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We investigate the effect of anatomical noise on the detectability of cone beam CT (CBCT) images with different slice directions, slice thicknesses, and volume glandular fractions (VGFs). Anatomical noise is generated using a power law spectrum of breast anatomy, and spherical objects with diameters from 1mm to 11mm are used as breast masses. CBCT projection images are simulated and reconstructed using the FDK algorithm. A channelized Hotelling observer (CHO) with Laguerre-Gauss (LG) channels is used to evaluate detectability for the signal-known-exactly (SKE) binary detection task. Detectability is calculated for various slice thicknesses in the transverse and longitudinal planes for 15%, 30% and 60% VGFs. The optimal slice thicknesses that maximize the detectability of the objects are determined. The results show that the β value increases as the slice thickness increases, but that thicker slices yield higher detectability in the transverse and longitudinal planes, except for the case of a 1mm diameter spherical object. It is also shown that the longitudinal plane with a 0.1mm slice thickness provides higher detectability than the transverse plane, despite its higher β value. With optimal slice thicknesses, the longitudinal plane exhibits better detectability for all VGFs and spherical objects.
© 2016 Optical Society of America
1. Introduction
In X-ray breast imaging, anatomical noise is the dominant factor that affects lesion detection performance [1–4]. Anatomical noise in the breast is structured, and arises owing to variations in the breast tissue (e.g., variations in adipose and glandular tissue textures). This noise can be characterized by a power law spectrum of the form α/fβ, where the exponent β typically falls in the range of 1.5 to 3.5 [2, 5–7]. Studies by Burgess et al. showed that a smaller β yields better detectability of breast masses in two-dimensional (2D) mammographic background images [5,6]. Since then, β has been measured in several studies for breast computed tomography (bCT) and digital breast tomosynthesis (DBT) systems, and its correlation with human-observer performance on lesion detection tasks has been studied [2,7–10]. These studies provide evidence that a cone beam CT (CBCT) imaging system is capable of effectively recovering the three-dimensional (3D) breast tissue structure, and that it is associated with smaller values of β and improved human performance on lesion detection, compared with planar mammography and DBT [2, 7–10].
While conducting a human-observer study is the most desirable way to evaluate the detection performance of an imaging system [9, 10], it is time consuming and expensive. Moreover, it would be infeasible to conduct a human-observer study to optimize a large space of many imaging parameters of the CBCT system. Thus, past studies have used mathematical observers to evaluate the imaging performance of the CBCT system with anatomical noise, and have investigated the effects of patient age and breast size, slice thicknesses, and X-ray photon energies on signal detection [1, 11, 12]. In our previous work [13], we used a channelized Hotelling observer (CHO) [14] to compare the detectability in the transverse and longitudinal planes of CBCT images with a uniform background. We found that the longitudinal plane exhibited higher detectability for small lesions since the FDK [15] reconstruction yielded different noise characteristics for the two different planes (i.e., a high-pass noise structure in the transverse plane and a low-pass noise structure in the longitudinal plane) [16].
The purpose of this work is to evaluate the detectability of CBCT images with anatomical noise. The impacts of slice thickness on β and the corresponding detectability are presented for various volume glandular fractions (VGFs) and signal sizes. For the evaluation, both the transverse and longitudinal planes were used to investigate the effect of different noise characteristics on the detectability. Anatomical noise was generated by a computer simulation with different VGFs of 15%, 30%, and 60%. Spherical signals with diameters of 1mm to 11mm were used to model breast masses. The detectability of lesions in the transverse and longitudinal planes of CBCT images was measured for various slice thicknesses. We focus on the signal-known-exactly (SKE) binary detection task, and compute lesion detectability using a CHO with Laguerre-Gauss (LG) channels [14, 17–20]. Detectability computed using a CHO with difference-of-Gaussian (DOG) channels [21] is also presented.
2. Methods
2.1. Image generation
2.1.1. Anatomical background
The anatomical noise owing to the breast anatomy can be characterized by the following power law spectrum [1, 5]:
where f is the radial frequency, α is a constant, and β is the power law exponent. For mammograms, the value of β is ~3 [5]. According to the central slice theorem [22, 23], the power spectrum of a 2D projection at a specific angle is equivalent to a sampled 2D plane of the 3D power spectrum of the object at the same angle [9]. Thus, 3D anatomical noise can be generated by extending the power law spectrum in Eq. (1) to 3D, although this approach does not account for morphological features in the breast.We filtered 512×512×512 voxels of 3D white noise using a power law kernel (i.e., 1/f3/2) [9,24]. The infinite kernel value at the origin was prevented by setting it to be twice that of the first nonzero radial frequency [6]. Then, we extracted the central spherical volume with a diameter of 128 voxels to avoid the wrap-around effect owing to the discrete Fourier transform (DFT). The image voxel size was 0.2×0.2×0.2mm3 and the full volume size was 25.6 × 25.6 ×25.6mm3. Breast anatomy comprises two dominant tissues, glandular and adipose [2]. Therefore, we classified each voxel of the filtered noise into either glandular tissue or adipose tissue, based on the voxel value. We sorted voxel values of the filtered noise in descending order, and assigned the attenuation coefficient of the glandular tissue to the top z % of voxel values; the attenuation coefficient of the adipose tissue was assigned to the lower (100 − z) % of voxel values [3, 24, 25]. In this context, the parameter z is the VGF, which represents the breast density. We used z = 15, 30, and 60 in modeling different breast densities. The attenuation coefficient was 0.80cm−1 for the glandular tissue and 0.46cm−1 for the adipose tissue at 20keV monochromatic energy, which is the mean energy of the nominal 28kVp incident spectrum [24]. After the tissue classification, β was changed to 3.15, 3.29, and 3.34 for 15%, 30%, and 60% VGF images, respectively. To compare the results in the present study with those in our previous work [13], we also generated images with a uniform background. The attenuation coefficient of this uniform background was set at 0.80cm−1 to maintain signal detectability in order to enable a proper comparison with the image containing anatomical noise; that is because the average attenuation coefficients comparable to those of anatomical noise yield higher detectability in the case of a uniform background. Figure 1 shows the central planes of the generated 3D anatomical noise volumes for different VGFs.
Fig. 1 Central planes of generated 3D anatomical noise volumes for (a) 15% VGF, (b) 30% VGF, and (c) 60% VGF. The white region indicates glandular tissue, whereas the gray region indicates adipose tissue. The display window is [0 0.8]cm−1.
2.1.2. Signal
We used spherical objects with diameters of 1mm, 2mm, 3mm, 5mm, 8mm and 11mm to model breast masses. Each object was inserted at the center of the 3D anatomical noise volumes by replacing the values of anatomical noise in the region of the signal with 0.84cm−1, which is equivalent to the attenuation coefficient of a breast mass at 20keV monochromatic energy [26].
2.1.3. Data acquisition and reconstruction
Projections of the generated 3D anatomical noise volumes were acquired by calculating the radiological path along the ray that connected the X-ray source and each of the detector pixels [27]. The source to iso-center distance was 460mm, the source to detector distance was 880mm, and the detector pixel size was 0.388×0.388mm2 [12]. The detector array size was 150×150 pixels (i.e., 58.2×58.2mm2).
In discrete-to-discrete projection, using a voxel size greater than the detector pixel size can introduce discretization artifact [3]. In our simulation, the detector pixel size magnified at the iso-center was 0.2028 × 0.2028mm2, and thus a 0.2×0.2×0.2mm3 voxel size of the anatomical noise volume was small enough to avoid discretization artifact. Figure 2 shows the background power spectra of the projected anatomical noise volume with four different voxel sizes (i.e., 0.8×0.8×0.8mm3, 0.4×0.4×0.4mm3, 0.2×0.2×0.2mm3, and 0.16×0.16×0.16mm3). The discretization artifact was clearly seen in the power spectra when the voxel size was larger than 0.4×0.4×0.4mm3. In contrast, the discretization artifact was negligible when the voxel size was less than 0.2×0.2×0.2mm3.
Fig. 2 Background power spectra of projected 30% VGF anatomical noise volume for (a) 0.8×0.8×0.8mm3, (b) 0.4×0.4×0.4mm3, (c) 0.2×0.2×0.2mm3, and (d) 0.16×0.16×0.16mm3 voxel sizes.
Two hundred projection data over 360° were acquired with a detector quarter offset to avoid aliasing. For quantum noise generation, we used uniform Poisson noise with 200 photons per detector pixel which corresponds to the dose level of 1.5mGy when a ray passes through an 8.3cm diameter breast with 15% VGF [24]. Note that the typical dose level in breast imaging ranges from 1.5mGy (one-view mammographic exam [24]) to 4mGy (two-view mammographic exam [9]). Log normalization was applied to the generated Poisson noise and added to the noiseless projection data. The noisy projection data were reconstructed using the FDK algorithm [15]. We used a Hanning weighted ramp filter with a cutoff frequency of 2.4655mm−1 as a reconstruction filter and voxel-driven back-projection with linear interpolation. The reconstructed voxel size was selected as half of the detector pixel size at the iso-center (i.e., 0.1014×0.1014×0.1014mm3) to avoid noise aliasing, and the reconstructed volume size was 25.9×25.9×25.9mm3 (256×256×256 voxels).
2.1.4. Image preparation for evaluating signal detectability
To evaluate detectability, we used central 13×13×13mm3 volumes (128×128×128 voxels) from the reconstructed volumes. The transverse and longitudinal planes of reconstructed CBCT images were used for evaluating signal detectability for different slice thicknesses. By averaging image slices along the transverse and longitudinal directions [12], we generated eight different slice thicknesses: 0.1mm, 1.9mm, 3.8mm, 5.6mm, 7.5mm, 9.3mm, 11.1mm, and 13mm. Figures 3 and 4 show examples of transverse and longitudinal plane images with 30% VGF for 0.1mm and 13mm slice thicknesses, respectively. In the thinner slice images, anatomy superposition was resolved but higher quantum noise was presented, as shown in Fig. 3. Thicker slice images contained reduced quantum noise owing to the averaging procedure, but anatomical superposition obscured the signals, as shown in Fig. 4 [12]. Note that the 13mm slice thickness is equivalent to the projection of the entire central volume onto one plane.
Fig. 3 0.1mm slice thickness image of 30% VGF along the (a) transverse and (b) longitudinal directions. Signal diameter increases from 1mm (left) to 11mm (right). The display window is [0.2 1]cm−1.
Fig. 4 13mm slice thickness image of 30% VGF along the (a) transverse and (b) longitudinal directions. Signal diameter increases from 1mm (left) to 11mm (right). The display window is [0.4 0.85]cm−1.
2.2. Binary detection task
We considered an SKE binary detection task in order to evaluate signal detectability. The two hypotheses (i.e., H0 for the absence of signal and H1 for presence of signal) are given by:
where g is the observed image, fb is the background, fs is the background containing a signal, and fn is the noise. In the present study, fb was an anatomical background, fs was an anatomical background containing spherical signals, fn was a quantum noise, and g was a 2D transverse or longitudinal plane with varying slice thickness.2.3. CHO
2.3.1. LG channels
A CHO with LG channels can approximate the performance of a Hotelling observer when the background statistics are isotropic and the signals are rotationally symmetric at a known location [14, 17–20]. LG channels are defined as the product of Laguerre polynomials and a Gaussian function:
where r represents a 2D spatial coordinate and au is the width of the Gaussian function. The Laguerre polynomials, Lp(x), can be defined as follows: where p is the order of the polynomial.For each spherical object diameter, image plane, and slice thickness, the value of au that maximizes the corresponding signal detectability was chosen by a brute-force search throughout the range of 3 to 50 pixels. The optimal value of au was proportional to the diameter of the spherical object. We used 20 LG channels because detectability saturated when more than 20 channels were used. Figure 5 shows example images of 20 LG channels with au=10.
2.3.2. Dense-DOG (D-DOG) channels
DOG channels are designed to mimic the human visual system by employing multiple bandpass filters and suppressing the DC component [14, 21]. DOG channels are defined as
where ρ is the radial frequency, Q is the multiplicative factor, and σj is the standard deviation of the j-th channel, defined as σj = σ0αj. We used D-DOG channels with the following parameters: σ0 = 0.005, α = 1.4, Q = 1.67 and j=1~10, as given in [21]. Figure 6 shows example images of 10 D-DOG channels.2.3.3. Figures of merit
A channelized image v is given as follows:
where T is the channel matrix and ϵ is the internal noise. For LG channels, T is composed of discrete sampled values of Eq. (4). For DOG channels, T is composed of discrete sampled values of the inverse Fourier transform of Eq. (6).ϵ is set to zero in this study.A CHO template is computed by:
where Kv is the average of the covariance matrices of the channelized signal-present and signal-absent images, and Δv is the vector of the sample channelized mean difference between the signal-present and signal-absent images.The decision variable for each channelized test image vj is calculated as:
A total of 800 image pairs were used for the training observer, and two different independent sets of 400 image pairs were used, respectively, for estimating the vector Δv and the matrix Kv. To analyze the observer variability, we generated five different observers by estimating Δv and Kv with five independent image data sets. For observer testing, another 400 image pairs independent of the training sets were used to compute the decision variables.
At this stage, the task signal-to-noise ratio (SNR) can be computed as follows [28]:
where E[·] is the expectation operator, t0 and t1 are decision variables of signal-present images and signal-absent images, respectively, and σ0 and σ1 are the standard deviations of t0 and t1, respectively. We estimated the variance of the task SNR by bootstrapping the decision variables 1000 times in order to analyze case variability [29]. We denoted the task SNR for the LG CHO and D-DOG CHO as SNRLG and SNRD−DOG, respectively.2.4. Estimation of β
To estimate the power law exponent, β, we computed a 2D noise power spectrum (NPS) using 500 signal-absent images in the transverse and longitudinal planes. To avoid spectral leakage caused by the finite length of DFT, we multiplied a spatial window W to the mean subtracted images [2, 30].
where r is the pixel distance from the center, and D is half of the image width.The NPS was computed by averaging the square of the absolute value of the FT of the windowed images. Radial averaging of the 2D NPS within 20° was performed along transverse, longitudinal-fx, and longitudinal-fz planes, and the natural logarithm was applied to the radially averaged NPS.
We computed β using linear regression by changing the fitting frequency ranges, and chose the values of β that maximized the correspondence between the given data (i.e., logarithm-applied radial NPS) and the predicted data (i.e., linear regression). The goodness of fit was parameterized by calculating the coefficient of determination (i.e., R2) [1, 2].
3. Results
Figures 7 and 8 show SNRLG and SNRD−DOG for the transverse and longitudinal planes as a function of the slice thickness, for the cases of uniform background and anatomical backgrounds with VGFs of 15%, 30% and 60%. The images with anatomical noise yield much lower SNRLG and SNRD−DOG values compared with the images with uniform background. Both SNRLG and SNRD−DOG decrease as VGF increases because the attenuation coefficient of the signal is similar to that of the glandular tissue. SNRD−DOG is lower than SNRLG, especially for the large signals; this is because the energy of the large signals is concentrated more in the low-frequency region, which is suppressed by the D-DOG channels. The optimal slice thicknesses that maximize SNRLG and SNRD−DOG correlate with signal diameters. A larger signal diameter has its maximum task SNR with a thicker slice. In this study, the optimal slice thicknesses of images with anatomical noise fall in the range of 0.1mm to 5.6mm for all signal diameters.
Fig. 7 SNRLG as a function of the slice thickness with 95% confidence interval for (a) 15% VGF, (b) 30% VGF, (c) 60% VGF, and (d) uniform background.
Fig. 8 SNRD−DOG as a function of the slice thickness with 95% confidence interval for (a) 15% VGF, (b) 30% VGF, (c) 60% VGF, and (d) uniform background.
In Fig. 9, the SNRLG ratios of longitudinal over transverse planes are plotted for 0.1mm, 1.9mm, 3.8mm, and 5.6mm slice thicknesses. For the 0.1mm slice thickness, the ratio is above 1 for all signal sizes and VGFs, indicating that the longitudinal plane yields better detectability than the transverse plane in the case of anatomical noise. The ratio decreases with increasing slice thickness, but remains above 1 in most cases, except for the case of an 11mm diameter signal with 60% VGF. Task SNR trends for images with anatomical noise are different from those for images with uniform background, where the transverse plane yields better detectability for signals with diameters larger than 3mm.
Fig. 9 SNRLG ratio of longitudinal over transverse planes with 95% confidence interval for (a) 0.1mm, (b) 1.9mm, (c) 3.8mm and (d) 5.6mm slice thicknesses.
In Fig. 10, the SNRD−DOG ratios of longitudinal over transverse planes are plotted for 0.1mm, 1.9mm, 3.8mm, and 5.6mm slice thicknesses. Overall, the SNRD−DOG difference between transverse and longitudinal planes is lower than that of SNRLG, but significant loss is observed for signals with diameters larger than 5mm. Note that using a different signal intensity can change the task SNR. However, the task SNR ratios of the longitudinal over transverse plane remain the same since the task SNR is linearly proportional to the signal intensity.
Fig. 10 SNRD−DOG ratio of longitudinal over transverse planes with 95% confidence interval for (a) 0.1mm, (b) 1.9mm, (c) 3.8mm and (d) 5.6mm slice thicknesses.
Table 1 summarizes the efficiency of D-DOG CHO relative to the LG CHO. For images with anatomical noise, the efficiency decreases with increasing signal size, and is lower in the longitudinal plane than in the transverse plane, indicating that low-frequency information suppressed by D-DOG channels more significantly affects signal detection performance for large signals and images in the longitudinal plane. By contrast, the observer efficiency for images with uniform background is lower in the transverse plane.
Table 1. Efficiency of D-DOG CHO relative to the LG CHO (0.1mm slice thickness).
Figure 11 shows β values of transverse and longitudinal planes as a function of the slice thickness for different VGFs. The fitting frequencies range from 0.22 cyc/mm to 0.61 cyc/mm, and R2 is higher than 0.9 for all estimated β values. The higher VGF yields a higher β value, resulting in the reduced task SNR, as shown in Figs. 7 and 8. The β value increases as the slice thickness increases, and saturates when the slice thickness is greater than 5.6mm, showing a similar trend with the value of β in [8]. While the maximum task SNR of a 1mm diameter spherical object appears at a 0.1mm slice thickness with the smallest β value, all other signals achieve the maximum task SNR for thicker slices. The results indicate that, depending on the signal size, a higher task SNR can be achieved with a thicker slice, despite its higher β value. It is also shown that for the case of the 0.1mm slice thickness, the longitudinal plane has a higher β value but a better task SNR compared with the transverse plane.
The difference between the task SNRs and β values for the transverse and longitudinal planes is due to the difference in the noise structure for each plane, as shown in Fig. 12. We show the NPS images for 0.1mm and 5.6mm slice thicknesses, because the task SNR ratios for the 1.9mm and 3.8mm slice thicknesses are similar to those for the 5.6mm slice thickness, as shown in Figs. 9 and 10. Although the simulated anatomical noise is isotropic, the FDK algorithm [15] applies the reconstruction filter only along the transverse direction; thus, the 3D NPS of the reconstructed volume contains anisotropic statistical features (i.e., symmetric in the transverse plane and asymmetric in the longitudinal plane). Figure 12 shows the logarithm-applied NPS images for which display window levels are adjusted to accentuate the different noise structures in the transverse and longitudinal planes.
Figure 13 shows the radially averaged NPS along the transverse, longitudinal-fx, and longitudinal-fz directions. The radial NPS is shown up to 1cyc/mm, because the anatomical noise power is concentrated at frequencies below 0.5cyc/mm. For the 0.1mm slice thickness, the noise power in the transverse plane is higher than that in the longitudinal plane, resulting in the higher SNRLG in the longitudinal plane, despite the higher β value. For the 5.6mm slice thickness, the noise power in the transverse and longitudinal-fx become similar; thus, the difference between the SNRLG in the transverse and longitudinal planes is reduced. Since D-DOG CHO suppresses the low-frequency information, the difference between the task SNRs in the transverse and longitudinal planes is significantly reduced for large signals as compared with LG CHO.
Figure 14 shows the sampled transverse and longitudinal images for different slice thicknesses. Smaller (larger) signals show better detectability for thinner (thicker) slices, as predicted in Fig. 8. In particular, the longitudinal plane shows better detectability of small signals for the 0.1mm slice thickness, as predicted in Fig. 10.
Fig. 14 (a) 0.1mm, (b) 1.9mm, (c) 3.8mm, and (d) 5.6mm slice thicknesses images of 30% VGF along the transverse and longitudinal directions. Signal diameter increases from 1mm (left) to 11mm (right).
4. Discussion and conclusion
We investigated the effect of anatomical noise on the detectability of CBCT images for different slice directions, slice thicknesses, and VGF values. With the presence of anatomical noise, the longitudinal plane provided better detectability for various signal sizes, VGFs, and slice thicknesses. While the β value increased as the slice thickness increased, thicker slices yielded higher task SNRs for all signals, except for the case of a 1mm diameter spherical object. In addition, the longitudinal plane with a 0.1mm slice thickness provided a higher task SNR than the transverse plane, despite its higher β value.
The simulated anatomical noise was isotropic, but the transverse and longitudinal plane images differed in their noise structure after image reconstruction using the FDK algorithm. For the 0.1mm slice thickness, the longitudinal plane had a higher SNRLG than the transverse plane, and the SNRLG ratio of the longitudinal over transverse planes approached 1 as the slice thickness increased (i.e., 1.9mm, 3.8mm, and 5.6mm). We reported task SNR ratios for slice thicknesses of up to 5.6mm, because the optimal slice thicknesses were less than 5.6mm in this study. For images with slice thicknesses larger than 5.6mm, the task SNR ratios and the estimated β values were similar to those for images with a 5.6mm slice thickness. Compared with SNRLG, the difference between the SNRD−DOG of the transverse and longitudinal planes was reduced, especially for large signals, owing to the suppression of the low-frequency information by D-DOG channels.
In this study, we used a CHO with LG channels because it has been shown to approximate the Hotelling observer [17]. Although we presented the logarithm-applied NPS images to highlight the asymmetry of the longitudinal NPS, this effect was not significant in the original NPS images since the anatomical noise power was highly concentrated in the low-frequency region. We used a CHO with D-DOG channels because it has been shown to fit human observer data in previous studies [21, 31]. To predict human-observer performance, more appropriate channel parameters and internal noise levels should be determined in human-observer studies. This will be the subject of our future research. The application of this study can be extended to 3D tasks using a 3D mathematical observer (e.g., multi-slice CHO [32]). For each slice direction, the task SNR will increase, but similar results are expected.
While the previous study showed similar β values for different slice directions [8], our results produced higher β values in the transverse and longitudinal-fx direction, as shown in Fig. 11. This difference results from using different reconstruction filters during the backprojection. Compared to the Shepp-Logan filter used in [8], the Hanning filter produces more blurring on the projection data. Since the Hanning filter reduces the high-frequency components more, the β values in the transverse and longitudinal-fx direction increased. Using an unweighted ramp filter produces similar β values in both planes, as presented in [8]. We used the Hanning-weighted ramp filter with linear interpolation since it produced the highest task SNR in the transverse and longitudinal planes. Note that the β values for a 13mm slice thickness in the longitudinal-fz direction (i.e., 3.10, 3.31, and 3.38 for 15%, 30%, and 60% VGFs, respectively) are similar to the β values of the anatomical background after the binary process (i.e., 3.15, 3.29, and 3.34 for 15%, 30%, and 60% VGFs, respectively) as the NPS of a 13mm slice thickness image is equivalent to the central plane of a full 3D NPS.
We generated anatomical noise with glandular and adipose tissue types, which are predominant over other tissue types (e.g., Cooper’s ligaments [33]); however, breast tissue orientation [34] was not considered in the current work. The detection performance was evaluated at the iso-center of the CBCT system. However, the CBCT system yields different noise structures in different local regions [16], which will vary significantly along the longitudinal direction owing to the large cone angle. It is expected that the tissue orientation and the non-stationary noise structure of the CBCT system affect signal detectability. This is another interesting question that merits further investigation.
In this study, we focused on detecting spherical lesions in the presence of anatomical noise. We chose spherical lesions because LG channels are efficient for rotationally symmetric signals. In addition, spherical lesions are appropriate for examining the effect of reconstructed anatomical noise in transverse and longitudinal planes on the same task object. Detectability trends for other lesion shapes would not be much different from our results if the lesions have no preferred orientation. We considered low-frequency characteristics of breast images in which anatomical noise was dominant over quantum noise [2]. In a low-dose regime, quantum noise increases, but anatomical noise is still expected to be a dominant factor that determines the lesion detection performance, owing to the high-frequency nature of CT noise. The effect of quantum noise becomes more significant for detecting micro-calcifications. In our simulation, 20 keV was used as the X-ray energy for achieving high contrasts of soft tissues. In breast imaging, much higher X-ray energies (e.g., 80 kVp) can be used to deliver sufficient fluence to the detector [2,35]. With increased X-ray energy, the image contrast will be reduced; thus, task SNRs in the transverse and longitudinal planes will be reduced. However, it is expected that the SNR ratios of the longitudinal over transverse planes will remain the same because the human breast anatomy is independent of the X-ray energy values [35].
With a uniform background, the longitudinal (transverse) plane yielded higher detectability for small (large) lesions, as shown in our previous work [13]. While the presence of anatomical noise significantly reduces signal detectability, it is shown that the longitudinal plane provides better detectability for all VGFs and spherical objects with optimal slice thicknesses.
Funding
Institute for Information & Communications Technology Promotion (IITP) (2015-R0346-15-1008); National Research Foundation of Korea (NRF) (2015R1C1A1A01052268, 2015K2A1A2067635).
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