Classification of ring artifacts for their effective removal using type adaptive correction schemes
Introduction
High resolution computed tomography (CT) scanners such as, micro-CTs, C-Arm CTs or modern dental CTs, are often equipped with digital X-ray detectors which in most cases use charge-coupled devices (CCDs) or flat panel detectors (FPDs). Since photon receiving area of CCDs is much smaller than that of FPDs owing to demagnifying optics, CCDs are known to have better uniformity in pixel sensitivity than FPDs. FPDs, particularly CMOS (complementary metal oxide semiconductor) based FPDs, are believed to have bigger non-uniformity in sensitivity of detecting elements [1]. FPDs, with the photon receiving area as big as 40×30 cm2, are more susceptible to defective pixel errors which make pixel intensity be non-proportional to the input X-ray intensity. Defective pixels are either totally malfunctioning producing white or black pixel values or partially malfunctioning producing biased pixel values. If FPDs are used for X-ray tomography like micro-CTs or C-arm CTs, the defective pixels often make ring artifacts in the cross-sectional images as impurities or dusts on the scintillator crystal do [2], [3]. The ring artifacts caused by totally malfunctioning pixels (dead pixels) will appear in the reconstructed image as sharp rings with varying intensity. On the other hand, partially malfunctioning pixels (mis-calibrated pixels) lead to less strong ring artifacts in the reconstructed image [4]. It is often the case that the ring artifact patterns change when we change the tube voltage, which even complicates the ring artifact removal problem. As the gray level of the reconstructed images are also affected by these ring artifacts, it is necessary to remove them, otherwise, post processing, such as noise reduction or segmentation of the regional or interests, becomes significantly difficult.
A common approach to reduce these ring artifacts is known as the flat-field correction [5]. In this technique, an image is first measured without placing a sample in the X-ray beam. The non-uniformity in the resulting flat field includes the effects of inhomogeneities in the incident X-ray beam, non-uniform response of the scintillator, and non-uniform response of the detector elements. However, the flat-field correction usually leave residual ring artifacts since it does not take into account the noise in the flat-field measurement and the dependency of the flat field on the input X-ray intensity [6]. In another approach, the effect of the non-uniform sensitivity of different detector elements is masked by moving the detector array during the acquisition [7]. Thereby, the characteristics of all the detector elements are averaged, which usually leads to significantly reduced ring artifacts [8], [9]. However, it requires a special hardware to accomplish this type of ring artifact reduction.
Instead of hardware-based correction, image processing is an effective way to eliminate the ring artifacts and two different image processing-based approaches have been already reported in the literature for the correction of ring artifacts in the CT image. One of them is the sinogram processing during the reconstruction [10], [11], [12], [13], [14] and the other is the post-processing [6], [15] that directly works on the reconstructed CT image. As the ring artifacts in a tomographic slice is equivalent to the stripe artifacts in a sinogram image, it is relatively easier to eliminate the ring artifacts in the sinogram domain than the reconstructed image domain. In [2], [10] efficient methods have been proposed to remove the rings by smoothing the sum curve computed from the corrupted sinogram using an appropriate moving average filter and then normalizing the sinogram. These methods, however, fail to remove the varying intensity sharp rings (called type I ring in this paper) [10]. Furthermore, if a strong ring is present in the sinogram, this method [2] creates an extra band ring around the original ring. Recently, a work based on combined wavelet and Fourier filtering has been proposed in [3]. This method presents a general analysis for eliminating the stripe artifacts from a digital image and it is also applied for removing the ring artifacts from a tomographic slice. It is observed that the performance of this algorithm significantly degrades when an image is particularly corrupted by non-ideal type I rings. Most recently, a work based on center-weighted median filter has been reported in [11] to eliminate the ring artifacts from a tomographic image. But this technique does not figure out each type of rings to deal with them separately which is a prerequisite to an effective ring removal technique.
In [15] two post-processing techniques, both using mean and median filtering but working in different geometric planes (i.e. polar and cartesian), are proposed for the correction of ring artifacts. The authors have shown that the algorithm in polar coordinate (RCP) is more effective than that in the cartesian coordinate for removing artifacts from the images acquired by a FPD-based C-Arm CT system. Furthermore, in [16] it has been shown that the RCP method can also remove ring artifacts from the micro-CT images. The method may, however, fail to effectively eliminate the often seen varying intensity rings in the images. Because they generally contain significant high frequency information but the mean (low-pass) filtering in the RCP method is not appropriate to retain the varying intensity ring structures correctly in the difference image.
In this paper, a novel ring artifact removal scheme is proposed based on the classification, detection and correction of stripes in the sinogram domain. As the classification of stripes is critically important for accurate detection and correction of ring artifacts, we, therefore, categorize them first according to their statistical characteristics, and then propose the corresponding detection and correction algorithms for each category. Based on the faults observed, the stripes are classified into two types: Type I and type II. Type I stripe is the result of the defective detector elements and damaged scintillator screens. On the other hand, type II stripe is generated because of the mis-calibration of the detector elements. We propose here defective stripe detection and correction methods and we verify the method using the experimental projection data obtained with a home-made micro-CT.
This paper is organized as follows. Analysis of type I stripe is presented in Section 2 and that of type II stripe in Section 3. The description of the CT system and, the experimental results and discussions are presented in 4 The micro-CT system, 5 Results and discussions, respectively. Finally, Section 6 presents some concluding remarks.
Section snippets
Model
To develop the theory for type I stripe classification and detection, we start from the basic idea of an ideal stripe as stated in [3]. An image having ideal stripes of type I is defined aswhere P(n,j) is a clean image (with no ring generating defects), PI(n,j) is the corrupted image with ideal type I stripes only, Aj is a constant, JI is the set of stripe positions, i.e., ; jk {k=1,2,…, NI} are the positions of the stripes, and NI is the total
Model
As the responses of the dead pixels in a digital detector are naturally very different from the mis-calibrated ones, it is necessary to use different equations for modeling the sinogram with two different stripes. Therefore, unlike in [3], where all types of stripes were modeled using (1), we first define a mathematical model of a sinogram containing only type II stripes. As the type II stripes are created from the responses of mis-calibrated detector elements, we can model them as the sum of
The micro-CT system
The test images were acquired with a home-made micro-CT. The micro-CT consists of a CMOS FPD and a micro-focus X-ray tube (L8121-01, Hamamatsu, Japan). The micro-focus X-ray source is a sealed tube with a fixed tungsten anode having an angle of against the electron beam and with a beryllium exit window. The emitted X-ray beam span angle is about . The source has a variable focal spot size from 5 to depending on the applied tube power (Watt or kVp mA). The maximum tube
Results and discussions
In this section, we test the effectiveness of our algorithm using real micro-CT images and also present comparative results with moving average (MA) filter [2], wavelet-Fourier (WF) filter [3] and RCP [15] methods. The MA method is selected as a representative of the solely normalization scheme-based ring correction methods. The WF method is shown to be very effective in the removal of stripe artifact from a digital image. Since our algorithm also removes stripe artifacts for the correction of
Conclusion
In this paper, a novel method has been presented to classify ring artifacts in the FPD-based micro-CT images using their statistical characteristics in order to facilitate accurate detection and correction of these artifacts in the sinogram domain. According to the proposed classification schemes, the rings are classified as type I and type II and different detection and correction techniques have been adopted for different types. The results of our experimental tests on real micro-CT images
Conflict of interest statement
None declared.
Acknowledgments
This work was supported in part by the National Research Foundation (NRF) of Korea funded by the Korean government (MEST) (No. 2009-0078310).
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