^{1}

^{2}

^{3}

^{4}

^{2}

^{2}

^{4}

^{1}

^{1}

^{1}

^{*}

Low-count SPECT images are well known to be smoothed strongly by a Butterworth filter for statistical noise reduction. Reconstructed images have a low signal-to-noise ratio (SNR) and spatial resolution because of the removal of high-frequency signal components. Using the developed robust adaptive bilateral filter (RABF), which was designed as a pre-stage filter of the Butterworth filter, this study was conducted to improve SNR without degrading the spatial resolution for low-count SPECT imaging. The filter can remove noise while preserving spatial resolution. To evaluate the proposed method, we extracted SNR and spatial resolution in a phantom study. We also conducted paired comparison for visual image quality evaluation in a clinical study. Results show that SNR was increased 1.4 times without degrading the spatial resolution. Visual image quality was improved significantly (p < 0.01) for clinical low-count data. Moreover, the accumulation structure became sharper. A structure embedded in noise emerged. Our method, which denoises without degrading the spatial resolution for low-count SPECT images, is expected to increase the effectiveness of diagnosis for low-dose scanning and short acquisition time scanning.

In recent years, dose reduction has attracted attention in many fields, e.g., pediatric examination in nuclear medicine. The image quality of nuclear medicine, however, largely depends on the acquisition count (dose and acquisition time) [

Noise removal of raw SPECT projection data has been typically conducted by a low-pass filter to eliminate high-frequency noise which causes artifacts of SPECT reconstruction [

Retaining high-frequency signal components requires selective noise reduction for low-count SPECT imaging. This study specifically examined bilateral filters, which are extremely useful in Gaussian noise reduction with edge preservation [

Using a new filter algorithm based on the bilateral filter, we developed the robust adaptive bilateral filter (RABF), which has robust edge-preserving and smoothing effects for low-count data. We propose a new pre-processing method using the RABF as pre-stage filter of the Butterworth filter for low-count SPECT imaging. The low-count explained herein is a limited count such as that is used for pediatric examinations.

Butterworth filter, a high-frequency cut-off filter, is the standard choice of the pre-processing filter of SPECT image reconstructions. Frequency dependence of the Butterworth filter B ( f ) is

B ( f ) = 1 1 + ( f f c ) n , (1)

where n is the filter order and f_{c} is the cut-off frequency. f_{c} must be lowered to reduce large amounts of noise, but high-frequency signal components might thereby also be removed along with noise. A low-pass filter such as the Butterworth filter is generally effective to prevent artifacts, but it degrades image quality for low-count data.

We propose a new pre-processing method for low-count data using the robust adaptive bilateral filter (RABF) as a pre-stage filter of the Butterworth filter (

Bilateral filters are edge-preserving smoothing filters [

g ( i , j ) = ∑ m = − w w ∑ n = − w w f ( i + m , j + n ) exp ( − m 2 + n 2 2 σ s 2 ) exp { − [ f ( i + m , j + n ) − f ( i , j ) ] 2 2 σ I 2 } ∑ m = − w w ∑ n = − w w exp ( − m 2 + n 2 2 σ s 2 ) exp { − [ f ( i + m , j + n ) − f ( i , j ) ] 2 2 σ I 2 } (2)

where g ( i , j ) represents the filtered pixel value at pixel ( i , j ) . In addition, f ( i , j ) denotes the original pixel value. σ s signifies the standard deviation of spatial Gaussian kernel for smoothing. σ I stands for the standard deviation of intensity Gaussian kernel for edge-preservation.

The bilateral filter distinguishes between edges and noise based on their difference in intensity. This filter smoothes intensity variations smaller than σ I as noise and preserves intensity differences greater than σ I as edges. For noisy images as SPECT projection data, the intensity of the Gaussian kernel does not function well because the intensity difference itself includes large amounts of noise. Outliers with large intensity difference are preserved. Edges buried in noise are smoothed where the difference is slight.

This newly developed filter achieves robust noise reduction and edge-preservation, even in noisy images. Retaining a general algorithm of the bilateral filter in Equation (2), the RABF replaces f ( i , j ) with the mean value μ ( i + k ^ , j + l ^ ) as a measure against outliers.

This new parameter is calculated over the 3 × 3 kernel centered on pixel ( i + k ^ , j + l ^ ) , which was selected from the pixel and its eight surrounding pixels to obtain the stable intensity difference without adverse effects by outliers. Therein, k ^ and l ^ are given as

k ^ , l ^ = arg min k , l ∈ A ∑ s , t ∈ A [ f ( i + k + s , j + l + t ) − f ( i , j ) ] 2 , (3)

where A is { − 1 , 0 , 1 } . The flow of determining the calculated area is shown in (

This filter can also adopt the standard deviation value σ I ( i + k ^ , j + l ^ ) from the same kernel as intensity weight σ I . The selected kernel avoids outliers and edges. An example of new parameter determination is presented in

The resulting RABF is given as

g ( i , j ) = ∑ m = − 2 2 ∑ n = − 2 2 f ( i + m , j + n ) exp ( − m 2 + n 2 2 σ s 2 ) exp { − [ f ( i + m , j + n ) − μ ( i + k ^ , j + l ^ ) ] 2 2 σ I 2 ( i + k ^ , j + l ^ ) } ∑ m = − 2 2 ∑ n = − 2 2 exp ( − m 2 + n 2 2 σ s 2 ) exp { − [ f ( i + m , j + n ) − μ ( i + k ^ , j + l ^ ) ] 2 2 σ I 2 ( i + k ^ , j + l ^ ) } (4)

where the kernel size in this study is 5 × 5 and σ s = 1 . New parameters are updated for each processing pixel.

The Gaussian intensity kernel of RABF operates sufficiently well using μ ( i + k ^ , j + l ^ ) instead of f ( i , j ) if the processing pixels have an outlier (

We assessed the RABF to confirm that it works on SPECT projection data as expected. We also compared the results to those obtained using the bilateral filter. Then, using a digital phantom to evaluate image quality, we extracted the spatial resolution and SNR as an objective evaluation.

To evaluate image quality objectively, we extracted the spatial resolution and SNR with a digital phantom. We used a digital brain phantom produced by software (Prominence Processor Ver.3.1; Prominence Conference, Japan) [

Collection condition | Parameter |
---|---|

Matrix size | 128 × 128 (2 mm/pixel) |

Collection angles | 4˚ (90 step) |

Radius of gyration | 13 cm |

System resolution FWHM at 13 cm | 8 mm |

Counts | 30 k counts/projection |

Ratio of concentration | 4:1 (Gray matter:White matter) |

both RABF and Butterworth filtering and with single Butterworth filtering as the RABF and conventional methods (

We used filtered back projection which is routinely used for SPECT reconstruction. The value of f_{c} was found based on the normalized mean square error (NMSE) between reference images and reconstructed images [

NMSE = ∑ i = 1 N ∑ j = 1 128 ∑ k = 1 128 [ T ( i , j , k ) − R ( i , j , k ) ] 2 ∑ i = 1 N ∑ j = 1 128 ∑ k = 1 128 R ( i , j , k ) 2 , (5)

where N represents the number of images, and where R ( i , j , k ) and T ( i , j , k ) respectively denote the normalized pixel value at (i, j, k) in reference and reconstructed images. Optimal f_{c} was found as the frequency at which NMSE was minimized.

We evaluated the full width at half maximum (FWHM) from the fitting curve around the striatum (the ellipse in

SNR = 20 log SD image SD noise ( dB ) , (6)

where SD image represents the standard deviation of all pixel values. Also, SD noise represents the standard deviation of the peripheral region of the brain on the image (outside of the dotted ellipse in

To evaluate the usefulness of the RABF method for clinical data, two patient data with different acquisition count were compared. We examined significant differences in the visual inspection using the paired comparison method to verify the visual effects of RABF method. All data were anonymized before analysis.

The SPECT projection data were ^{99m}Tc ethyl cysteinate dimer (^{99m}Tc-ECD) SPECT scan data of cerebral blood flow pattern measurements from two patients at Teikyo University Hospital. We used data only after anonymization. We found a low dose patient having an approximate weight of adults. To compare with this data, we prepared normal dose data with similar weight and collection conditions. Their disease types were intermittent epilepsy and suspected dementia with Lewy bodies, respectively, and there were no abnormal findings. The two patients, an adolescent (men, 17 years old, 60 kg) and an adult (female, 76 years old, 65 kg), had been respectively administered 350 and 840 MBq doses. The total counts were respectively 2.3 million and 6.5 million. We respectively designated the data of the adolescent and adult as low and normal dose data. Other conditions are presented in

The optimum f_{c} was not known for clinical images. Therefore, we adopted three f_{c} values for each datum as following: (0.45, 0.50, and 0.55 cycles/cm) and (0.55, 0.60, and 0.65 cycles/cm) for low-dose and normal data, respectively. _{c} values used for low-dose and normal-dose projections, where L, N, R, and C denote low-dose, normal dose, RABF and conventional method, respectively. In addition, R and C respectively represent the RABF and conventional method. Subscripts signify the used f_{c}. Here, the filter order of the Butterworth filter was 8. Six images obtained for each datum are presented in

Collection condition | Parameter |
---|---|

γ camera | e.cam signature (Toshiba Corp.) |

Collimator | LEHR (FWHM: 7.4 mm) |

Energy window | 140 keV ± 10% |

Collection angles, mode | 4˚ (90 step), Continuous mode |

Acquisition time | 16 min |

Turning radius | About 13.0 - 15.0 cm |

Matrix size | 128 × 128 (2.1 mm/pixel) |

Attenuation correction | Chang algorithm, μ = 0.09 cm^{−}^{1} |

Color scale, window width | Rainbow White, 100% - 0% |

Low dose images (350 MBq) | Normal dose images (840 MBq) | |||||
---|---|---|---|---|---|---|

f_{c} (cycles/cm) | 0.45 | 0.50 | 0.55 | 0.55 | 0.60 | 0.65 |

RABF + Butterworth | L (R_{0.45}) | L (R_{0.5}_{0}) | L (R_{0.}_{5}_{5}) | N (R_{0.}_{5}_{5}) | N (R_{0.}_{60}) | N (R_{0.}_{6}_{5}) |

Butterworth | L (C_{0.45}) | L (C_{0.5}_{0}) | L (C_{0.}_{5}_{5}) | N (C_{0.}_{5}_{5}) | N (C_{0.}_{60}) | N (C_{0.}_{6}_{5}) |

We compared the visual image quality of reconstructed images with those obtained with the conventional and the RABF method using Scheffe’s method of paired comparison (modified method by Ura) [

The psychological scale of image quality comparison has five grades (−2 to 2, 0 means equality). Here, the image quality was defined as the visibility of the accumulated structure, which depends on the noise and spatial resolution. The subjects were 2 doctors and 18 radiological technologists. This evaluation was conducted with one display without looking back. We calculated the average preference score of every object using analysis of variance.

We also ascertained whether significant differences were found among the objects using yardstick Y, which is given as

Y ∅ = q ∅ ( t , f e ) V e t n , (7)

where ∅ represents a significance level of 0.05 or 0.01, t signifies the number of objects, n denotes the number of subjects, and f_{e} and V_{e} respectively stand for the degrees of freedom and a variance of errors. Now, q ∅ ( t , f e ) is obtained from the Studentized range distribution. Significant difference between the two evaluation objects was inferred if the absolute value of difference among the average preference scores was found to be higher than Y.

Filtered projection data obtained using RABF and the bilateral filter are shown in

Resulting images with optimum f_{c} are depicted in _{c} of the conventional and RABF method were, respectively, 0.55 and 0.60 cycles/cm.

Here, the filter order was 8. Although the RABF method used higher f_{c}, the noise became less than that obtained using the conventional method.

Visual evaluation indicated improvement by the RABF method for each f_{c} in low-dose images (_{0.50}) and 0.042

using the conventional method L(C_{0.55}).

Reconstructed low-dose images L(C_{0.55}) and L(R_{0.50}) in

However, not as much difference as we had expected was found in normal dose images (

Use of the Butterworth filter alone degrades image quality considerably for low-count SPECT data because it removes high-frequency signal components along with noise. Using RABF, we strove to remove noise without degrading the spatial resolution for low-count SPECT imaging.

The RABF worked robustly even with noisy images from SPECT projection data. This result cannot be obtained with the bilateral filter (

Our phantom study revealed that the RABF improved SNR without degrading the spatial resolution. The SNR was increased considerably (1.4 times) by the RABF method despite using high f_{c} . This result indicates that the RABF method has the same effect of doubling the count in nuclear medicine. It is expected to be very effective for low-count clinical practice.

Significant (p < 0.01) difference in visual image quality was confirmed from this clinical study. Visual observation shows that the accumulation structure was clarified (

We propose a new pre-processing method using RABF as a pre-stage filter for denoising without degrading the spatial resolution of low-count SPECT data, such as those from pediatric examinations. This filter, which had robust edge-preserving and smoothing effects, produced the benefits of improving SNR while preserving the spatial resolution. Results of a clinical study demonstrated that the RABF method clarified the accumulation structure that had been obscured within a considerable amount of noise. This method is expected to be adequate for low-dose scanning and short acquisition time scanning.

This work was partly supported by a Japan Society for the Promotion of Science (JSPS) KAKENHI Grant (No. 18K07646).

The authors declare no conflicts of interest regarding the publication of this paper.

Nakabayashi, S., Chikamatsu, T., Okamoto, T., Kaminaga, T., Arai, N., Kumagai, S., Shiraishi, K., Okamoto, T., Kobayashi, T. and Kotoku, J. (2018) Denoising Projection Data with a Robust Adaptive Bilateral Filter in Low-Count SPECT. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 7, 363-375. https://doi.org/10.4236/ijmpcero.2018.73030