Computed tomography (CT) is one of the most common and beneficial medical imaging schemes, but the associated high radiation dose injurious to the patient is always a concern. Therefore, postprocessing-based enhancement of a CT reconstructed image acquired using a reduced dose is an active research area. Amoeba- (or spatially variant kernel-) based filtering is a strong candidate scheme for postprocessing of the CT image, which adapts its shape according to the image contents. In the reported research work, the amoeba filtering is customized for postprocessing of CT images acquired at a reduced X-ray dose. The proposed scheme modifies both the pilot image formation and amoeba shaping mechanism of the conventional amoeba implementation. The proposed scheme uses a Wiener filter-based pilot image, while region-based segmentation is used for amoeba shaping instead of the conventional amoeba distance-based approach. The merits of the proposed scheme include being more suitable for CT images because of the similar region-based and symmetric nature of the human body anatomy, image smoothing without compromising on the edge details, and being adaptive in nature and more robust to noise. The performance of the proposed amoeba scheme is compared to the traditional amoeba kernel in the image denoising application for CT images using filtered back projection (FBP) on sparse-view projections. The scheme is supported by computer simulations using fan-beam projections of clinically reconstructed and simulated head CT phantoms. The scheme is tested using multiple image quality matrices, in the presence of additive projection noise. The scheme implementation significantly improves the image quality visually and statistically, providing better contrast and image smoothing without compromising on edge details. Promising results indicate the efficacy of the proposed scheme.
Computed tomography (CT) has served as a fundamental tool for human internal anatomy visualization since its development and subsequent commercialization; with considerable benefits for mankind [
Sparse-view CT is a particular type of CT scans where the number of data acquisition views is reduced, while keeping the X-ray tube current at the standard level. The sparse-view CT benefits in reducing radiation dose and scan time in cardiac CT [
Amoeba-based filtering [
In this reported work, the amoeba-based image filtering is customized for CT images acquired through filtered back projection (FBP) using sparse projection data. The proposed and customized amoeba scheme enhances the quality of the degraded sparse-view FBP reconstructed image. The amoeba kernel is derived from a pilot image based on the Wiener filter. The Wiener filter is much superior in image denoising and restoration than many other techniques, such as simple inverse filtering, Gaussian filtering, and mean filtering [
The detail of the proposed research methodology and case study is given in the next section, followed by Results and Discussion, and then by Conclusion.
Many modern reconstruction techniques, including advanced reconstruction techniques, use sophisticated postprocessing/image processing techniques for better representation of the reconstructed image. The dynamic and adaptive nature of Amoeba filtering makes it a strong candidate for CT application. Amoeba filtering (Lerallut et al. 2007) [
It is noteworthy that the amoeba kernel is derived from a pilot image. Classical amoeba filters [
As the shape of the amoeba is dependent upon the center pixel of the sliding window, it is essential that the amoeba is not wrapped around a noisy pixel. As a remedy, the amoeba shape is calculated from a pilot image instead of the degraded reconstructed image. Wiener filter is very efficient in image denoising and restoration applications as it uses image degradation function and noise statistics [
The Wiener filtered image (
where each pixel index
where
The proposed amoeba adapts its shape with respect to the internal image contours and edges. The amoeba filter uses the classical sliding window model for image filtering, where the window is centered at each pixel of the image. The shape of the amoeba kernel is initialized as the entire sliding window (square), which then adopts the shape based on window contents. The amoeba shaping algorithm is inspired by automated segmentation applications and techniques, such as active contours models and its variants [
In the proposed amoeba shaping mechanism, a “region” is referred to a cluster of contagious pixels, of uniform/near-uniform image intensities, inside the sliding window. The surrounding contour is automatically detected by the proposed algorithm. The amoeba shape remains square on sliding windows with little/no image intensity variation. However, with multiple variations in intensities, amoeba takes the shape of the region containing the window-center pixel. The amoeba shaping process is illustrated on a test image in Figure
Self-shaping amoeba based on the location of sliding window. (a) Sample image. (b) Initially, square shape kernel is modified at different spatial locations within the image.
The sliding window,
where region
where
The final amoeba kernel shape,
The effectiveness of the proposed self-shaping amoeba filter kernel in computed tomography applications is showcased in Figures
Adopted amoeba kernel shape at various spatial location of sliding window. Each row (a–d) contains a sample of sliding window at a spatial location, along with an enlarged view of the window content and the adopted amoeba shape.
The most basic and common head CT phantom, Shepp-Logan, was used in this implementation as the subject to acquire the projection data. It is a standard test image and synthetic phantom. The size of the head phantom was kept as
Sparse-view FBP reconstruction of simulated phantom (a) Shepp-Logan phantom. (b) 2-degree angularly sampled FBP reconstruction of (a).
The acquired projection data contains noise from numerous factors including photons, quantization, and electronics. In the literature, various medical imaging techniques use different types of noise models in which the Gaussian model is commonly used for CT [
The smoothness of the reconstructed image was lost due to undersampled FBP reconstruction. The amoeba filtering was used for smoothening without compromising on edge details. The size of the sliding window was kept as
The proposed amoeba denoising scheme was also implemented to clinically reconstructed CT head image from Phillips CT healthcare case study, available at [
Clinically reconstructed head CT phantom acquired from Phillips CT healthcare case study, available at [
The quality of the scheme was evaluated using multiple full-reference objective image quality metrics [
RMSE is computed by taking the square root of the average of squares of the differences of the corresponding pixels in the test and reference images and is given as
where
The PSNR is expressed in terms of decibels (dB), calculated as
where
PSNR and RMSE use pixel intensity differences to evaluate the image quality, which although have clear mathematical and physical significance but offer very less in terms of human visual perception of image quality [
where
where
The edge preservation index (EPI) indicates the amount of edges that are preserved in the test image [
where
Sharpness index (SI) is a no-reference image quality metric based on the image Fourier phase spectrum, which contains important information such as image geometry and contour details [
where
Structural content (SC) is a full-reference image quality metric based on image structural similarity and spatial arrangement of pixels in an image [
Normalized absolute error (NAE) is a full-reference image quality metric measuring the statistical difference between the reference and test images [
To investigate the efficacy of the proposed RBS amoeba shaping mechanism, the proposed scheme is compared with the existing classical amoeba distance-based shaping. The two schemes are compared using Shepp-Logan-based sparse projections and a pilot image obtained from the Gaussian filtering. Mean filtering is then applied to the acquired amoeba shapes/kernels and evaluated based on the abovementioned image quality metrics, as shown in Figure
Comparison of sparse-view FBP reconstructed image with proposed RBS amoeba and classical amoeba schemes, using Gaussian filtering-based pilot image. (a) 2-degree angular sampling-based sparse-view FBP reconstruction. (b) Classical amoeba distance-based image denoising of sparse-view FBP. (c) Proposed RBS amoeba-based denoising using Gaussian-filtered pilot image.
The comparison of sparse-view FBP image with classical amoeba and proposed RBS amoeba schemes are shown in Figure
The proposed RBS amoeba shaping is visually better as compared to the classical amoeba scheme, with better SSIM, EPI, SI, SC, and NAE values, while presenting very similar quality in terms of PSNR and RMSE, as seen in Table
Image quality comparison of proposed and classical shaping mechanisms.
Scheme name | RMSE | PSNR (dB) | SSIM | EPI | SI | SC | NAE |
---|---|---|---|---|---|---|---|
Sparse-view FBP | 0.074 | 22.61 | 0.24 | 0.211 | 121 | 0.988 | 0.428 |
Amoeba distance (with Gaussian pilot) | 0.059 | 24.56 | 0.42 | 0.253 | 332.8 | 0.990 | 0.286 |
RBS amoeba shaping (with Gaussian pilot) | 0.059 | 24.51 | 0.52 | 0.261 | 1683.9 | 1.008 | 0.235 |
The proposed scheme, RBS amoeba with Wiener pilot, is compared with the classical amoeba scheme (Gaussian pilot), as shown in Figure
Comparison of sparse-view FBP reconstructed image with classical and proposed amoeba schemes. (a) 2-degree angular sampling-based sparse-view FBP reconstruction. (b) Classical amoeba filtering-based image denoising of (a). (c) Proposed scheme with RBS amoeba denoising of (a) using Wiener pilot image.
Image quality comparison of the proposed Wiener filtering-based RBS amoeba scheme with the classical amoeba filtering scheme.
Scheme name | RMSE | PSNR | SSIM | EPI | SI | SC | NAE |
---|---|---|---|---|---|---|---|
Sparse-view FBP | 0.074 | 22.61 | 0.24 | 0.211 | 121 | 0.988 | 0.428 |
Classical amoeba | 0.059 | 24.56 | 0.42 | 0.253 | 332.8 | 0.990 | 0.286 |
Proposed RBS amoeba | 0.052 | 25.56 | 0.58 | 0.376 | 1739.8 | 1.002 | 0.233 |
For better visualization and focused analysis of this comparison, Figure
Comparison of enlarged ROI in sparse-view FBP reconstruction image with proposed amoeba and classical amoeba schemes. (a) 2-degree angular sampling-based sparse-view FBP reconstruction. (b) Classical amoeba distance-based image denoising of (a). (c) Proposed RBS amoeba denoising of (a) using Wiener pilot.
Image quality comparison of schemes using enlarged ROI images.
Scheme name | RMSE | PSNR | SSIM | EPI | SI | SC | NAE |
---|---|---|---|---|---|---|---|
Sparse-view FBP | 0.048 | 26.28 | 0.32 | 0.266 | 0.48 | 0.936 | 0.300 |
Classical amoeba | 0.030 | 30.23 | 0.54 | 0.410 | 1.50 | 0.987 | 0.185 |
Proposed RBS amoeba | 0.024 | 32.23 | 0.68 | 0.423 | 32.70 | 1.000 | 0.131 |
The comparison of sparse-view FBP reconstruction of clinically reconstructed CT image, available at [
Comparison of sparse-view FBP reconstructed image with classical and proposed amoeba schemes, applied on clinically reconstructed CT image. (a) 2-degree angular sampling-based sparse-view FBP reconstruction. (b) Classical amoeba filtering-based image denoising of (a). (c) Proposed scheme with RBS amoeba denoising of (a) using Wiener pilot image.
The proposed RBS amoeba shaping outperforms the classical amoeba scheme in terms of various image quality metrics, as shown in Table
Image quality comparison of the proposed and classical schemes in real clinical head CT-based implementation.
Scheme name | RMSE | PSNR | SSIM | EPI | SI | SC | NAE |
---|---|---|---|---|---|---|---|
Sparse-view FBP | 0.085 | 21.32 | 0.22 | 0.211 | 5.75 | 0.959 | 0.290 |
Classical amoeba | 0.053 | 25.46 | 0.37 | 0.210 | 40.17 | 0.993 | 0.179 |
Proposed RBS amoeba | 0.047 | 26.52 | 0.44 | 0.289 | 350.3 | 1.002 | 0.142 |
The robustness of the scheme was also tested by analyzing the image quality at various projection noise levels. Shepp-Logan phantom of size
Robustness comparison of sparse-view FBP reconstruction with classical and proposed amoeba schemes, SSIM performance of the schemes at various noise levels in projection data.
Robustness comparison of sparse-view FBP reconstruction with classical and proposed amoeba schemes, on the basis of RMSE performance of the schemes at various noise levels in projection data.
The effectiveness of the scheme was also evaluated by analyzing the image quality at various projection view sampling. Shepp-Logan phantom of size
Comparison of sparse-view FBP reconstruction with classical and proposed amoeba schemes, SSIM performance of the schemes using FBP reconstructions at various projection view sampling.
The results demonstrate that the proposed RBS amoeba scheme has improved results as compared to the classical amoeba scheme. The sparseness in projections results in missing data; however, the human anatomy with symmetric and naturally contagious pixels serves as prior knowledge and enables the proposed scheme to perform better in this scenario. Therefore, the proposed scheme is a more suitable candidate for CT images. Moreover, the RBS scheme provides better contrast as compared to the classical amoeba distance-based denoising, as shown in enlarged ROI-based comparison.
The proposed scheme is more robust and performs significantly better than the classical amoeba filtering in the presence of projection noise. The scheme inherits significant image noise reduction, Gaussian, and otherwise, due to dependence on Wiener and Amoeba filtering [
A limitation of the proposed scheme is its dependency on Otsu’s multilevel thresholding method which makes it computational expensive and, therefore, is not appropriate for real-time applications. However, this can be mitigated by the use of advanced and high-speed processors, such as GP-GPU (general purpose graphical processor units), as the scheme has potential to run in parallel. Therefore, the future research directions may include scheme optimization for real-time applications and implementation on GP-GPU. Moreover, the adaptive nature of the proposed amoeba-based filtering indicates scheme implementation in many dynamic applications is worth investigating, signifying future application of the scheme on denoising of natural images, industrial-CT, and nondestructive testing (NDT) data.
This paper presents an efficient and novel postprocessing scheme for CT radiation dose reduction and enhancement of FBP reconstructed image from sparse-view noisy CT scans. In this work, a new type of amoeba filtering is presented, which is customized for CT images. Region-based segmentation (RBS) using multilevel thresholding was used in the amoeba kernel shaping, which is more effective in medical imaging applications as it is similar to the symmetric and region-based nature of the human body anatomy. The pilot image uses Wiener filter, which helps in noise suppression while keeping the edge and contour details required for amoeba shaping. The scheme is supported by computer simulations using fan-beam projections of clinically reconstructed and simulated head CT phantoms. The results demonstrate that the proposed Wiener filter-based RBS amoeba scheme is visually and statistically better than classical amoeba filtering for CT image, as evaluated using various image quality matrices. The presented scheme is more robust to noise in CT projections and effective for enhancing few-view reconstruction. In the future, the implementation of the scheme on more medical as well as industrial phantoms will be undertaken. The introduction of the Wiener filter-based RBS amoeba scheme makes way for a family of morphological, median, and other filters based on the presented framework. The algorithm has the potential to run in parallel; thus, implementation of the proposed scheme on GP-GPU will also be a possible future avenue.
The pseudo algorithm to scan and segment connected regions is given below:
On the first pass: 1. Raster scan the sliding window (iteratively scan pixels by one row at a time) 2. If the pixel is not the background (i.e., 0) i. Get the neighboring pixels of the current pixel ii. If there are no neighbors, uniquely label the current pixel and continue 3. Otherwise, label the current pixel with the smallest neighbor label 4. Store the equivalence between neighboring labels (if neighbors have different labels) On the second pass: 5. Raster scan the sliding window (iteratively scan pixels by one row at a time) 6. If the pixel is not the background (0) i. Relabel the pixel with the lowest equivalent label
Pseudocode to scan and segment connected regions, using 4-connected component mask, is given below:
LabelCount =0 ; //Initialize Label counter. EquivalenceTable = [] ; //Initialize equivalence table of labels Neighbors = [Label(u,v-1), Label(u-1,v)]; //Get neighbor labels (one pixel above, and one on left/prior) ; //Note: neighbors for 8-connected mask include pixels to the ; //top-right, top, top-left and left of the pixel(u,v) Label(u,v) = LabelCount+1 ; //uniquely label the pixel LabelCount = LabelCount+1 ; //increment label counter EquivalenceTable = [EquivalenceTable, ((min(Neighbors), max(Neighbors))] ; //Record equivalencies of neighbor labels (Mx2 matrix) Neighbors = [ ] ; //Reset neighbor pointer. End For ; Second Pass: Relabeling equivalencies EqualityCount = rows(EquivalenceTable) ; //Total equivalencies = number of rows in Table Do L1 = EquivalenceTable (EqualityCount,1) ; //Smaller label in selected Equivalence Table entry L2 = EquivalenceTable (EqualityCount,2) ; //Larger label in selected Equivalence Table entry Labels(find(Labels = = L2)) = L1 ; //Relabel all instances of larger label with smaller label EqualityCount = EqualityCount – 1 ; //Decrement to target next equivalency
No data were used to support this study.
The authors declare that there is no conflict of interest regarding the publication of this paper.