In Single-Photon Emission Computed Tomography (SPECT), the reconstructed image has insufficient contrast, poor resolution and inaccurate volume of the tumor size due to physical degradation factors. Generally, nonstationary filtering of the projection or the slice is one of the strategies for correcting the resolution and therefore improving the quality of the reconstructed SPECT images. This paper presents a new 3D algorithm that enhances the quality of reconstructed thoracic SPECT images and reduces the noise level with the best degree of accuracy. The suggested algorithm is composed of three steps. The first one consists of denoising the acquired projections using the benefits of the complementary properties of both the Curvelet transform and the Wavelet transforms to provide the best noise reduction. The second step is a simultaneous reconstruction of the axial slices using the 3D Ordered Subset Expectation Maximization (OSEM) algorithm. The last step is post-processing of the reconstructed axial slices using one of the newest anisotropic diffusion models named Partial Differential Equation (PDE). The method is tested on two digital phantoms and clinical bone SPECT images. A comparative study with four algorithms reviewed on state of the art proves the significance of the proposed method. In simulated data, experimental results show that the plot profile of the proposed model keeps close to the original one compared to the other algorithms. Furthermore, it presents a notable gain in terms of contrast to noise ratio (CNR) and execution time. The proposed model shows better results in the computation of contrast metric with a value of 0.68 ± 7.2 and the highest signal to noise ratio (SNR) with a value of 78.56 ± 6.4 in real data. The experimental results prove that the proposed algorithm is more accurate and robust in reconstructing SPECT images than the other algorithms. It could be considered a valuable candidate to correct the resolution of bone in the SPECT images.

Single-Photon Emission Computed Tomography (SPECT) is an emission imaging modality based on the administration of radiopharmaceuticals to patients. A gamma photon detector rotates around the patient to register multiple projections of the radioactive concentration at different angles. A computer must reconstruct these projections to obtain a 3D volume of the object. Tomographic reconstruction aims to extract axial, coronal and sagittal slices of the object from its finite number of projections. This reconstruction reflects the functional information about metabolic activity and lets the doctors effectively diagnose the radiopharmaceutical distribution in anybody slice [

On another side, the cascaded hybrid framework has been proposed for improving the quality of SPECT image reconstruction. In their work, Tiwari et al. [

This paper is organized as follows:

Tomographic reconstruction aims to estimate an explored region from a finite number of acquired projections. The reconstruction algorithms present the region to be explored in multidirectional slice images. This reconstruction reflects functional information of metabolic activity in any slice of this region. There are two types of reconstruction, analytic and iterative.

Two classes of the analytic algorithm are developed, simple back-projection (SBP) and filtered back-projection (FBP) [

The iterative algorithm consists of linking numerous forwarding projections and back-projection operations since initial data. The initial image is an estimated image created arbitrarily. The successive estimate stopped when the projection of the reconstructed image similar to the measured projections. These methods reduce the significant artifacts and enhance the reconstructed image quality.

The (ML-EM) algorithm is the standard iterative reconstruction method which consists of two alternating steps: an E-step creates a function for computing the expectation of the log-likelihood which evaluates the similarity between simulated and measured sinograms, and an M-step which finds the next estimate image by maximizing the expected log-likelihood found on E-step while taking into account the fact that the first estimate image is positive and that a noisy Poisson attains the measured sinograms. The MLEM algorithm is presented in

The OSEM algorithm [

The iterative reconstruction algorithms improve the reconstructed image quality and reduce the generated streaking artifacts [

In this section, we present the proposed algorithm to improve the quality of reconstructed bone SPECT images. We start with a global introduction of the proposed model. Then, we detail each step.

In the following, we will introduce our methodology in subtleties by concentrating on the next steps.

To reduce the noise efficiently in the projection image as much as possible with preserving the image details, we explore the benefits from the complementary properties of both the Wavelet transform and Curvelet transform. During the first step, we exploited the ability of Wavelet transform to detect the edges. Indeed, we applied the Curvelet transform on the residual image. The later image is the result of subtracting the original image from the filtered image. The filtered image is composed of fine details, structure and noise.

The DWT is a powerful multi-scale transform for denoising because of its ability to separate noise from signal [

To analyze the anisotropic features of projections, we used the second generation of Curvelet transform (Candes, 2006) [

where

At scale 2^{–j}, the Curvelet’s family

where

The refraction coefficient of each unknown function f is expanded in term of curvelet

where j is the scale parameter, l is the location parameter and k is the location parameter that corresponds to directional features of f.

As explained previously, WT and CT present complementary behaviors; the number of directional elements in the wavelets is fixed independently from the scale. Therefore, the WT does not perfectly restore the anisotropic element like the outlines and the edges. While the CT presents high directional anisotropy elements, this transform does not handle small isotropic elements properly. So, we exploited both transforms in the same model to improve the denoising methodology of acquired projections.

The combined denoising scheme is illustrated in

To reduce the image reconstruction time, we used the 3D-OSEM reconstruction algorithm which allows a simultaneous reconstruction of all axial slices. In the first step, the sequence of projection data is converted into a 3D matrix. Therefore, a 3D-sinogram is assembled simultaneously from the projection image matrix. Then and in the second step, a 3D image of axial slices is reconstructed simultaneously from the 3D matrix of sinograms and not successively which is the case of 2D OSEM reconstruction (slice-by-slice) [

where:

Slices reconstructed with the 3D-OSEM technique are still noisy with attenuated details which agree with the researchers’ results [

where

The PDE is an anisotropic diffusion model [

In this model, a median filter is applied to the gradient of the image. The PDE algorithm is given as follows:

Compute the gradient and the diffusion function.

Compute the sharpening diffusion coefficient.

Then a refining function is added to the edge-stopping rule. The proposed formula is given by

where

where K is the thresholding and α is the weight of the sharpening coefficient function.

We extracted a sequence of coronal slices and a sequence of sagittal slices from enhanced axial slices. Each slice has a thickness equal to 1 pixel, displayed respectively from posterior to anterior and right to left, allowing the doctors to perform a diagnostic in any slice of the object.

To choose the best combination of parameters for the proposed algorithm, we applied our algorithm on 31 abnormal bone SPECT images, and each image contains hyperfixation in the bone. Then, we calculatedthe means contrast, the means contrast to noise ratio (CNR) and the means signal to noise ratio (SNR) of the resulted slices as described in the following equations:

where

We performed the Jarque-Bera test to test whether the series were usually distributed. From the statistics, Jarque-Bera normality, the assumption can accept some values during our study. Performing the One-Way ANOVA-test, the optimum combination of parameters for the proposed method has the highest value of contrast, CNR and SNR. Numerical results of all patient data revealed that maximum contrast, CNR and SNR could be obtained using the Curvelet transform with a threshold value equal to 0.01, the Wavelet transform with an order equal to 4, a PDE model with K = 0.2 and α = 0.01, combined with an OSEM3D algorithm with 4 subsets and 8 iterations.

This section presents a description of phantoms and bone SPECT database obtained from the nuclear medicine department of the National Oncology Institute “Salah AZAIZE” of TUNIS. Then, we present the different results and performance analyses of the proposed method.

The proposed method was tested on two different SPECT phantoms: Shepp-Logan phantom and Jaszczak phantom, and our bone SPECT database.

To evaluate the robustness of our reconstruction algorithm, we used a tomographic digital Shepp–Logan phantom. The distribution of projection data is assumed to be generated by 128 angular views (distributed in the range of 180 degrees).

Four objective criteria were used to evaluate the performance of the reconstructed axial slices. They are the Mean Square Error (MSE) [

To evaluate the accuracy of our reconstruction algorithm, we used a Data Spectrum Corporation Jaszczak phantom composed of bars and six cold spheres of diameter: 31.8, 25.4, 19.1, 15.9, 12.7, 9.5 mm. The Jaszczak phantom was filled with a radioactive solution containing 2 mCi of a uniform ^{99m}Tc solution. The acquisition of the Jaszczak phantom image was affected using 180° non-circular orbit for each detector, with 96 projection angles, a 128 * 128 matrix size, and an electronic zoom of 1/1 provided a pixel size of 4.795 mm.

The tomographic Jaszczak phantom image reconstruction using the proposed method was performed using 8 iterations and 4 subsets, combined with a Curvelet denoising wavelet with a threshold value equal to 0.01 and an EDP thresholding value

To evaluate the reconstructed image quality, we draw a circular region of interest (ROI)s of 20 cm diameter for each of the 5 jaszczak spheres in the uniform section of the phantom. A background ROI was also created using five (ROI)s on five central slices.

Contrast is calculated using

where

A bone SPECT dataset is taken from the nuclear medicine department of the National Oncology Institute “Salah AZAIZE” of TUNIS, which contains 31 bone SPECT exams, 10 males and 21 females aged between 45 and 75. The acquisitions were made using a Symbia gamma camera equipped with a parallel collimatorusing 180° non-circular orbit for each detector with 128 projection angles, a 128 * 128 matrix size, a pixel size of 4.795 mm. For each methodand for 31 bone SPECT exams, we calculated the values of contrast defined in

The sequence of Shepp-Logan projections was additionally randomized with a Medium Poisson noise level. The Poisson noise level was used by scaling the sinogram value to 50%. Then, we applied the reconstruction methods to the noisy sequence. To present the phases introduced in

To present the phases presented in

To evaluate the performance of the proposed method of reconstruction, we conducted a qualitative and quantitative comparison with four other reconstruction approaches available in the literature which are: MLEM [

Reconstruction method | MSE | MAE | SSIM | PCC | Time (sec) |
---|---|---|---|---|---|

Proposed method | 0,0012 | 0,013 | 0,987 | 0,975 | 68.57 |

CNNR | 0,0041 | 0,029 | 0,811 | 0,922 | 101.53 |

2D-OSEM + Metz | 0,0057 | 0,037 | 0,720 | 0,883 | 107.23 |

MLEM | 0,0062 | 0,040 | 0,719 | 0,836 | 278.36 |

2D-OSEM | 0,0085 | 0,044 | 0,674 | 0,801 | 68,96 |

Axial slices reconstructed from a SPECT image of a Jaszczak by various reconstruction methods are shown in

From

From

These curves illustrate that the proposed algorithm gives a better result for each metric than the other algorithms. This result shows the efficiency of our proposed algorithm in noisy artifacts reduction with conservation of contrast, improvement of SNR and image resolution.

The reconstructed bone SPECT image with: MLEM (120 iterations) (A), 2D-OSEM (8 iterations and 4 subsets) (B), 2D-OSEM (8 iterations and 4 subsets) with a 3D-post-filtering with a Metz filter (order = 9.5, FWHM = 7.8 mm) (C), CNNR (D) and the proposed method (E) are shown in

We can note from

For each method and each exam, we calculated the mean values of contrast, SNR and execution time for 31 bone SPECT exams described in

The qualitative assessment of the various directional feature regions of the bone SPECT image, illustrated in

For all the 31 thoracic SPECT exams, we can note from

Using multi-scale denoising on the acquired bone SPECT projection images allows more considerable noise reduction with accurate radioactivity concentration and quantitative information measures. This technique is based on localized fine-scale functions, which allow better reconstruction of various details at multiple scales. Using the novel 3D-OSEM based on parallelization computation brings the convergence much faster than the traditional 2D-OSEM with robust and accurate reconstruction. The anisotropic diffusion is based on a nonlinear sigmoidal function, which generates various degrees of edge sharpening, accentuates and sharpens different details of the reconstructed thoracic SPECT image without affecting the neighboring regions’ background. In conclusion, this model allows a fast, robust and accurate reconstruction of thoracic SPECT exams.

As shown in

In this paper, we presented a novel 3D algorithm to enhance bone SPECT image reconstruction. In fact, after applying a new type of filter exploring the possibility of combining two different multi-scale techniques, Wavelet transform and discrete Curvelet transforms, on 128 projections. One hundred twenty-eight axial slices are reconstructed by the 3D-OSEM algorithm and enhanced by one of the newest anisotropic diffusion models. The proposed method was tested on two different SPECT phantoms: Shepp-Logan phantom and Jaszczak phantom, and our bone SPECT database to demonstrate its accuracy and robustness in reconstruction. Summing up the results, it can be concluded that the proposed algorithm can improve the quality of thoracic SPECT images in terms of noise reduction, accuracy and reconstruction robustness. This novel method provides a notable gain, in contrast, SNR, CNR, MSE, MAE, SSIM, PCC and computation time compared to other algorithms. In this work, we proposed a user interface graphic for SPECT image reconstruction that allows the practitioner to correct the spatial resolution of the bone in SPECT image. A limitation of this study is that the parameters of this algorithm are chosen according to the statistic study carried out and the database used. Based on the promising results presented in this article, we propose a combination of this algorithm with a deep learning method as a possible direction of research in the future to obtain an optimal and innovative method of bone SPECT image reconstruction.