Different reconstruction algorithms and filters can be used in CZT SPECT imaging to achieve different purposes, such as reducing star artifacts, suppressing noise, and restoring or enhancing signals. FBP is the most widely used reconstruction method in clinical SPECT. It has the advantages of simplicity, rapidity, and high computational efficiency. It included two steps: filtering of data and back-projection of the filtered data . Chang AC has been the most commonly used AC in FBP reconstruction. The iterative method is a step-by-step mathematical calculation method, which first sets all the pixel values in the image to be reconstructed to the same value, and then compares the projection values of the image in all directions with the actual collected projection values. All pixel values of the image are recalculated, and the image is updated according to their differences. Then, the projection value of each point is calculated for the updated image. The above steps are repeated, and when the difference between the projection value obtained from the image and the actual projection value are small to a certain extent, the iterative process ends and the image reconstruction is completed . Among them, OSEM was the most commonly used iterative reconstruction method, which greatly reduced the number of iterations required. The OSEM-used RR method has been shown to improve the spatial resolution, contrast, and quantitative accuracy of cerebral perfusion SPECT [14, 15]. CTAC has been considered to be the most accurate AC method for measuring radioactivity in real areas .
The filter was used to reduce the noise of the image and also compensate for the loss of details in the image. The Butterworth filter was a low-pass filter that allowed low frequencies to remain unchanged and prevented high frequencies from passing through. It had two parameters: the “cutoff frequency(fc)” and the “order(n)”. The fc defined the frequency above which the noise was eliminated. n controls the slope of the filter function and characterises the steepness of the roll-off. Because the Butterworth filter could not only change the cut-off frequency, but also change the steepness of the roll, it could not only smooth the noise, but also maintain the image resolution. Among them, the selection of fc was of great significance in reducing noise and retaining image details . A higher fc value would improve the spatial resolution and retain more details, while a lower fc value could enhance the smoothing effect of the images but reduced the contrast of images. A Gauss filter is a kind of linear smoothing filter, which is very effective in eliminating Gaussian noise with normal distribution, that is suitable for image smoothing denoising of uniform tissue imaging, such as brain tissue. The width of the Gaussian filter was represented by FWHM in the image processing software, and FWHM determined the smoothness of the image. The larger the FWHM, the wider the frequency band of the Gauss filter and the better the smoothness . By adjusting the FWHM parameter, we could make a compromise between the excessive blur (over-smoothing) of image features and the existence of too much noise and unnecessary details (under-smoothing) in the images. For a given image reconstruction task, the choice of filter was usually a balance between noise reduction and contrast enhancement .
Clinically, different reconstruction algorithms and filters are often selected for different diseases in order to achieve the best quality of tomographic images. The SPECT images of patients with brain defects such as cerebral infarction and epilepsy  usually used the reconstruction methods of FBP + Bw and OSEM + Bw, while for the SPECT images of patients with Parkinson's disease, the reconstruction method of OSEM + Gs was often used [20, 21]. Similarly, different processing parameters could also meet the needs of image reconstruction in different situations. Winz et al.  reported that the relatively low filter cut-off frequency in OSEM reconstruction reduced the image quality to some extent, but the resulting low-noise image was beneficial to the definition of the reference area in dopamine transporter imaging and avoided uptake asymmetry in the posterior putamen, which could avoid misdiagnosis as neurodegeneration. In this study, using the reconstruction method of OSEM + Bw and choosing a slightly higher fc value could improve the contrast of small lesions in patients with brain defects and avoid missed diagnosis.
In this study, phantom analysis and clinical verification were performed for cerebral blood flow perfusion tomography imaging. First, in the phantom tomographic images, the integral uniformity, RMS noise, and contrast of FBP + Bw increased with increasing fc value, but CNR decreased with an increase in fc value. This difference was caused by the enhancement of the high-frequency noise. The higher the fc value was, the more high-frequency components were enhanced, which increased the detection of the image and focus edge and also increased the high-frequency noise. Therefore, the smaller the size of the focus to be resolved, the higher the fc value in order to meet the diagnostic requirements of the image, but not an excessively high fc value because it would lead to excessive amplification of noise and increase of artifacts, affecting image quality. At the same time, the integral uniformity, RMS noise, and CNR of the image increased with an increase in order, but when the n value was greater than 10, the integral uniformity and RMS noise converged uniformly. Therefore, we determined that the best reconstruction parameter of conventional brain imaging was ‘fc = 0.40 ~ 0.45, n = 10 ~ 30’. Khorshidi et al.  reported that in conventional NaI SPECT studies, the ideal image quality of brain defects could be obtained when the order of Bw was 7 ~ 10 and the cut-off frequency was 0.45 ~ 0.50. This conclusion was similar to the results of this study.
Second, the integral uniformity, RMS noise, and contrast in OSEM + Bw increased with the increase in EM, but CNR decreased with the increase in EM. It might be that with the increase in EM, the effect on image noise exceeded the influence of contrast, but when EM ≥ 60, the contrast and CNR converged uniformly. Compared with FBP + Bw, the best reconstruction parameter of OSEM + Bw was that ‘EM = 60, fc = 0.45, and n = 10’ was more accurate in the diagnosis of small lesions. Van Laere et al.  reported that in traditional NaI SPECT studies, the best processing parameter for normal brain imaging was OSEM (4 iterations, 6 subsets) + Butterworth (fc = 0.40, n = 8).
The integral uniformity and RMS noise in OSEM + Gs decreased with the increase in FWHM, while the contrast increased with the increase in FWHM, and the overall quality of the image was not as good as that of the combination of the other two processes. Lingfeng et al.  showed that the pure noise reduction of 3D Gaussian filters in post-filtering would lead to a decrease in image contrast with the reduction of noise. However, in a study by Matsutomo et al.  of conventional NaI SPECT, the reconstruction method of OSEM + Gs could improve the performance and image quality of 123I-Nomega-fluoropropyl-2beta-carbomethoxy-3beta-(4-iodophenyl)nortropane (123I-FP-CIT) SPECT dopamine transporter imaging during the ‘EM = 90, FWHM = 6.6mm’. Therefore, it was speculated that the reconstruction method of OSEM + Gs in CZT SPECT imaging might be more suitable for 123I-FP-CIT SPECT imaging. This imaging method has been widely used in the diagnosis of Parkinson's disease and Lewy body dementia .
In the semi-quantitative analysis of the cold sphere diameter ≥ 2 cm group, the contrast and CNR of FBP + Bw were significantly higher than those of OSEM + Bw and OSEM + Gs (p > 0.05). It was suggested that FBP + Bw had higher identifiability of large lesions, so more attention should be paid to the quality of image uniformity and noise in image reconstruction. For the semi-quantitative analysis of cold sphere diameter < 2 cm, the recognisability of FBP + Bw was lower than that of OSEM + Bw; therefore, in the case of small ischemic lesions, the OSEM reconstruction algorithm could increase the contrast between lesions and normal tissue and improve the recognisability of lesions, so as to avoid a missed diagnosis. These results were preliminarily verified in clinical cases of cerebral ischemia in this study.
In the acquisition process of phantom imaging, a narrower energy window (140 KVp ± 7.5%) was used compared with the traditional SPECT (140 KVp ± 10%) because the digital SPECT improved the energy resolution. In the phantom image, the size of these cold spheres was smaller than the actual size of these cold spheres, especially in the smaller structure (i.e. the solid balls of 19.1 mm, 15.9 mm, 12.7 mm), which was partly due to the influence of partial volume effect (partial-volume effects, PVE). Matsuda et al.  reported that SPECT images could reflect not only the loss of brain volume, but also the changes in brain function, and the regional cerebral blood flow (rCBF) could be measured more accurately by using PVE correction in cerebral perfusion SPECT. In addition, in OSEM reconstruction, the visual distortion of circular cold spheres might be caused by the use of the RR algorithm .
The limitations of this study are as follows. First, the unexplained radioactive sparse area in the phantom image might be caused by the examination table. Due to the large size of the phantom, it was impossible to use a clinical dedicated headrest. Second, in order to simulate the current clinical acquisition methods, the matrix size was 128×128. If a matrix size of 256×256 was used, a better image spatial resolution could be obtained, which may improve the image quality. Finally, we did not evaluate the impact on image quality and quantisation by the number of subsets, although image quality was generally not affected by the number of subsets . Further research is underway, and we will increase clinical studies to prove the feasibility of different reconstruction methods for different lesion sizes. This result may be helpful in improving the accuracy of clinical diagnosis, especially for some small lesions that are easily missed.