Comparative Analysis between Different Linear Filtering Algorithms of Gamma Ray Spectroscopy

Transcription

1 Comparatve Analyss between Dfferent Lnear Flterng Algorthms of Gamma Ray Spectroscopy Mohamed S. El_Tokhy, Imbaby I. Mahmoud, and Hussen A. Konber Abstract Ths paper presents a method to evaluate and mprove the performance of gamma ray spectroscopy. A comparson between dfferent technques of accomplshng the gamma rays s presented. A reference sgnal from radaton source 137 Cs was acqured by data acquston system s used n ths comparson. We are concluded that lnear flterng approach s the weak technque of gamma ray spectroscopy. However, wth ncreasng count rate, the hghpass flters requred to shorten pulse length and ncrease throughput also degrade sgnal-to-nose rato (SNR), and ultmately, energy resoluton. Index Terms multchannel analyzer, pulse pleup, gamma ray spectroscopy I. INTRODUCTION The advantages of a dgtal system for gamma ray spectroscopy n comparson wth a classcal analog system are reflected n the possbltes of mplementaton of complex algorthms and smple modfcaton of algorthms used for sgnal processng. In ths way the hghest qualty of measurements s acheved both at low and at hgh countng rates and usng varous radaton detectors. Other advantages of dgtal spectrometers, such as smple storage of the spectrum, spectrum processng and analyss and presentaton of results, need not be emphaszed [1-2]. Performances of the dgtal spectrometer are drectly determned by characterstcs of the appled ADC and dgtal processor [3]. The rapd development of technology and archtecture of electronc crcuts leads to Manuscrpt receved May 9, M. S. El Tokhy s wth the Engneerng Department, Nuclear Research Center, Atomc Energy Authorty, Inshas, Egypt (correspondng author phone: ; fax: ; e-mal: engtokhy@gmal.com). I. I. Mahmoud, s wth the Engneerng Department, Nuclear Research Center, Atomc Energy Authorty, Inshas, Egypt. H. A. Konber s wth the Electrcal Engneerng Department, Al Azhar Unversty, Caro, Egypt. the appearance of ncreasngly fast dgtal components of hgh capabltes, so that ncreased throughput of the system and hgher resoluton can be acheved by deployment of faster components but preservng the proposed concept of operaton of the system. Tradtonal approaches to pulse processng, whether mplemented n analogue or dgtal systems, are forced to trade off energy resoluton and throughput by adjustng pulse shapng parameters. The current algorthms for dealng wth pulse pleup are to dentfy pulses that have pled up on top of each other, reject that nformaton, and then analyze only 'clean' pulses [4-5]. Although ths approach mproves the accuracy of the spectrum, the tme requred to collect suffcent statstcs dramatcally ncreases. In many applcatons as much as 80% of nformaton can be lost to the effects of dead tme and pulse pleup. The effects of pulse pleup n applcatons of nuclear technques nclude: mposng a fundamental lmt on detector throughput (and therefore source ntensty); decreased spectral accuracy and resoluton, as peaks n the energy spectrum spread; reduced peak-to-valley ratos due to false detecton of pulses; and causng sgnfcant detector dead tme n the system [6]. The possblty of reprogrammng and flexblty are sgnfcant characterstcs of the dgtal systems. Due to these characterstcs, n the evaluaton of system characterstcs, t was possble to mplement dfferent algorthms for sgnal processng wthout changng the hardware. It s mportant to note that these changes can be ntroduced quckly and whle the system s n explotaton. Ths property of the system s extremely sgnfcant when measurements are performed wth a large number of detectors. In such cases manual adjustment of system parameters s very tme consumng and prone to errors. 116

2 II. THE PROPOSED ALGORITHM OF LINEAR FILTER OF GAMMA RAY SPECTROSCOPY A sgnal processng core based on feld programmable gate arrays (FPGAs) s developed for processng of scntllaton detector sgnals by [8]. Ths core s mplemented to apply the forward wavelet transform and nterpolaton technque. The man purpose of that s to denose, compress and reconstruct these sgnals by whch the processng speeds and storage s optmzed. Moreover, In ths subsecton an effort s made to reduce the noses n gamma ray spectroscopy by [8]. They ntroduce an algorthm for nose removal for scntllaton sgnals usng Haar wavelet transform and reconstruct t usng nterpolaton nstead of nverse wavelet transform. Moreover, we wll ntroduce more wavelet transform technques and compare wth ther results. A. Sgnal statstcs The expermental and analyss of dfferent wavelet sgnals have been performed usng Matlab. Dfferent methods for reconstructon of the sgnal were used for the evaluaton of the test sgnal. The compresson performance s the bass for the choce of these wavelets among the dfferent wavelet famles n terms of peak sgnal to nose rato (PSNR), mean squared error (MSE), sum of squares due to error (SSE), mean squared root error (RMSE), eucldean dstance (ED), and correlaton coeffcent (CC). Sgnals n ths case are the scntllaton detector sgnals, and the nose s the error ntroduced by compresson. A.1. Peak sgnal to Nose Rato (PSNR) It s the fgure of mert that used to judge on the reconstructon accuracy. In some cases one reconstructon may appears to be closer to the orgnal sgnal than another, even though t has a lower PSNR. Moreover, Hgher PSNR would normally ndcate that the reconstructon s of hgher qualty. PSNR s defned by [8-9]; 2 MAX PSNR = 10 log 10 MSE where, MAX s the maxmum possble sample value of the sgnal, and MSE denotes the mean square error. A.2. Sum of Squares Due to Error (SSE) Ths parameter measures the total devaton of the ftted response from the orgnal response values. It s also called the summed square of resduals. It s usually abbrevated as SSE, and s gven by the followng equaton. (1) ths algorthm gves them all mportant features of the sgnal such as countng, shapng, pulse heght and multchannel analyzer. Ths algorthm s depcted n Fg. 1. n ω ( ) 2 (2) SSE = x y = 1 where, x represent the orgnal sgnal and y represent the reconstructed sgnal. A closer value of SSE to 0 ndcates a better ft. A.3. Mean Squared Error (MSE) It s the mean square error or the resdual mean square error. For two vectors x and y of scntllaton detector sgnals wth length N where one of the sgnals s consdered a nosy of the other, MSE s defned as MSE=SSE/N (3) A.4. Mean Squared Root Error (RMSE) Ths parameter s also known as the ft standard error and the standard error of the regresson. It s gven by; RMSE = MSE (4) A.5. Eucldean dstance (ED) ED of two seres x and y s gven by N (5) 1 (, ) = ( ) 2 ED x y x y A.6. Correlaton Coeffcent (CC) The correlaton between two sgnals (cross correlaton) s a standard approach to feature detecton as well as a component of more sophstcated technques. It s well known that CC can be effcently mplemented n the transform doman, the CC preferred for feature matchng applcatons. It does not have a smple frequency doman expresson. CC s a standard method of estmatng the degree to whch two seres are correlated. The cross correlaton between the two vectors x and y s defned as follows; CC = N ( ( x m x )( y m y )) = 1 N N ( x m x ) ( y m y ) = 1 = 1 (6) 117

3 137 Cs Radaton Source Scntllaton Detector Data Acquston System Sgnal Pre-processng A.1. Background Correcton Ths step s used to remove the exstng background radaton, whch s the level of the sgnal before the measurements of the radaton source. Because of the cosmc rays radaton contnuously bombardng the earth's atmosphere and the exstence of natural radoactvty n the envronment, all radaton detectors record some background sgnal [7]. The amount of ths background vares greatly wth the sze and type of detector and wth the extent of sheldng that may be placed around t. Because the magntude of the background sgnal ultmately determnes the mnmum detectable radaton level, background level s mportant n those applcatons nvolvng radaton sources of low actvty. A useful technque can be appled to reduce background radaton n low level countng as follow; Fg. 1 Block dagram of the underlned algorthm III. SIMULATION AND EXPERIMENTAL RESULTS A. Sgnal preprocessng Dfferent Wavelet Transform Reconstructon by Interpolaton and other Methods Countng the Number of Peak Pulses Dsplay the Energy Spectrum The collected data usng the DAS at the output of the system s shown n Fgure 2.a. The expermental data contans statstcal fluctuatons and other parastc nfluences. To determne the spectroscopy, the sgnal should be processed wthout nose, so that some of data preprocessng steps are carred out usng the MATLAB software. These steps nclude background correcton, and afterpulse removal. These steps are brefly explaned below Background Correcton Sgnal=M s - B s (7) Where, M s denotes the measured sgnal from the radaton source that s depcted n Fg.2.a and B s s the measured background sgnal that s shown n Fg. 2.b. The result of ths step s shown n Fg. 2.c. A.2. Afterpulse Removal In ths subsecton, afterpulse problem n the gamma ray spectroscopy s removed. It was orgnated from sngle or few count of pulses [7]. Ths step s used to elmnate the fluctuatons resultng from countng statstcal nose or electronc nose. Removng the afterpulse s prorty n gamma ray spectroscopy because t has a great effect on the number of counts n the gamma ray spectroscopy. It s performed wth a fnte mpulse response (FIR) flter wth the transfer functon: H ( z ) 1+ z + z + z = (8) The choce of a flter of order 3 s to guarantee the smoothng of the measured data and avod the complexty and oversmoothng problems assocated wth hgher order flters. The output of the flter C f (n) can be expressed as: 1 ( ) ( ( ) ( 1) ( 2) ( 3) ) Cf n = C n + C n + C n + C n (9) 4 where C (n) s the flter nput. The result of ths step s shown n Fg

4 Tme (ns) Fg. 2 Background Correcton sgnal Tme (ns) Fg. 3 Afterpulse Correcton sgnal B. Lnear flter results The decomposton process can be terated, wth successve s beng decomposed n turn, so that one sgnal s broken down nto many lower resoluton components. Ths s called the wavelet decomposton tree as depcted n Fgs Reconstructon of frst method by dfferent nterpolaton methods s depcted n Fgs Reconstructon of thrd method by dfferent nterpolaton methods s depcted n Fgs Tables 1-2 llustrate a comparson between dfferent wavelet transform technques at varous nterpolaton methods for both Symlet and Coflet wavelet transform as depcted n Fgs.4-11, respectvely. a b c By countng the number of pulses between UPD and LPD, t was found to be 12 and 13 for Symlet and Coflet as shown n Fgs , respectvely. The countng effcency of dfferent wavelet transform technques usng FFT and nterpolaton methods was calculated, and depcted n Table 3. From the results n Table 3, we noted that, Dscrete Meyer gves an accurate number of counts n comparson wth other wavelet methods usng both nterpolaton and FFT. Also, nterpolaton s much better than FFT, because FFT ntroduces low accuracy counts wth all types of wavelet transform. We are concluded that, current approaches to dgtal pulse processng rely on lnear flterng methods, whch attempt to reduce the pulse length to mprove resoluton. Unfortunately, much of the pulse energy s at low frequences. However, n order to reduce pulse length, hgh pass flters are necessary. The consequence of ths approach s to sgnfcantly reduce sgnal energy resultng n a loss of sgnal to nose rato (SNR). Ths loss of SNR can lead to reduced spectral accuracy, and false detecton of pulses, both effects servng to reduce spectral resoluton and ncrease spectral nose. In addton, such lnear flterng algorthms are unable to resolve closely spaced pulses; consequently pulse pleup remans a problem. Fg. 4 Wavelet decomposton tree by Symlet wavelet transform. 119

5 Fg. 5 Wavelet decomposton tree by Coflet wavelet transform. Fg. 7 Reconstructed sgnal from frst of Coflet wavelet transform by dfferent nterpolaton methods. Total Number of Counts Fg. 6 Reconstructed sgnal from frst of Symlet wavelet transform by dfferent nterpolaton methods. Fg. 8 Reconstructed sgnal from thrd of Symlet wavelet transform by dfferent nterpolaton methods. 120

6 Total Number of Counts Fg. 9 Reconstructed sgnal from thrd of Coflet wavelet transform by dfferent nterpolaton methods. Fg. 11 Total numbers of count by Coflet wavelet transform usng nterpolaton method. Total Number of Counts Total Number of Counts Fg. 10 Total numbers of count by Symlets wavelet transform usng nterpolaton method. 121

7 Table 1 Statstcs of dfferent methods for reconstructon by sym2 Wavelet Method MSE PSNR CC Inverse Wavelet Transform Level 1 Level 2 Level 3 FFT from 1 st level FFT from 2 nd FFT from 3 rd nearest from 1 st splne from 1 st cubc from 1 st nearest from 2 nd splne from 2 nd pchp from 2 nd cubc from 2 nd nearest from 3 rd splne from 3 rd pchp from 3rd cubc from 3 rd x x x x NaN NaN NaN NaN NaN NaN NaN NaN x x x Table 2 Statstcs of dfferent methods for reconstructon by cof1 Wavelet Method MSE PSNR CC Inverse Wavelet Transform Level 1 Level 2 Level 3 FFT from 1 st level FFT from 2 nd FFT from 3 rd splne from 1 st pchp from 1 st cubc from 1 st nearest from 2 nd splne from 2 nd pchp from 2 nd cubc from 2 nd nearest from 3 rd splne from 3 rd pchp from 3rd cubc from 3 rd x x x x NaN NaN NaN x NaN NaN NaN x x x

8 Table 3 Number of counts of dfferent wavelet transform technques usng FFT and nterpolaton Wavelet Method Number of Count usng FFT Number of Count usng nterpolaton Haar 7 12 Symlet 7 12 Coflet 7 13 Daubeches 7 12 Dscrete Meyer BorSplnes 7 12 IV. CONCLUSION Ths paper presents a method to evaluate the performance of lnear flter algorthms of gamma ray spectroscopy. Haar wavelet s the most common known technque n gamma ray spectroscopy n the lterature. To determne the accuracy of ths technque, a comparson study between dfferent wavelets approaches such as Haar, db, sym2, cof1, and Dmeyer wavelets are prepared. Ths comparson s based on a reference sgnal from 137 Cs acqured by data acquston system. We concluded that usng the Dscrete Meyer wavelet ntroduces better results over other wavelet transform for gamma ray spectroscopy. Also, t has low accuracy for achevng gamma ray spectroscopy, because t reduces sgnal to nose rato and consequently energy resoluton. REFERENCES [1] M. Bolc, and V. Drndarevc. (2002). Dgtal gamma-ray spectroscopy based on FPGA technology. Nuclear Instruments and Methods n Physcs Research. 482, pp [2] E. G.-Torano and J. M. Los Arcos. (1994). Lqud scntllaton countng by dgtal pulse heght analyss. Lqud Scntllaton Spectrometry, pp [3] I. I. Mahmoud, (2006). Sngle chp realzaton of a fast counter/tmer crcut used n dgtal pulse heght analyss. Arab Journal of Scence and Applcatons 39(1). [4] M. W. Raad and J. M. Noras. Moment preservng parameter estmaton and dgtal onlne peak localzaton algorthms for gamma ray spectroscopy. Avalable: [5] Optmzng the energy resoluton wth the DGF-4C, DGF-4C applcaton notes DGF-AN-001, Avalable: Pdf. [6] R. M. Lndstrom and R. F. Flemng. (1995). Dead tme, pleup, and accurate gamma-ray spectrometry. Radoactvty and Radochemstry 6(2). [7] G. F. Knoll, (2000). Radaton detecton and measurement. 3rd ed. John Wley and Sons, NY. [8] A. Aboshosha, M. Sayed, M. Ashour and A. Safwat, "Refnng of scntllaton detector sgnals relyng on nterpolated wavelets on a FPGA prototype," Arab Journal of Nuclear Scence and Applcatons, 2009, to be publshed. [9] M. Kamel, "Developng a DSP Core usng an FPGA Prototype for Scntllaton Detector Sgnals," Master of Scence Thess, Faculty of Engneerng, Al Azhar Unversty,