Fast algorithm for the determination of the optimum lter for bone SPECT image reconstruction

In SPECT, the reconstructed images are strongly affected by poisson noise, poor spatial resolution and bad contrast due to the radioactivity disintegration and procedures acquisition. In this paper, we propose an algorithm to improve the traditional FBP reconstruction and to choose the most suitable technique for bone SPECT image denoising. The proposed approach is composed of two steps. The rst one consists of denoising the acquired sinograms using successively eight currently used lters in nuclear medicine: Wiener, Metz, Hamming, Hann, Shepp-Logan, Parzen, Butterworth and Gaussian combined with Butterworth lters. The second step is a simultaneous reconstruction of the axial slices using a new 3D FBP algorithm for each lter. A comparative study of these lters is tested and evaluated on a dataset containing thirty one bone SPECT image. The results show that the difference between these lters is statistically signicantly different from each other (p<0.05) and the 3D FBP with the combination between Butterworth and Gaussian provide the best performance. The selected method is compared to three denoising methods. These methods are tested on a Shepp Logan phantom and bone SPECT images. Experimental results show that the 3D FBP reconstruction with the pre-processing combination (Gaussian (Std=0.3) + Butterworth (fc=0.47, ordre=3)) lter is more accurate and robust compared to other methods. It provides the highest performance in term of contrast, SNR, CNR ensuring a shorter processing time. It accelerates the reconstruction, reduces noise and artifacts while preserving detailed features. This approach could be considered as a valuable candidate to enhance the quality of the reconstructed bone SPECT image.


Introduction
Single photon emission computed tomography (SPECT) is a non invasive functional imaging modality which enables in vivo examination of organs' function. SPECT based on the administration to patients of a gamma emitter labeled radiopharmaceutical for diagnostic or therapeutic purpose. The head of detection of the gamma camera is mounted on a frame rotates around the patient to record multiple projections of the radioactive concentration under different angles of view. The projection images are stored on the computer where it will be recombined mathematically for reconstructing either sequences of tomographic slices in 3 directions. This technique allows the doctors to perform an accurate diagnostic of the radiopharmaceutical distribution in any slice of the body. Reconstructive methods are divided into two approaches: analytic and iterative methods. The analytic method, such as Filtered Back-Projection (FBP), is the standard reconstruction algorithm currently used in nuclear medicine tomography because of its facility and speed [1]. Versus the iterative method which requires a longer computational time. The analytic reconstruction method requires su cient projection data with low noise. However, in practical experiment in nuclear medicine the number of projection sets is limited provoking streak artifacts, inducing more noise, masking same organs, reducing lesion detection and making the obtained images unreadable. To overcome these problems, the data must be ltered prior the back-projection [2]. For de-noising the reconstructed SPECT image, several studies of ltering have been investigated [3] [4]. Many of them proved that the low-pass lters obscure the signi cance of small lesions, smoothen the details and reduce the sensitivity of the methods [5]. However, the restoration lters increase image contrast, improve lesion detection, amplify the artifacts at certain frequencies and reduce the speci city of the methods [6] [7]. In [8], a comparison made between the FBP reconstruction with Butterworth pre-processing lter and OSEM iterative reconstruction. The previous work demonstrated that the FBP method with a Butterworth lter provides the optimal SPECT image quality. Furthermore, this method is more e cient for standardizing the reconstruction parameter for the head and chest images, but these parameters were more operator-dependent for the abdomen. In [9], S. YU and al proposed a new approach for SPECT image denoising, called 'the patch con dence Gaussian lter (PCG)', and compared their performance to three methods: Pre and post denoising median lter and the pre-processing Gaussian lter followed by the Maximum Likelihood Expectation Maximization (MLEM) iterative reconstruction. they demonstrated that their method enhances e ciently the quality of SPECT image. In [10] M. T. Madsen and al show that the Gaussian lter enhance the contrast and suppress noise in the reconstructed bone SPECT slices.
On the other hand, there has been a signi cant con ict in the selection of the appropriate lter and adjustment of their parameters to individual cases [11] [12]. In the literature, several studies have been proposed to choose the appropriate lter with the best parameters for each region and for each organ. In [13] To summarize, much research demonstrates that the FBP reconstruction, particularly the FBP based on both Gaussian lter and Butterworth lter, provide the best SPECT image quality. Other studies show that the major drawback of this approach is the severity and the extend of the artifact, which makes the denoising process inaccurate and di cult near the hyper xation activity. In this paper, we continue the research in this area, we use the previous studies results as a starting point and we research on the performance of eight pre-processing widely used lters in nuclear medicine with various parameters, followed by a proposed 3D FBP for improving the reconstruction of a dataset composed of Tc99m-HMDP bone SPECT images, taken from the radiology department of National Oncology Institute"Salah AZAIZE" of TUNIS. First, we investigate the performance and the capability of the following lters to reduce the artifact: Wiener and Metz lters as restoration lters and Hamming, Hann, Shepp-Logan, Parzen, and Butterworth lter as smoothing lters [4]. Then we propose a combination between the contrast enhancement Gaussian lter with the noise reducing Butterworth lter. For each lter various parameters are tested. After that, the pre-processing technique which provides the highest performance is compared to three methods: 3D FBP based on Gaussian lter, 3D FBP based on Butterworth lter and 2D FBP based on Gaussian combined with Butterworth lter. Furthermore, the quantitative values of the proposed method are compared to those of some previous study methods. The rest of this paper is structured as follows: section 2 describes the used methods, section 3 presents the obtained results and compares the used reconstruction methods, section 4 presents the discussion and in section 5 the paper concludes this work.

Materials And Methods
The method proposed to accelerate the reconstruction as well as improve the quality of reconstructed images includes two steps: pre-processing step using different ltering conditions and a reconstruction step based on a ramp 3D Back Projection implementation. Fig 1. Shows the block diagram of the proposed algorithm.
In the following, we will present our approach in details by focusing on the following steps.

Sinogram images denoising:
The acquired tomosintigraphic projection images suffer from bad resolution and uctuations due to the Poisson distribution [15]. In order to choose the optimum lter for bone SPECT image that reduces e ciently the noise as much as possible preserving the image details, we applied eight widely used lters in nuclear medicine, in frequency domain, as shown in g2, which is used in [10] for one lter: FILTRATION:To cover the whole range of variables, a total of 137 ltering conditions were considered as shown in TABLE1. The 2D Back projection reconstruction using ramp lter assures the retro-projection of one image. So, the reconstruction of a 3D image requires a longer time. To accelerate the reconstruction step, we propose a 3D Back projection based on ramp lter, where we convert the input sequence of sinogram images to a 3D matrix, then we apply the 3D Back projection presented in g3. Therefore, a 3D axial slice image is reconstructed simultaneously and not successively in the interactive calculation, contrariwise to the 2D Back projection reconstruction (slice-by-slice).

2.3.Optimization of the proposed method for bone SPECT image reconstruction:
To select the optimum lter for bone SPECT image reconstruction, We analyzed eighty anonymous bone SPECT images taken from the radiology department of National Oncology Institute "Salah AZAIZE" of TUNIS, generated by a double-head gamma camera-CT model with a parallel collimator, equipped with a low dose CT scan characterized by a low energy and ultra-high-resolution characteristics. All patients are injected standard doses according to EANM guidelines. The bone scan tomographies are performed according to protocols (32 projections per head and twenty seconds per projection). The protocols are standardized for all patients. This dataset acquired during the period from the 6th July 2015 to the 29th June 2016 for diagnosis of metastasis in oncology patients. We chose thirty one (31) studies with a signi cant abnormal increased uptake on bone scan, 9 males and 21females aged between 45 and 75 years. Each DICOM image is a sequence of 128 projections (720°) as shown in g4 and a 128*128 matrix with a pixel spacing equal to 4.795 mm. After reconstruction, we calculated some criteria including mean contrast, mean signal to noise ratio (SNR) and mean contrast to noise ratio (CNR) of all the slices containing the lesion for each exam as follows: Two experts in nuclear medicine draw the ROIs through the hyperfuctionning bone locations from the normal bone to abnormal region and further in the transverse views of bone image, using MATLAB (R2013a) environment as shown in Fig. 5. These regions are the same for all the ltered slices that contain the lesion for each exam (in our case, the number of slice for each exam didn't exceed 13 slices).
For each patient and for each lter, the number of SPECT transverse slices containing bone lesions multiplied by the total number of combinations (305 combinations) was analysed. We measured the maximum count in normal bone, maximum count in hyperfuctionning bone and minimum count in the background for each slice.
Then, by using all of these measurements, we calculated the contrast, signal to noise ratio (SNR) and Contrastto-noise Ratio (CNR) as follows: Where Nmax(Normal) is the maximum count in normal bone, Nmax(abnormal) is the maximum count in hyperfuctionning bone, Nmin(background) is the minimum count in the background and σ is the standard deviation in the background.
Quantitatively, the optimum lter has the highest value of contrast, CNR and SNR. So, the rst purpose of this work is to select the best combination of parameters for each lter. The second purpose is to choose the best lter. We evaluate the performance of each combination of lter parameters. In fact, the combination of lter parameters that provides the highest CNR, SNR and contrast as the most suitable for bone SPECT image denoising. Numerical results on all the patients' data revealed that maximum contrast, CNR and SNR could be obtained using the Butterworth (cutoff 0.2-0.7, order 3-9), Hanning (cutoff 0.15 -0.5), Hamming (cutoff 0.15 -0.5), Shepp-Logan (cutoff 0.23-0.48),Parzen(cutoff 0.15-0.5), Metz (order=9.5,FWHM=7.8mm), Wiener (order=9.5,SNR=11) and Butterworth(cutoff=0.47,order=3) combined with Gaussian (Std=0.3), that's why we use the statistical Analysis. We performed Jarque-Bera test for testing whether the series were normally distributed, this test is based on the sample skewness and sample kurtosis.The asymmetry coe cient (coe cient of skewness) is near 0 for most values. As for the kurtosis (kurtosis coe cient), we noted that all distributions had a coe cient greater than 3, so they are leptokurtic (the presence of fat tails). From the point of view of statistics Jarque-Bera normality, assumption can accept some values during our study.
Performing One-Way ANOVA-test, signi cant difference (P<0.05) was observed between contrasts, SNR and CNR generated by Butterworth, Hamming, Hann, Shepp-Logan, Parzen, Metz, Wiener and Butterworth combined with Gaussian lters as shown in Table1 ,2 and 3.   The smoothing lters had a quite similar effect on image quality; these lters attenuate the details and the shape of the image. The streaking artifacts persisted in the ltered image.
Metz and Wiener lters have characteristics of both the smoothing and blurring compensation. The Wiener lter is a linear lter widely used to reduce the noise in scintigraphic images. The aim of this lter is to nd an image with a minimum mean squared error between the original image and the restored image. The smoothing power of Metz lter increases as the system spread function attens. In our study, these lters provides blurred image with streaking artifacts.
Butterworth lter combined with Gaussian provides the best quality of image; this combination reduces the streaking artifacts with the best degree of accuracy and minimal degradation of the boundaries of the regions and the small detail.
Clinical sensitivity and speci city evaluation: Two expert radiologists evaluated the ltered slices by the proposed method. The possible outcomes of this evaluation were calculated as follows: true positive=10, true negative=1, false positive=2 and false negative=17. From these values, the corresponding sensitivity= 90, 9 %, Speci city=89, 5 %, positive predictive value (PPV) =83,3%, negative predictive value (NPV) =94,4% and accuracy=90%. This results show that the proposed method was able to provide potentially useful information for the interpretation of bone SPECT images. Furthermore, the clinical sensitivity and speci city diagnosis in Bone SPECT images rise if SNR and Contrast increase.

Results
In this section, we present a description of the phantom and bone SPECT database obtained from radiology department of National Oncology Institute "Salah AZAIZE" of TUNIS. Then we present the different results and performance analysis of the proposed method.
1. database description: (a) Three-dimensional Shepp-Logan phantom To evaluate the methods in term of robustness of reconstruction and image quality, we tested the different algorithms on a 3D Shepp-Logan phantom. The distribution of projection data assumed to be generated by 128 angular views (distributed in the range of 180 degrees).
For simulation study of the different reconstruction methods, we added the Poisson noise to the projection data. Then, we tested various parameters to select the best one for each method.
The performance of the different method was evaluated from the following objective criteria: Patients studies For each method, we calculated the value of SNR de ned in equation (1), the contrast de ned in equation (2) and the time of execution for 31 bone SPECT exam.

Shepp-Logan phantom Result:
To illustrate the phases presented in Section 2, Fig. 11 shows the different results of the proposed method at gray level images. Column (A) depicts the original phantom image, column (B) presents the original projection, column(C) presents the noisy projection, column (D) presents the noisy sinogram, column (E) presents the ltered sinogram and column (F) shows the reconstructed phantom image.

data results:
In this part, we present the reconstructed slice images at three standard planes of the bone SPECT image presented in Fig.4. The sequence of transversal, coronal and sagittal slices of bone images ltered by the best Filter (Butterworth (cutoff=0.47, order=3)+Gaussian (Std=0.3)) are presente in Fig.11, Fig12 and Fig.13 2.4. Performance evaluation: To evaluate the performance of the proposed method, we compared qualitatively and quantitatively the capability of our proposed method to 3D FBP based on Butterworth lter, 3D FBP based on Gaussian lter and 2D FBP based on Gaussian lter combined with Butterworth. First, a comparison is made between different performances for different parameters for the same technique, then a comparison is performed between the four methods with best parameters.

B. The ltering methods:
To obtain the best parameters of each algorithm; we applied the different method with different combinations of parameters on the sequence of sinograms as listed in table4. In the case of 3d FBP, the sequence of ltered sinograms were converted to 3 dimensional matrix, and back projected simultaneously by the proposed 3D back-projection. Whereas, in the case of 2D FBP, the sequence of ltered sinograms were successively backprojected by a direct inversion of the radon transform. Then, we quanti ed the resulted transverse slices (we choose one slice contain the lesion for each exam).
3D FBP based on Gaussian lter: The sequence of sonograms multiplied successively by the Gaussian lter. Table5 lists the different standard deviations used. We tested and compared the performance of each one. The obtained results shows that the Gaussian lter with (std= 0.4) provide the highest performance.
3D FBP based on Butterworth lter: The sequence of sinograms multiplied successively by the Butterworth lter. We tested the different parameters and we compared the performance of the resulted slices. The obtained results show that the Butterworth lter with (fc= 0.57 and =9) provide the highest performance.
3D FBP based on Gaussian lter combined with Butterworth lter: We tested the different combinations as listed in Table 5 for 3D FBP based on Gaussian combined with Butterworth lter and compared the performance of the resulted slice, the obtained results show that the Butterworth lter (fc=0.47 and order=3) combined with Gaussian lter (STD=0.3)) provide the highest performance.
2D FBP based on Gaussian lter combined with Butterworth.
We tested the different combinations as listed in Table 5    We present the values of performance of each method applied on the Shepp-Logan phantom image in Table6. The tomo graphic bone SPECT slices reconstructed by the four methods with best parameters are present in  For each method we calculated the mean value of contrast, SNR and time of execution for 31 bone SPECT exam as described in equations 1 and 2. Table 8, 9 and 10 shows the highlight of our contribution in term of contrast, SNR and processing time for 31 exams.  approach on two myocardial axial slices using the signal to noise ratio de ned as follows: Where Y and X are respectively the standard deviation of the count value of the object of interest region (ROI) and the mean counts value inside the same region.We implemented the Patch Con dence Gaussian (PCG) algorithm and we applied this technique on our bone SPECT images. We noticed that the Gaussian with Butterworth pre-ltering combined with MLEM reconstruction provide the highest performance in term of SNR and time of execution. In fact, the back projection ltering (FBP) provide a high value of SNR in a shorter time of execution compared to the iterative technique MLEM. We can conclude that FBP using the preprocessing combination (Gaussian+Butterworth) is better than the other technique for bone SPECT denoising.
As shown in Figure 15 and Figure 16, we develop a user graphical interface to facilitate the manipulation and display the desired slices according to the choice of the user. In rst interface, the user can display the selected original projection and the ltered one ltered by a chosen lter. In second interface, the user can display, slice by slice or in montage, the slices according to the chosen lter and their parameters.

Discussion
In this paper, we proposed a novel 3D FBP reconstruction algorithm with eight currently used lters in nuclear medicine. This method presents a novel solution that allows the doctors to apply these lters successively on all the exams and reconstruct the slices in a shorter time than the conventional direct inversion of the radon transform. The main concern of this paper was to nd the best lter, based on FPB method of reconstruction, which improve the bone SPECT image quality and reduce e ciently the generated streaking artifacts. This study shows that the 3D FBP reconstruction based on the contrast enhancement Gaussian (Std=0.3) combined with the noise reducing Butterworth (cutoff=0.47, order=3) method outperformed the other methods in terms of SNR, resolution and contrast, gain in reconstruction time, best reduction of artifacts and improved lesion detection of bone SPECT images reconstruction. To validate qualitatively and quantitatively the e ciency of our proposed algorithm, we compared in rst step, the used pre-reconstruction lter with seven other lters. For a qualitative assessment, the ltered bone slices obtained from cited lters are illustrated in gure6. These results agree with I.Gunes and al [15] studies which showed that the Butterworth lter return the more e ciency anatomic details than other lters. In contrast to some reports in the literature, we found that Metz and Shepp-Logan lters provide the worst image quality in term of resolution and contrast. In addition, these lters return images tainted both by a pixelization effect and by a smoothing.
We observe that the combination between Gaussian lter and Butterworth lter provide the best image quality in terms of noise and streaking artifacts reduction and preservation of the small details and the limit of region. Unlike the hanning, Hamming, Parzen and wiener lters which degrade the image quality by smoothing transitions and attenuating details which making delicate the extraction and the location of the contours.
Indeed, the results of these lters contain a more artifacts in the form of oscillations which can be visually unpleasant. For quantitative assessment, the means SNRs, the means CNRs and the means contrasts are computed for each method. Table 1 shows that the means contrast of our proposed method is signi cantly superior to the other lter, this is explained by the e ciency of our proposed method to reduce the noisy artifact. Table 2 demonstrates that the proposed algorithm provides the highest means SNR values compared with the other lters which means that the coupling between Gaussian and Butterworth pre-reconstruction ltering succeeds to compromise between the poison noise reducing and the signal detail preservation.
Table3 shows that the proposed algorithm provides the highest means CNR values compared with the other lters which means that the combination between Gaussian and Butterworth pre-reconstruction ltering succeeds to reduce the noisy artifacts.
In second step, a comparison was made between the proposed technique and the 3D FBP based on Gaussian lter method and a 2D FBP based on Gaussian with Butterworth lter method both applied on a Shepp-Logan phantom image and a bone SPECT database.
For a qualitative assessment, gure12 represent the reconstructed Shepp-Logan images obtained from noisy projection using different method of reconstruction. This gure indicates that the proposed method allows the preservation of the original structure during the reconstruction by removing noise and conserving contrast. In fact, we can see that the reconstructed Shepp-Logan phantom image with the proposed method is the most similar to the original one. Figure 14 shows that the 3D FBP based on Gaussian combined with Butterworth lter provides an improvement in the spatial resolution of the bone SPECT image. In fact, unlike the conventional 2D FBP where the slices are reconstructed successively in the interactive computation, the 3D FBP uses the full information content of the reconstruction volume which provides an accurate reconstruction of the distribution of the activity on the slice. Compared with our proposed technique, the 3D FBP based on the Gaussian lter method appears much noisy, which attenuate the detail by giving a blur effect on the edges and making delicate the extraction and the location of the contours. However, our proposed technique ensures good poison noise suppression with an accuracy preservation of the limit of region.
Quantitatively, Table5 shows the CNR and the reconstruction time of the different reconstruction methods applied on a Shepp-Logan phantom image. The value of these metrics favored the proposed method which demonstrates the e ciency of our proposed algorithm in reduction of noisy artefacts. Furthermore, table 5 shows that the proposed approach requires a shorter time of execution compared to other methods. reconstruction methods. The result shows that the pro le resulting from the proposed method is closer to the original pro le than the other methods, which demonstrate the better preserves of the edges by removing noise, conserving contrast, while smoothing the region. Table 6 presents a comparison between the performances of the three denoising methods applied on the bone SPECT image presented in Fig.4. It is clear that the proposed method provides the highest performance.
Indeed, it is clear from Tables 7, 8, 9 and 10 that the SNR, the CNR and the contrast of our proposed method, tested on another 30 bone SPECT exam, is signi cantly higher than those in 2D FBP based on Gaussian with Butterworth lter, 3D FBP based on Gaussian and 3D FBP based on Butterworth for all the patient groups, which demonstrates the e ciency of our proposed algorithm in preservation of resolution and contrast, reduction of noisy artifacts and accuracy detection of lesion.
From Tables 11 and 12, we note that the processing time of our proposed approach is lower than the 2D FBP based on Gaussian combined with Butterworth lter due to the simultaneous reconstruction of slices. The 3D FBP based on Gaussian requires also a shorter time for processing, but still longer than our approach. To conclude, we can con rm that the proposed method achieve better result than the other methods in the enhancement of the quality of bone SPECT image reconstruction.

Conclusion
Filtered back projection reconstruction is the most currently used in nuclear medicine tomography and remains the standard for all the reconstruction algorithms. The aim of this paper was to choose the best de-noising lter for the tomography bone SPECT image reconstruction. Firstly, we applied a novel 3D FBP reconstruction algorithm with eight preprocessing lters on a dataset containing thirty one bone SPECT exams. Then, we evaluated their performance on the transverse slices. From the qualitative and quantitative comparative study that has been carried out, the 3D FBP based on Gaussian combined with Butterworth lter is the most e cient denoising method which can provide a notable gain in term of contrast, SNR, CNR and time of computation.
Moreover, it can remove the noise from images with the best degree of accuracy and reduce the artifact without degradation of the contours and the small detail. Finally, it is possible to conclude that this approach is applicable to improve the quality of bone SPECT images reconstruction. In our future research we intend to concentrate on the preprocessing step of the proposed technique, more tests will be needed to enhance the quality of the tomography bone SPECT image reconstruction and devoid completely of artifacts.

Key Points
QUESTION: Any lter in nuclear medicine is the optimal for image reconstruction for Bone SPECT imaging?
PERTINENT FINDINGS: In a cohort study comparing the quality of the reconstructed image, for bone SPECT imaging, ltered by eight currently used lters in nuclear medicine. Each lter combined with a proposed fast reconstruction algorithm is tested and evaluated on a dataset containing thirty one bone SPECT image. The results show that the difference between these lters is statistically signi cant different from each other (p<0.05) and the 3D FBP with the combination between Butterworth and Gaussian provide the best performance in term of noise and artifacts reduction, with detailed features preservation and gain of reconstruction time.
IMPLICATIONS FOR PATIENT CARE: The streaking artifacts generated with the FBP reconstruction is reduced using the proposed method, more tests will be needed to enhance the quality of the tomography reconstruction and devoid completely the artifacts in bone SPECT imaging.