converting from RF into IQ. A cascade of three interpolation filters with a stopband attenuation of 60 dB and a passband ripple of 0.1 dB, a stopband attenuation of 40 dB and a passband ripple of 1 dB, and a cascade of two interpolation filters with a fifth filter order were tested for the process of reconverting from IQ into RF. The spectra of both the sample and reference phantom and the RMSE of the BSC are shown in Fig. 7

Figure 7.

The Spectra and BSC comparison among different filters for both RF2IQ and IQ2RF. (a) Sample spectrum of RF2IQ; (b) Reference spectrum of RF2IQ; (c) Ratio of sample spectrum over reference spectrum of RF2IQ; (d) BSC of RF2IQ; (e) Sample spectrum of RF2IQ2RF; (f) Reference spectrum of RF2IQ2RF; (g) Ratio of sample spectrum over reference spectrum of RF2IQ2RF; (h) BSC of RF2IQ2RF; (i) RMSE of RF2IQ; (j) RMSE of RF2IQ2RF

In Fig. 7, different filter designs will lead to differences in the spectra, i.e., changing the ripples and the bandwidth with different filter order and stopband ripple settings. However, their BSC plot is similar to each other, and the RMSE of the BSC with different filter designs does not change appreciably. The reason is that when the QUS parameter is calculated, both sample and reference spectra are changed with the same filter. As a result, the effects of ripples or the change of the bandwidth on QUS calculation are somewhat cancelled. This shows that QUS calculation with IQ and RF is not much affected by the filter design performance as long as the filter satisfies the basic requirement such as anti-aliasing. Therefore, we demonstrated that the QUS calculation with IQ data is a stable method without a fine filter design.

All the data were processing on the PC with an Intel(R) Core(TM) i9-10900X CPU, and a NVIDIA Quadro P2000. Because IQ data are decimated compared to RF data, the processing time for IQ data is much reduced compared to RF data. The processing time could be found in Fig. 8. The processing time for RF2IQ was less than the RF-based processing even taking the conversion time into account. For the phantom case and the ACS maps, the processing time for IQ-based data was 38.06% less compared to the RF-based data. When doing the full angular compounding, the time differences become more evident because more processing times are used to create ACS maps from each view. The processing time for RF2IQ data was 59.36% less than from RF-based data formats. Therefore, the results suggests there are advantages to convert RF data into IQ data first, and do the QUS spectral calculations on the IQ data.

Figure 8.

The processing time comparison with both simulation and phantom case for ACS estimation

For future work, because the estimation from RF2IQ data has minor differences compared to estimates from the RF data, but saves much more processing time, real-time QUS estimation using IQ is more desirable. Because most imaging machines provide beamformed IQ data, with the reference phantom data precalculated and an accelerated QUS estimation version with the GPU code, a real-time QUS imaging map is possible. Compared to previous QUS work, there is no need to convert IQ back into RF if raw RF is not provided. As a result, this work shows the possibility of real-time QUS estimation in the future using the IQ data.

Conclusion

In this paper, estimation accuracy and precision of two QUS parameters using either RF data or IQ data were analyzed. The results from both BSC and ACS estimates indicate that there were only small differences when converting from RF data into IQ data, and vice versa. As a result, in situations where only IQ data is available from an ultrasound scanner, spectral-based analysis can still be accomplished using only the IQ data without converting the data back to RF. However, knowledge of the frequency used to demodulate the original RF data is still required.

Appendix

Reference phantom method

For a homogeneous reference phantom in the same imaging system, we assume that $BS{C}_r\left(f,z_p\right)=BS{C}_r\left(f,z_d\right)$, and $\frac{D_s\left(f,z_p\right)}{D_s\left(f,z_d\right)}=\frac{D_r\left(f,z_p\right)}{D_r\left(f,z_d\right)}$. We could model the spectrum of two windows for the reference phantom in the same way:

$$S_r\left(f,z_p\right)=T\left(f,z_0\right)D_r\left(f,z_p\right)BS{C}_r\left(f,z_p\right)e^{\left(-4{\alpha }_s\left(f\right)\left(z_p-z_0\right)\right)}$$ (9)

$$S_r\left(f,z_d\right)=T\left(f,z_0\right)D_r\left(f,z_d\right)BS{C}_r\left(f,z_d\right)e^{\left(-4{\alpha }_s\left(f\right)\left(z_d-z_0\right)\right)}$$ (10)

As a result, we can get the result:

$$\frac{D_s\left(f,z_p\right)}{D_s\left(f,z_d\right)}=\frac{S_r\left(f,z_p\right)}{S_r\left(f,z_d\right)}{e}^{\left(-4{\alpha }_r\left(f\right)\left(z_d-z_p\right)\right)}.$$ (11)

Because ${\alpha }_r\left(f\right),\frac{S_r\left(f,z_p\right)}{S_r\left(f,z_d\right)}$ are both known for the reference phantom, we could calculate the diffraction effect.