A New Algorithm for Joint Reconstruction and Compression of Industrial Computed Tomography Images

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1 A New Algorithm for Joint Reconstruction and Compression of Industrial Computed Tomography Images Roozbeh Hojjatpanah 1, Mehrdad Taki 1, Karim Zarei 2 More info about this article: 1 Department of Electrical Engineering, University of Qom, Qom, Iran, Roozbeh.hp@gmail.com, m.taki@qom.ac.ir 2 imec-visionlab, University of Antwerp, Wilrijke, Belgium, karim.zareizefreh@uantwerpen.be Abstract We develop a new algorithm for compression of CT images along with its reconstruction from the projections. We compress the projection data in an intermediate file where just the most important part of data is acquired. Our proposed algorithm relies on Fourier slice theorem where images are reconstructed from their 2D Fourier transform. The most important frequency atoms are selected based on the required compression rate and quality. Numerical evaluations show the high efficiency of the new scheme for compression while the visual quality is reserved and also the signal to noise ratio of the image is in an appropriate level. Our algorithm provides various compression rates for various size of images. For example, the CT image may be compressed up to 5% of the original one with excellent spectacle. Keywords: Industrial CT, Compression, Reconstruction 1. Introduction By the modern industrial computed tomography (CT) scan, interiors of the objects may be inspected without any harm or destruction to the objects themselves. Industrial CT scanners as in medical types take multiple projections from various angles of the object by which the final image may be reconstructed. There are various reconstruction methods for CT images among them, reconstruction based on the fourier slice theorem is a basic and fast one [1]. One of the main draw backs for CT imaging is enormous size of projections. This makes compression inevitable for the storage and transmission. A CT image may be considered as a regular image and is compressed by the conventional algorithms like [2]-[8], regardless the nature and specifications of CT images. In this paper, for the first time we propose a joint reconstruction and compression scheme by which compression is done in the middle of reconstruction. In other words, just the most important data for the reconstruction is acquired and stored in an intermediate file. Various compression rates may be achieved by our scheme. In the following in section 2, the proposed algorithm is described. Section 3 is devoted to numerical evaluations and experimental results. 2. Description of the proposed Algorithm In the proposed scheme, one dimensional fast Fourier transform (FFT) is applied to projections, then the FFTs are circularly placed in a 2D plane to create the 2D FFT of the final CT image. At this stage if 2D IFFT is applied to the resulting 2D FFT, the desired image is reconstructed based on the Fourier slice theorem [1]. In our proposed scheme the resulting 2D FFT is compressed in a file with the extension of rmk, the extension name is acquired from on the names of authors Roozbeh, Mehrdad and Karim. The rmk file may be extracted at the end user and is passed through 2D IFFT to reconstruct the main image. The block diagram of the proposed scheme is depicted in Figure 1. 1

2 FFT Frequency domain FFT Compression.rmk FFT 2D IFFT Figure 1: The block diagram of the joint compression and reconstruction The compression stage consists of three steps, dividing 2D FFT by a lookup table, round and sort the elemnts of the rounded divided 2D FFT and finally applying Run Length Encoding (RLE). These stages are explained in the following. 2.1 dividing by a lookup table Different frequency atoms in CT images have different importance and effects on the image quality. Using this fact, the resulting transform in the previous stage is divided by a predetermined lookup table. Lookup table is a matrix of integers with the same size of 2D FFT. A standard rule is contracted to generate lookup table based on the image size and the required compression rate. The values of 2D FFT atoms are divided point by point to the elements of lookup table. Till this stage the transform is quite invertible as each user could generate the lookup table by its own and multiply it by the divided 2D FFT to reproduce the original one. A sample for the lookup table is shown in the following for a specific percentages of compression. In the lookup table, the points corresponding to the higher importance frequency atoms have lower values while they have higher values corresponding to the lower important atoms Figure 2: A sample of lookup table 2

3 2.2 round and resort of divided 2D IFFT At this stage the values of divided 2D IFFT are rounded to their nearest integer values. As in the next stage RLE compression is used, the values of rounded divided 2D IFFT are sorted and placed in a row vector. The method for the sorting of the elements is shown in the Figure 3. By this method higher values are placed at the beginning of the vector and the lower ones are placed at the end. Figure 3: The method for sorting the elements of divided 2D FFT in a row vector 2.3 RLE Run-length Encoding is a simple lossless method for compression. This method is quite efficient for sparse vectors. In a vector of zeros and ones a run of zeros or ones are expressed by a number as a count and a value e.g is expressed by 50. Noting to the applied lookup table and the method for the scan of elements of divided 2D FFT, roughly, it could be said that elements at the beginning of the final vector have the higher values compared to the elements at the end of final vector. This means that RLE could efficiently compress the data. 2.4 Decomprssion and Reconstruction The compressed image in a rmk file is stored or transmitted and the end user could reconstruct the CT image. The block diagram of decompression and reconstruction is shown in Figure 4. At first data is passed through a RLE inverse block. Then the uncompressed data is stored in a 2D matrix based of the sorting method as explained in 2.2 and shown in Figure 3. As the lookup table is generated based on a standard rule; the end user could generate the lookup table by its own. The resulting 2D matrix in the previous stage is multiplied by the lookup table to regenerate an estimate of 2D FFT of image. Finally a 2D IFFT is applied to reconstruct the desired image. rmk RLE inverse Sort data in a 2D matrix Multiply by Lookup table 2D IFFT Image Figure 4: The block diagram of decompression and reconstruction 3. Experimental Results and Numerical Evaluation To evaluate the proposed algorithm, we utilized both synthetic and real CT images. We acquired our real CT images using the ultra-fast setup of the TOMCAT beamline at Swiss Light Source (SLS) on a 2.9 T superbend as source with a critical energy at 11.9 kev. The phantom was placed at about 25 m downstream from the source. Filtered polychromatic X-rays (dumping 5 % of the total power) with a mean energy of 30 kev were incident on the sample attached to the tomography stage with three translational and one rotational degrees of freedom. The X-rays passing through the sample were converted to visible light by a LuAG:Ce converter and detected by an in-house developed 12 bit CMOS camera (giga-frost) providing continuous acquisition up to 8GB/s. The camera was attached to the scintilator through a high numerical aperture microscope with continuous zoom option in the range of 2 4 in our case set to an effective pixel size of 4.4µm [9]. The TOMCAT ultra-fast setup is shown in Figure 5. 3

4 (a) (b) (c) Figure 5: Ultra-fast setup at the TOMCAT; (a) The beamline vacuum fly tube and beam conditioning tower. (b) 2-4x continuous magnification microscope: Elya Solutions. (c) Rotation stage and giga-frost camera on top of the microscope. We used QRM-MicroCT-Barpattern (Figure 6) as a phantom to acquire a real dataset with Ultra-fast setup. The exposure time was 800us. Figure 6: QRM-MicroCT-Barpattern [10]. The phantom comprises two silicon chips placed in a full resin cylinder, one orientated inplane and one perpendicular (axial) orientated to it. Reconstructed compressed images are evaluated visually and quantitatively. Due to the lack of space at this section we compare the constructed shepp logan standard image with and without compression. As shown in Figure 8, there is no difference, which can be sensed by a normal human eyes. 4

5 Original Compressed 5% Compressed 20% Compressed 30% Compressed 50% Original-Compressed 5% Original-Compressed 20% Original-Compressed 30% Original-Compressed 50% Figure 7. A sample image with different compression rates Percentage of compressed image 5% 20% 30% 50% Original to the original SNR CNR Table 1: Various Compression rates and their corresponding SNR and CNR 5

6 As shown in Table 1, the CNR of 50% compression is lower than the original. Reason of this disorder is that in the scheme, at first, image will loss its noises and other undesirable features then main quality will be reduced. According to this fact in 50% and over compression rates the quality standards may be better. Original Compressed 5% Compressed 20% Compressed 30% Original-Compressed 5% Original-Compressed 20% Original-Compressed 30% Figure 8: Shepp logan with different compression rate More over, for quantitive evaluation of the compression effect, we calculate the peak signal to noise ratio (PSNR) for the images. As seen a quite negligible loss is occurred on the quality. 6

7 Percentage of compressed image to 5% 20% 30% Original the original PSNR Table 2: Various Compression rates and their corresponding PSNR 4. Conclusion A new joint compression and reconstruction algorithm was developed for computed tomography image. Stage by the proposed scheme, based on the required compression rate an estimate of 2D FFT of image is compressed in a file with rmk extension. The compressed 2D FFT is a quantized version of original 2D FFT where different quantization levels are assumed for different frequency atoms. The key idea in our scheme is that in a CT image the higher frequency atoms have more importance in spectacle and thus they are quantized with a more precision. Numerical evaluations have shown the acceptable performance of the proposed scheme. References [1] Zhao S.R. and H.Halling (1995). "A New Fourier Transform Method for fan Beam Tomography". published in 1995 Nuclear Science Symposium and Medical imaging Conference Record: [2] P. Bharti, S. Gupta and R. Bhatia, "Comparative Analysis of Image Compression Techniques: A Case Study on Medical Images," Advances in Recent Technologies in Communication and Computing, ARTCom '09. International Conference on, Kottayam, Kerala, 2009, pp [3] Tzi-Cker Chiueh, Chuan-Kai Yang, Taosong He, H. Pfister and A. Kaufman, "Integrated volume compression and visualization," Visualization '97., Proceedings, Phoenix, AZ, USA, 1997, pp [4] Yung-Gi Wu and Shen-Chuan Tai, "Medical image compression by discrete cosine transform spectral similarity strategy," in IEEE Transactions on Information Technology in Biomedicine, vol. 5, no. 3, pp , Sept [5] Yao-Tien Chen, Din-Chang Tseng and Pao-Chi Chang, "Wavelet-based medical image compression with adaptive prediction," 2005 International Symposium on Intelligent Signal Processing and Communication Systems, 2005, pp [6] Yung-Gi Wu, "Medical image compression by sampling DCT coefficients," in IEEE Transactions on Information Technology in Biomedicine, vol. 6, no. 1, pp , March [7] T. Phanprasit, "Compression of medical image using vector quantization," Biomedical Engineering International Conference (BMEiCON), th, Amphur Muang, 2013, pp [8] R. Pizzolante, B. Carpentieri and A. Castiglione, "A Secure Low Complexity Approach for Compression and Transmission of 3-D Medical Images," Broadband and Wireless Computing, Communication and Applications (BWCCA), 2013 Eighth International Conference on, Compiegne, 2013, pp [9] Zefreh KZ, Welford FM, Sijbers J. Investigation on the effect of exposure time on scintillator afterglow for ultra-fast tomography acquisition. Journal of Instrumentation Dec 7;11(12):C [10] 7