A method and algorithm for Tomographic Imaging of highly porous specimen using Low Frequency Acoustic/Ultrasonic signals

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1 More Info at Open Access Database A method and algorithm for Tomographic Imaging of highly porous specimen using Low Frequency Acoustic/Ultrasonic signals Subodh P S 1,a, Reghunathan Nair G 2,b, Byju C 3,c, Milu Mary Mathew 4,d 1 Centre for Development of Advanced Computing, Thiruvananthapuram, Kerala, India Centre for Development of Advanced Computing, Thiruvananthapuram, Kerala, India Centre for Development of Advanced Computing, Thiruvananthapuram, Kerala, India Centre for Development of Advanced Computing, Thiruvananthapuram, Kerala, India a subodh@cdac.in, b reghu@cdac.in, c byjuc@cdac.in, d milu@cdac.in Keywords: Tomography, Porous Material, Non destructive testing ABSTRACT Tomographic imaging provides detailed insight on the internal structure of materials which can help in identifying flaws non destructively. Tomography based imaging can be done in highly attenuating porous materials using low frequency acoustic/ultrasonic waves. This finds application in the evaluation of highly porous materials used for thermal shielding. Low energy X-ray CT used in medical applications is not suitable for Tomography of porous materials which are highly attenuating. High energy X-rays are not suitable for continuous use due to safety reasons. Conventional Non destructive test equipment also cannot be employed for taking tomogram of highly attenuating materials due to its high frequency of operation. Acoustic/ low frequency ultrasonic based method is less harmful and the product realized using this method will be less costly. The feasibility of computed tomography for highly porous specimen using low frequency is established in this paper, which involves selection of suitable parameters, optimization/modifications of existing computational algorithms related to back projection and image reconstruction. We conducted a detailed study and developed suitable algorithms for creation of tomogram using acoustic/ultrasonic waves penetrating through the specimen of interest. We also developed methods for correction of the artifacts caused by high attenuation of the specimen as well as due to the low resolution caused by the low frequency operation. The forward projection data obtained from scanning is subjected to image reconstruction using an algorithm which takes the back-projection data as the apriori, followed by iterations. Image enhancement techniques were subsequently used for better visualization of the output tomogram for scientific analysis and decision making. 1. INTRODUCTION A Tomography based Non Destructive Test System consists of an array of transducers, transceivers, signal processing hardware/software and tomography software, all designed around a high performance PC. Even though acoustic tomography is a well-known technique, application of this technique for non destructive testing of highly attenuating materials are not popular due to the

2 constraints arising out of low frequencies needed for testing of such materials. The selection of projection data, the algorithm used for extracting the projection data from the received signal, the algorithms for generating tomograms and image processing methods to enhance the information content of tomograms determine the usability of computed tomography in highly porous materials. Tomogram of highly attenuating non-metallic materials can be used for analysis of the properties of such materials. 2. THEORY AND METHOD Images of inhomogeneity inside a specimen can be reconstructed by means of tomographic techniques, which utilize the propagation of sound waves in the target medium. The technique described here utilizes acoustic and low frequency ultrasonic waves. The basic principles used in Acoustic Tomography are closely related to those used in CAT (Computed Axial Tomography) scans in medical field Projection Data In Acoustic Tomography, the travel time or signal strength of sound waves are used as the projection data. This projection data is used to map inhomogenity in a "slice" of the specimen [1,2]. In non metallic porous specimen the attenuation is high for high frequencies. Hence only low frequencies can be used for creating tomograms. Studies conducted by Nebojsa Duric, Cuiping Li, Olivier Roy and Steve Schmidt [3] have shown that very low frequencies are suitable for the nondestructive imaging of materials similar to porous specimen. Our experiments on porous specimen resulted in finding out the frequency range of 1 KHz to 75 KHz is best suited for tomography of such specimen. The flaw detection capability of the system is directly related to the frequency of acoustic waves. Only flaws whose size is greater than λ/6 can be detected, where λ is the wavelength of the acoustic signal. Appreciable variation in signal start time will not occur because of the above specified relationship. However the signal strength over a specified window after the signal start shows appreciable variation even when flaw size is less than that specified in the above relation. Hence signal strength was used as the forward projection data for the reconstruction of the image Extraction Of Projection Data From Received Signal The method of operation for computed tomography imaging is to transmit a few cycles of acoustic/ultrasonic wave into the test material using a set of transducers and receive the wave after it passes through the material at various angles. The signal strength corresponding to the different paths forms the forward projection data. The steps involved in extraction of the projection data are Signal start identification & Signal Strength computation. The conditioned received signal is processed to find out the signal start. The signal is validated before processing it. One of the validation criteria is that the signal is valid if the received data amplitude crosses the threshold value at least N times & the frequency of this crossover is equal to the Tx Frequency Time interval between two samples in acquired signal 1/fs

3 Time interval between two consecutive crossovers of the threshold amplitude of valid signal: (fs/f) +/- tolerance. If there are n1 samples between two successive crossover of the threshold amplitude, it is a valid signal if, n1 = fs/f +/- tolerance The above condition should be satisfied for N consecutive crossover for the data to be termed as containing valid signal. The validated signal is filtered by Band Pass Filter. A Reference Sine Signal is Generated and correlated with the received data for finding the correlation coefficient. Correlation coefficient = (ΣX i Y i )/ (ΣX i 2 Y i 2 ). (1) Where X i is the generated signal amplitude and Y i is the received signal amplitude at point i. If the correlation coefficient rises above the Correlation coefficient threshold then that point in the received data corresponds to the signal start. Signal strength is computed from a fixed window in the received signal where the window starts from the signal start computed earlier and a window width corresponding to the transmission signal width Tomogram generation using Back Projection The receiving transducers are kept at different angles with the transmitting transducers in such a way that the wave penetrates through the specimen are received at different angles. The projection data of different paths of the acoustic wave are used to create a tomogram of the specimen. The projection angle is the angle, which the beam makes with the axis. The Radon transform of an image represented by the function f(x,y) can be defined as a series of line integrals through f(x,y) at different offsets from the origin.[2] r θ y Figure 1: Projection line l x The above figure shows line l in the xy coordinate system satisfying the equation r = x cos θ + y sin θ. (2) Where r is perpendicular distance of the line l from the origin, θ is the angle which the perpendicular of the line l makes with the x axis and (x, y) is an arbitrary point.

4 Radon transform is defined as the line integral, given by R( r, θ ) = f ( x, y) dl. (3) l The above equation is rewritten using Dirac delta function (δ) as. (4) for r, θ shown in the figure 1. The line integral gives value to R(r, θ) if delta function (δ) has value. δ (a) = 1; a = 0 = 0; a 0 Image reconstruction from the set of projection values contained in R(r, θ) is performed using a combination of Back projection and an iterative method, tailored to suite the low frequency imaging. An iterative reconstruction starts with an assumption, for example the apriori image of the object, and compares this assumption with the measured values, makes correction to bring the two into agreement, and then repeats the process over and over until the assumed and measured values are same or within acceptable limits (reference ). The correction sequence employed here involves the whole matrix. Hence it is a form of Simultaneous Iterative Reconstruction technique where all projections for the entire matrix are calculated at the beginning of the iteration, and all corrections are made simultaneously for each iteration. Mathematically, the back projection operation is defined as: 0 f ( x, y) = R( xcosθ + ysinθ, θ ) dθ. (5) where xcos θ + ysin θ = r. where R(r,θ) is the projection value and f(x,y) is the reconstructed image. The back projection operation simply propagates the measured sinogram back into the image space along the projection paths. In discrete domain = R( cos + f ( x, y) x θ ysinθ, θ ). (6) θ An iterative reconstruction [5] starts with an assumption, for example the apriori image of the object, and compares this assumption with the measured values, makes correction to bring the two into agreement, and then repeats the process over and over until the assumed and measured values are same or within acceptable limits. The algorithm for iterative back projection is as follows. 1. Initialization: We start the iteration by forming an initial estimate. The non zero estimate is obtained from simple back projection. Here we go for a non-zero estimate, since it involves

5 multiplication and division operation within the loop. The terms having the value zero, doesn t update itself in the iteration. 2. Forward Projection: Making use of the initial estimate, forward projection is performed using discrete radon transform. 3. Comparison: Comparison is performed, by dividing the original set of projection values, with the new set formed in the above step. The comparison result forms the error in forward projection. 4. Back Projection: Error in forward projection is then back projected, to form error in the estimate. The back projection is followed by normalization. This is done to make sure, the value in each cell, fits more or less to the range specified by the value of any projection line through that cell. 5. Update the estimate: The new estimate is now formed by multiplying, the error in estimate with the initial estimate. 6. Iteration: The initial estimate is updated by replacing it with the new estimate and the process is repeated (from step2) for a certain number of iterations. A mechanism to stop the iteration can be included by checking whether the absolute sum of error in the estimate goes below a certain value Information Enhancement Using Image Processing The output of the image reconstruction is the tomogram of the slice. Due to the low resolution of the image caused by the low frequency, the presence of artifacts will result in faulty interpretations. Image visualization techniques are applied to correct the artifacts and present the results more clearly. All the image processing techniques used are standard processing methods already documented. Its suitability for artefact correction is evaluated here. Smoothening is performed to ensure that rapid changes in the image data due to measurement noise is eliminated. A sequence of process involving low pass filtering and median filtering is employed to reduce the high frequency noise in the tomogram. The deviations in projection data will not be significant when the degree of inhomogeneity is low, resulting in an image whose contrast is poor. Histogram equalization technique is used to maximize the contrast and hence to ensure that pixel values fall in the available intensity ranges. Bilinear interpolation is performed to increase the resolution of the image. The bigger sizes of low frequency transducers do not permit acquisition of forward projection data with minimal spatial resolution. This results in reduced number of projection data, which yields low resolution image. To increase the resolution and to enhance the visibility of the information content, interpolation method is needed. Windowing needs to be performed for selective viewing of the intensities of interest. By applying the process of windowing, we can view the selected intensity range. This is equivalent to cutting down the intensity range of the displayed image. When two flaws which has varying degree of inhomogeneity appears in the same specimen, the flaw with higher variation tends to be prominent than the flaw with lower deviation in the tomogram. To examine whether flaws with lower deviation is present, selective windowing technique can be used. 3. EXPERIMENTAL SET UP The set up used for recording measurement is as shown in figure 2.

6 Figure 2: Set up for experiments Signal generation module generates sine burst signal. The acoustic signal traverse through the test specimen and the receiving transducers receives the attenuated (weak) acoustic signal. The receiving transducer converts the acoustic signal into electrical signal. The weak electrical signal is filtered from noise and amplified, to a suitable level by the signal conditioning (SC) module. The data acquisition module digitizes the conditioned signal. The data is sent to the processing module. Digital Signal Processing such as noise filtering, correlation, extracting time of flight/ signal strength /signal peak etc are done by the processing Module. Reconstruction of the image and image enhancement algorithm as described above follows this process. 4. OUTPUTS / RESULTS The tomogram of a porous test specimen, which contains an induced flaw is shown in Figure 3 Figure 3: Specimen and its tomogram The raw low resolution tomogram, is image processed and proper intensity windowing is applied to get an clear image of the flaw as shown in figure 4. Figure 4: Raw tomogram and processed image The experiments conducted to determine the suitable type of projection data, that is sensitive to non-homogeneity using the low frequency signal is shown in figure 5. Image using flight time projection data is shown in the left image, image using signal strength as the projection data is shown in the right.

7 Figure 5: (Left) Tomogram using flight time as projection data, (right) Tomogram using attenuation as projection data. 5. CONCLUSION Principles of Computed tomography are made good use of in creating tomograms of porous materials. We experimentally found out optimum frequencies, the suitable type of projection data, used back projection algorithm and found out the relevant image processing blocks for creating tomograms using sensors having low frequencies. 6. ACKNOWLEDGMENTS The authors would like to express their appreciation for the financial support by our organisation Centre for Development of Advanced Computing, an autonomous society under the Department of Electronics and Information Technology, Govt. of India. 7. REFERENCES [1] A. Asano, Radon transformation and projection theorem, Topic 5, Lecture notes of subject Pattern information processing, 2002 Autumn Semester, [2] Ge Wang, and Michael W. Vannier, "Computerized Tomography," Department of Radiology, University of Iowa, Iowa 52242, Iowa City (USA): [3] Analytic and Iterative Reconstruction Algorithms in SPECT [4] A study of iterative methods in image reconstruction and applications-federico Benvenuto [5] G. Hermann, Image reconstruction from projections: the fundamentals of computerized tomography. New York: Academic [6] Nebojsa Duric, Cuiping Li, Olivier Roy and Steve Schmidt. Acoustic Tomography: Promise versus Reality [7] J. Zimmerman, S. Pizer, E. Staab, E. Perry, W. McCartney, and B. Brenton, "Evaluation of the effectiveness of adaptive histogram equalization for contrast enhancement", IEEE Trans. Medical Imaging, pp