Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення
The noise in reconstructed X-ray Computed Tomography (CT) slices is complex, non-stationary and indefinitely distributed. Subsequent image processing is needed in order to achieve a good-quality medical diagnosis. It requires a sufficiently great ratio between the detailed contrasts and the noise co...
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| author | Petrov, Miroslav |
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| description | The noise in reconstructed X-ray Computed Tomography (CT) slices is complex, non-stationary and indefinitely distributed. Subsequent image processing is needed in order to achieve a good-quality medical diagnosis. It requires a sufficiently great ratio between the detailed contrasts and the noise component amplitude. This paper presents an adaptive method for noise reduction in CT images, based on the local statistical evaluation of the noise component in the domain of Repagular Wavelet Transformation (RWT). Considering the spatial dependence of the noise strength, the threshold constant for processing the high frequency coefficients in the proposed shrinkage method is a function of the local standard deviation of the noise for each pixel of the image. Experimental studies have been conducted using different images in order to evaluate the effectiveness of the proposed algorithm. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2019.4.04 |
| first_indexed | 2025-07-17T10:26:25Z |
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M.D. Petrov, 2019
Системні дослідження та інформаційні технології, 2019, № 4 39
TIДC
ПРОБЛЕМИ ПРИЙНЯТТЯ РІШЕНЬ ТА
УПРАВЛІННЯ В ЕКОНОМІЧНИХ, ТЕХНІЧНИХ,
ЕКОЛОГІЧНИХ І СОЦІАЛЬНИХ СИСТЕМАХ
UDC 004.93ʹ11
DOI: 10.20535/SRIT.2308-8893.2019.4.04
CT IMAGE DENOISING BASED
ON LOCALLY ADAPTIVE THRESHOLDING
M.D. PETROV
Abstract. The noise in reconstructed X-ray Computed Tomography (CT) slices is
complex, non-stationary and indefinitely distributed. Subsequent image processing
is needed in order to achieve a good-quality medical diagnosis. It requires a suffi-
ciently great ratio between the detailed contrasts and the noise component ampli-
tude. This paper presents an adaptive method for noise reduction in CT images,
based on the local statistical evaluation of the noise component in the domain of Re-
pagular Wavelet Transformation (RWT). Considering the spatial dependence of the
noise strength, the threshold constant for processing the high frequency coefficients
in the proposed shrinkage method is a function of the local standard deviation of the
noise for each pixel of the image. Experimental studies have been conducted using
different images in order to evaluate the effectiveness of the proposed algorithm.
Keywords: repagular wavelet transform, statistical noise reduction, X-ray computed
tomography.
INTRODUCTION
Because of its high productivity in obtaining images having very good spatial res-
olution, X-ray CT plays a central role in clinical diagnostics. The improvement of
this resolution is directly related to the radiation dose. However, its increase poses
a certain risk to the patient's health. On the other hand, lowering this dose can sig-
nificantly reduce the diagnostic value of the tomographic image obtained. The
protocol optimization for the corresponding clinical study is based on the balance
between preserving the fine details of the image, the noise level and the radiation
dose for the patient. Therefore, the development of algorithms for noise reduction
in CT images obtained at a reduced radiation dose, while maintaining the detailed
information, is a topical task. The statistical fluctuations of the X-ray quantas
reaching the corresponding detector are a source of quantum noise in the projec-
tion data. This noise, combined with the noise generated by the electronics of
workstations, is propagated by means of the reconstruction algorithms in the CT
slices. The methods for noise reduction in CT images obtained at a low radiation
dose are mainly divided into three groups [1]: methods in the projection data
domain; methods in the image domain; image and iterative-reconstructive
methods.
The algorithms developed in the Radon space most often use iterative, opti-
mization and filtering methods before the application of the Filtered Backprojec-
M.D. Petrov
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 40
tion. The low values of the signal-to-noise ratio in the sonogram lead to the loss
of structural information.
The methods for reducing the noise in the reconstructed CT slices can be di-
vided into two subgroups: spatial-domain denoising techniques and transform-
domain denoising techniques. The linear filters used in the spatial domain are not
very effective for the preservation of the small details in the image, because its
diagnostic value is reduced. Significantly better results are obtained with methods
based on anisotropic diffusion. Its iterative character allows for improved compu-
tational efficiency, but speckled or mosaic effects appear in the denoised CT
images [6–7]. Noise reduction algorithms in the transformation domain are based
on different multiscale transformations, with the possible use of noise assess-
ment [8–11].CT image is decomposed in the low and high frequency sub-bands
of the scale space. Usually, the high-frequency wavelet coefficients are subjected
to threshold processing because the noise components are located mainly in these
subbands. The denoised image is obtained by means of inverse multiscale trans-
formation.
The third group of CT noise reduction methods refers to iterative
reconstruction using iterative and optimization algorithms that are implemented
within the two spaces for obtaining CT images. The advantage is the direct use of
the statistics of the noise component in the projection data during the
implementation of the algorithm, but the problem is the increased computational
value [12–14].With the improvement of workstations, the iterative reconstruction
is a preferred alternative to the Filtered Backprojection. This helps to solve the
problem of reduced radiation dose while preserving the diagnostic properties of
the image [15–16].
The goal of this paper is to present a locally adaptive, shrinkage algorithm
for noise reduction in CT images, based on the individual reconstruction of a pair
of intersecting subsets of projection data and threshold processing in the RWT
field. The rest of the report is organized as follows: section 2 provides a brief de-
scription of the motivation for the proposed method. The multiscale RWT used in
this paper is presented in Section 3, and the following section provides a detailed
description of the implementation of the announced noise reduction algorithm in
CT images. Section 5 presents the outcome of the experimental studies carried
out, as well as some comparative assessments. The last section summarizes the
results obtained and the conclusions drawn.
MOTIVATION AND JUSTIFICATION
Generally, a certain statistical model of the distribution of the noise component in
the image is used in post-processing methods for noise reduction in CT slices and
it may lead to inaccurate reflection of the actual situation. The approximate de-
scription of the physical process of obtaining the projection data can be achieved
with Poisson statistics. However, the analytical description of the noise in CT
images is complicated by the fact that reconstruction methods generate a correla-
tion in the noisy data [17]. Therefore, [18,19] propose noise reduction by means
of a wavelet threshold method based on the correlation between two CT images
that are equivalent in terms of the information they contain.
The method this paper proposes is motivated by the announced in [19]
Adaptive Wavelet Shrinkage (AWShrink) algorithm of noise reduction by means
of several CT reconstructions. The authors use the fact that the noise in two KT
CT Image Denoising Based on Locally Adaptive Thresholding
Системні дослідження та інформаційні технології, 2019, № 4 41
images, equivalent in terms of information content, is uncorrelated, unlike their
structural information. The threshold processing in the method is based on the
local evaluation of the noise in the two images, obtained through their high fre-
quency wavelet coefficients. The noise-estimated image is obtained from the cor-
responding averaged low-frequency coefficients, as well from the modified high-
frequency coefficients by means of the inverse wavelet transformation.
REPAGULAR WAVELETTRANSFORM
The wavelet transformation used in this paper is the RWT, introduced by Poli-
akova and Krylov [20] in order to increase the accuracy when separating image
contours. A family of functions that are localized at one point is used as a basic
wavelet. Its scale change occurs not by a dilation operator, as in the usual wavelet
transformation, but by using functions of different regularity.
If )(ts is a signal with limited energy and ),( at is the base wavelet (with a
regularity parameter a , its continuous RWT can be set with the convolution
)()(),( btsbaW a
r
s , where ),()( atta . In the applications of the RWT
for basic wavelet, the function taat 2),(~ is often used and the corresponding
convolution is realized using the filter
}2,,2,2,1,1,2,2,,2{)}({ )1(22)1()1(2
0
aNaaaaaNN
na
aaanG
where aN2 is the number of filter coefficients. The values of the parameter a of
the RWT can be set by the formula 02 ja , where 0 is any fixed number
from the interval (0,1), and ,2,1,0j The change of j results in modifying
the regularity parameter, i.e. the transition from one scale level to another in RWT
is done by changing the parameter a .
THE PROPOSED METHOD
A Brief Overview of the Method
The overview of the proposed method can be seen in the block diagram in Fig. 1.
The first step consists in obtaining the couple of input images that differ only
in terms of their noise components. Their generation is realized by separate
reconstructions of two projection sets, equivalent in terms of information. One of
the possibilities of obtaining these projections is the double scan of the object
inputimage
I1
denoised
image
RWT
INVERSERADON
TRASFORM
NOISE
ESTIMATION
&
TRESHOLDING
even
odd
inputimage
I2
PROJECTION
DATA
IRWT
Fig. 1. A block diagram of the proposed method for reducing noise in CT images
M.D. Petrov
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 42
under identical conditions and using half of the total radiation dose. Another
option is the use of two non-intersecting subsets of projection data, whose
overlapping represents the entire set of projections. An example of such subsets
are respectively the sets of odd and even projections obtained at a single scan. In
this case, it is assumed that the noise between the adjacent parallel projections is
uncorrelated, since the cross disturbances of the detector are negligible. The
averaged image obtained from the pair of reconstructed images corresponds to the
reconstruction from the full set of projections. These methods are CT variants
with a single source and it is necessary to take into account certain factors, such
as the reconstruction method, the sufficient number of projections, etc. [21].
In case there is a dual-source CT scanner, obtaining the input images is not a
problem, if the pair of tubular detector systems uses the same protocol for scan-
ning and reconstruction [22].
The statistical evaluation of the noise in the reconstituted pair of images, and
hence in their averaged image, is obtained by means of their RWT coefficients.
The denoised image is obtained through the inverse RWT applied to the low-
frequency and the corrected high-frequency coefficients of the averaged image,
respectively. The resulting image corresponds to the reconstruction of the com-
plete set of projections but with an improved signal-to-noise ratio.
Noise Assessment
Let us denote with 1I and 2I the pair of images obtained by separate reconstruc-
tion of the even and odd numbered projections of a given scan, and the total num-
ber of the received projections is an even number. The noise in the pair of projec-
tion sets is uncorrelated and, through the reconstruction methods, it appears as
such in the CT slices. In addition, the noise components of the images are as-
sumed to have zero averages and approximately equal standard deviations (at a
given position of the pixel), as the number of the quantas that produces them is
approximately equal. Let us note that the noise level in each of the images in-
creases by a factor 2 compared to the noise level in the reconstructed image
corresponding to the full set of projections [23].
Because the structural information is common to both images, their
difference 21 IID can be used to estimate the noise in each of them, and
therefore in their averaged image )(5,0 21 III . Taking into account the zero
covariance between the pair of random variables, then )(2)()( 5,0
21 DII
and )(2)(2)( 1
1
5.0 DII .
Let )(, mjw be the coefficient of the thm pixel, at a scale of
),0( mjj , obtained through RWT. Since the transformation is linear, the
equality )()()( 2,1,, IwIwDw mjmjmj is valid. As it has been noted above, the
noise in CT images is non-stationary, i.e. its power is spatially dependent, which
implies a local evaluation of its standard deviation. Therefore, for each pixel m , a
neighbourhood m is selected that contains n pixels. Since the noise has a zero
average, then
mn
mjmj DwnD )()( ,
1
, and, finally, for the standard deviation
of the noise in the averaged image I , we obtain:
mn
mjmj DwnD )()( ,
1
, .
CT Image Denoising Based on Locally Adaptive Thresholding
Системні дослідження та інформаційні технології, 2019, № 4 43
Determining the Threshold Mask
There are different methodologies for selecting threshold values in shrinkage
methods. The nonlinear functions of the “hard” and “soft” thresholds proposed in
[24] are most often used. The noise-estimation algorithm includes: wavelet de-
composition of the signal; estimation of the coefficients from the high frequency
bands, by means of a certain threshold value; obtaining the estimated signal
through the inverse transform. A basic idea in noise reduction shrinkage methods
is the use of the rarity of the multiscale transformations. The carriers of the struc-
tural information of the image are a small number of coefficients, and noise re-
duction is based on the shrinkage of the rest to zero.
A problem for hard threshold processing are the small changes in the image
due to the discontinuity of the function used. The proposed method uses a
continuous function of the soft threshold, and the estimated coefficients of the
averaged image are )0),(|)((|max))((sgn)( ,,,
0
, rIwIwIw mjmjmjmj , where
)(2)( ,
1
, rrr mjmj , and 0r is a threshold parameter that regulates the
amount of the suppressed noise.
RESULTS ANDCOMPARATIVE ANALYSIS
Two types of measures are used to evaluate the quality of the denoised CT im-
ages. They are based on:
a) Pixel Difference Measurement — Mean Absolute Error (MAE) and Peak
Signal-to-Noise Ratio (PSNR);
b) Human Visual Measurement — Structural Similarity Index (SSIM) and
Universal Image Quality Index (UIQI).
The algorithms for calculating the listed measures are implemented in Matlab.
Two experiments are conducted in order to evaluate the effectiveness of the
proposed method for reducing noise in CT images.
Test CT Image
A medical Matlab 16-bit monochrome 3-D CT image (ankle) with 512×512 reso-
lution is used as a test image. Wavelet filtering of image CT-MONO2-16-
ankle.dcm is performed, to which Gaussian noise has been added. Each of the
images obtained is subjected to the Radon transform in order to obtain and sepa-
rate the projection data, numbered by odd and even numbers respectively. At the
next stage, the corresponding reconstructed CT slices are decomposed by RWT,
at a pre-selected level ofdecomposition.
MAE, PSNR and SIMM for the CT-MONO2-16-ankle.dcm image, at the
respective noise levels
AWShrink Proposed
, %
MAE PSNR, dB SIMM MAE PSNR, dB SIMM
=10 1,574 30,43 0,7 0,778 39,56 0,83
=15 1,585 28,82 0,59 0,966 36,39 0,72
=20 1,696 27,86 0,48 1,33 33,49 0,66
=25 1,732 27,43 0,43 1,594 30,77 0,59
=30 1,781 26,44 0,32 1,67 28,89 0,54
M.D. Petrov
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 44
AWShrink is used for the comparative analysis of the proposed method.
Table provides the corresponding values for three of the four of those quality
measures obtained when using the two methods.
Figures 2 and 3 show the results obtained when using the wavelet noise
reduction methods, whose standard deviation is 10 and 20 respectively.
a
c db
Fig. 3. Denoised results of CT-MONO2-16-ankle.dcm. (noise level 20 ) obtained by
the two wavelet-shrinkage methods: a — Original image; b — Noisy image, 20 ;
c — Denoised image and the corresponding residual information, obtained through AW-
Shrink; d — Denoised image and the corresponding residual information, obtained
through the proposed method
a
c db
Fig. 2. Denoised results of CT-MONO2-16-ankle.dcm. (noise level 10 ) obtained by
the two wavelet-shrinkage methods: a — Original image; b — Noisy image, 10 ;
c — Denoised image and the corresponding residual information, obtained through
A-Shrink; d — Denoised image and the corresponding residual information, obtained
through the proposed method
CT Image Denoising Based on Locally Adaptive Thresholding
Системні дослідження та інформаційні технології, 2019, № 4 45
Real CT Data
The purpose of the next experiment is to evaluate visually the effectiveness of the
proposed method, as well as to confirm it by means of the quantitative measure
UIQI. The comparative analysis is again conducted by means of the AWShrink,
using real CT images of the three groups of studied organs: pancreas, colon and
thorax. These images are obtained from publicly available medical databases
(https://www.cancerimagingarchive.net/) and are in DICOM format.
Figures 4–6 present the respective base CT slices and their denoised images,
accompanied by the values obtained for UIQI. In addition, the corresponding im-
ages containing the residual information, which has been removed from the image
when applying these two algorithms, are presented for each pair.
a
b c
Fig. 4. Results from the reduction of noise in the “Pancreas” image, obtained by the two
wavelet-shrinkage methods: a — Input test CT image; b — Denoised image
)632,0( UIQI and the corresponding residual information, obtained through AWShrink;
c — Denoised image )918,0( UIQI and the corresponding residual information, ob-
tained through the proposed method
a
b c
Fig. 5. Results from the reduction of noise in the “Colon” image, obtained by the two
wavelet-shrinkage methods: a — Input test CT image; b — Denoised image
)742,0( UIQI and the corresponding residual information, obtained through AWShrink;
c — Denoised image )862,0( UIQI and the corresponding residual information, ob-
tained through the proposed method
M.D. Petrov
ISSN 1681–6048 System Research & Information Technologies, 2019, № 4 46
Summarized Results
The results obtained from the two experiments, connected with the comparative
analysis and shown in Table and Figures 1–6, lead to the following conclusions:
For each of the test images obtained at different values of the proposed
method achieves lower values for MAE as well as higher values for PSNR and
SSIM.
In percentage terms, this advantage over AWShrink (in respect of the in-
dividual measures) is as follows: MAE (32%), PSNR (20%) and SSIM (33%).
Compared to AWShrink, the proposed method retains more textural de-
tails, not only in the images used in the two experiments, but also in other tested
images.
For each of the test CT images, the proposed method achieves better re-
sults for the quality measure UIQI(in percentage – 36%).
CONCLUSION
Based on indirect statistical estimation in the frequency domain, an adaptive
threshold algorithm for noise reduction in CT images is proposed. The proposed
method is implemented in the RWT domain and is based on the correlation be-
tween two CT images, which are equivalent in terms of information content. The
continuous function of the soft threshold is used for threshold processing of the
high frequency wavelet coefficients of the averaged image.
For the comparative analysis, two experiments are performed, in which the
proposed method shows better results in terms of the measures evaluating the
qualities of the noise-estimated image.
a
b c
Fig. 6. Results from the reduction of noise in the “Chest” image, obtained by the two
wavelet-shrinkage methods: a — Input test CT image; b — Denoised image
)646,0( UIQI and the corresponding residual information, obtained through AWShrink;
c — Denoised image )967,0( UIQI and the corresponding residual information, ob-
tained through the proposed method
CT Image Denoising Based on Locally Adaptive Thresholding
Системні дослідження та інформаційні технології, 2019, № 4 47
The assessment of the noise in the projection data and in the corresponding
reconstructed slice, as well as its reduction, is among the important tasks in the
area of diagnostic X-ray CT. Its solution can be included in the strategy of mini-
mizing the radiation risk to the patient and improving the quality of the diagnostic
image. The proposed adaptive wavelet shrinkage method is applicable when post-
processing the reconstructed projection data.
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Received 16.10.2019
From the Editorial Board: the article corresponds completely to submitted manu-
script.
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| institution | System research and information technologies |
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| language | English |
| last_indexed | 2025-07-17T10:26:25Z |
| publishDate | 2019 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
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| spelling | journaliasakpiua-article-1791392020-08-11T15:08:55Z CT image denoising based on locally adaptive thresholding Понижение шума в КТ изображении на основе локально адаптивной пороговой обработки Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення Petrov, Miroslav repagular wavelet transform statistical noise reduction x-ray computed tomography репагулярне вейвлет-перетворення статистичне шумозниження рентгенівська комп'ютерна томографія репагулярное вейвлет-преобразование статистическое шумопонижение рентгеновская компьютерная томография The noise in reconstructed X-ray Computed Tomography (CT) slices is complex, non-stationary and indefinitely distributed. Subsequent image processing is needed in order to achieve a good-quality medical diagnosis. It requires a sufficiently great ratio between the detailed contrasts and the noise component amplitude. This paper presents an adaptive method for noise reduction in CT images, based on the local statistical evaluation of the noise component in the domain of Repagular Wavelet Transformation (RWT). Considering the spatial dependence of the noise strength, the threshold constant for processing the high frequency coefficients in the proposed shrinkage method is a function of the local standard deviation of the noise for each pixel of the image. Experimental studies have been conducted using different images in order to evaluate the effectiveness of the proposed algorithm. Шум в срезах реконструированной рентгеновской компьютерной томографии (КТ) является сложным, нестационарным и неопределенно распределенным. Обработка изображения необходима для постановки качественного медицинского диагноза. Это требует достаточно большого соотношения между детальными контрастами и амплитудой шумовой составляющей. Представлен адаптивный метод снижения шума на КТ изображениях, основанный на локальной статистической оценке шумовой составляющей в домене репагулярного вейвлет-преобразования. Учитывая пространственную зависимость интенсивности шума, пороговая константа для обработки высокочастотных коэффициентов в предлагаемом способе сжатия является функцией локального стандартного отклонения шума для каждого пикселя изображения. Экспериментальные исследования проведены с использованием разных изображений для оценки эффективности предложенного алгоритма. Шум у зрізах рекунструйованої рентгенівської комп’ютерної томографії (КТ) є складним, нестаціонарним і невизначено розподіленим. Оброблення зображення потрібне для поставлення якісного медичного діагнозу. Це потребує досить великого відношення детальних контрастів до амплітуди шумової складової. Подано адаптивний метод зниження шуму на КТ зображеннях, що ґрунтується на локальній статистичній оцінці шумової складової в домені репагулярного вейлвет-перетворення. Ураховуючи просторову залежність інтенсивності шуму, порогова константа для оброблення високочастотних коефіцієнтів у запропонованому способі стискання є функцією локального стандартного відхилення шуму для піксела зображення. Експертне дослідження проведено з використанням різних зображень для оцінювання ефективності запропонованого алгоритму. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2019-12-23 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/179139 10.20535/SRIT.2308-8893.2019.4.04 System research and information technologies; No. 4 (2019); 39-48 Системные исследования и информационные технологии; № 4 (2019); 39-48 Системні дослідження та інформаційні технології; № 4 (2019); 39-48 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/179139/189974 Copyright (c) 2021 System research and information technologies |
| spellingShingle | репагулярне вейвлет-перетворення статистичне шумозниження рентгенівська комп'ютерна томографія Petrov, Miroslav Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title | Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title_alt | CT image denoising based on locally adaptive thresholding Понижение шума в КТ изображении на основе локально адаптивной пороговой обработки |
| title_full | Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title_fullStr | Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title_full_unstemmed | Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title_short | Зниження шуму в КТ зображенні на основі адаптивного порогового оброблення |
| title_sort | зниження шуму в кт зображенні на основі адаптивного порогового оброблення |
| topic | репагулярне вейвлет-перетворення статистичне шумозниження рентгенівська комп'ютерна томографія |
| topic_facet | repagular wavelet transform statistical noise reduction x-ray computed tomography репагулярне вейвлет-перетворення статистичне шумозниження рентгенівська комп'ютерна томографія репагулярное вейвлет-преобразование статистическое шумопонижение рентгеновская компьютерная томография |
| url | https://journal.iasa.kpi.ua/article/view/179139 |
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