FPGA Implementation of Ultrasonic S-Scan Coordinate Conversion Based on Radix-4 CORDIC Algorithm

Transcription

1 IACSIT Internatonal Journal of Engneerng and Technology, Vol. 7, No. 3, June 25 FPGA Implementaton of Ultrasonc S-Scan Coordnate Converson Based on Radx-4 CORDIC Algorthm Ruobo Ln, Guxong Lu, and Wenmng Tang Abstract To solve the exstng problems on tradtonal method of callng functon at ultrasonc S-scan coordnate converson, ths paper ntroduced the FPGA mplementaton of ultrasonc S-scan coordnate converson based on Radx-4 CORDIC algorthm. On the analyss of the Radx-4 Rotaton CORDIC algorthm, we selected 7-level ppelne structure on FPGA, used the preprocessng technque to solve the non-constant problem of scale factor. The smulaton results show that the maxmum error of Radx-4 Rotaton CORDIC algorthm s.5-3 and the computng latency s only 7T at 6 bt data-wdth under MHz FPGA. The scan converson rate speed up at least tmes, and the output effect of the mage s bascally the same as the tradtonal method. The algorthm has the characterstcs of low latency, hgh speed and hgh precson, sutable for real-tme sgnal processng applcatons. Index Terms Ultrasonc s-scan, coordnate converson, radx-4 cordc, FPGA, real-tme sgnal processng. I. INTRODUCTION Ultrasonc detecton technology was frst used n mltary radar and medcal B mode ultrasound, but now has been wdely used n ndustral phased array []-[3]. Dgtal Scan Converson (DSC) s one of the key technologes n sgnal processng, ncludng coordnate transformaton and lnear nterpolaton. Tradtonal method transfers the polar coordnates nto Cartesan coordnates by callng functon drectly, costng more tme, requrng larger space for data storng, and resultng a lot of redundant data. Therefore many scholars have studed varous algorthms on the dgtal scan converson, whch the CORDIC (Coordnate Rotaton Dgtal Computer) algorthm s one of the most typcal algorthms. For example, Skdar (2) used tradtonal CORDIC algorthm to realze the coordnate transformatons of B mode ultrasound lnear scan based on MAP-CA processor, wth onlne programmng and solvng the coordnate s converson effectvely []. Tan (23) realzed the coordnate converson of B mode ultrasound lnear scan based on tradtonal CORDIC algorthm, solvng the converson of Cartesan coordnate to polar coordnates [4]. The above research s focus on the B mode ultrasound lnear scan. However, the sector scan (S-scan) s manly used n ndustral Ultrasonc detecton. Many scholars have studed the applcaton of CORDIC algorthm on S-scan. Zeng (2) Manuscrpt receved June 3, 24; revsed July 22, 24. Ruobo Ln s wth the Department of Electrcal and Mechancal Engneerng, Jeyang Vocatonal and Techncal College, Jeyang, Chna (e-mal: lnruobo@26.com) Ruobo Ln, Guxong Lu, and Wenmng Tang are wth School of Mechancal & Automotve Engneerng, South Chna Unversty of Technology, Guangzhou, Chna used Radx-4 vector CORDIC algorthm to realze coordnate transformatons of B mode ultrasound, whch he ponted out the shortcomngs of Radx-2 algorthm and the advantages of Radx-4 algorthm, but they haven t dscussed n detal on the practcal applcaton yet [5]. Lu (24) studed the delay focusng and magng technology of ultrasonc phased array, and put forward the FPGA mplementaton of Radx-2 CORDIC algorthm usng complement method [6], [7]. Now the method of Lookup table or drectly callng functon on FPGA s stll used on ultrasonc scan coordnate converson wth the shortcomngs of long latency and slow speed. Ths paper wll use Radx-4 rotaton CORDIC algorthm to realze coordnate converson of ultrasound S-scan on FPGA, whch has an mportant practcal value n mprovng the real-tme sgnal processng. The paper s arranged as follows: the second part ntroduced the theory of ultrasonc S-scan converson prncple, the Radx-4 CORDIC algorthm mechansm and realzaton on FPGA, the thrd part ntroduced the smulaton and analyss of Radx-4 Rotaton CORDIC algorthm, fnally draw a concluson. II. THEORY A. Ultrasonc S-Scan Coordnate Converson Prncple There are many modes on ultrasound scan, such as A-scan, B-scan, C-scan and S-scan etc. Ultrasonc S-scan s that the ultrasonc transducer puts the dfferent transmt pulse sgnals to dfferent phase through dfferent array elements, and the probe scans the sector area along an angle, whch each orgnal beam rotates around the Y axs, and samples along the radal drecton on dfferent echo. All ponts of ultrasonc echo data are stored on polar form n the data memory. The polar coordnate system s converted nto the correspondng Descartes coordnate system after nterpolaton and flterng, and output 2-Dmenson mage on screen. Ths process of dgtal converson corresponds to the converson of polar coordnate to Cartesan coordnate system. The comparson chart of coordnate converson s shown n Fg., whch the frst method used tradtonal method of callng functon and the second used Radx4 CORDIC algorthm module. The tradtonal method drectly calls the DSP system functon usng a lot of multplers and dvder, whch causes the system resource overhead, long delay, and data congeston. For hgh precson, the Lookup table memory resources are n bg demand, whch s dffcult for real-tme processng. Ths paper used Radx-4 CORDIC algorthm module to realze coordnate converson, whch could convert a lot of trgonometrc functon operatons nto DOI:.7763/IJET.25.V

2 IACSIT Internatonal Journal of Engneerng and Technology, Vol. 7, No. 3, June 25 add operaton and shft operaton, wth sutable for FPGA mplementaton and real-tme processng. Coordnate converson DSP system Ultrasonc echo data (r,φ ) Interpolaton Focus Flter Callng sne and cosne functons Image data output (x,y ) Lookup table (a). Coordnate converson on tradtonal method of callng functon. Ultrasonc echo data (r,φ ) Interpolaton Focus Flter Radx4 CORDIC algorthm module Image data output (x,y ) (b). Coordnate converson on usng Radx4 CORDIC algorthm. Fg.. The comparson chart of coordnate converson on tradtonal mode and usng Radx4 CORDIC algorthm The model graph of Cartesan coordnates and polar coordnates s shown n Fg. 2. We defne the pont of Cartesan coordnates as P (x, y ), whch x and y are expressed as horzontal coordnates and vertcal coordnates of Cartesan coordnate system. We also defne the pont of polar coordnates as P(r, φ ), whch r and φ are expressed as the polar radus and polar angle. Thus the mathematcal expresson of polar coordnate to Cartesan coordnate system can be expressed as formula (). x = rcosϕ { y = r snϕ The mage data, wth huge data volume, demands a lot of work when converson processon. It s very mportant to mprove the coordnate converson of ultrasound scan f a CORDIC algorthm module on FPGA real tme operaton s desgned. φ P(r,φ ) r y V V V V 2 V 3 V (a). Polar coordnates (b). Cartesan coordnates Fg. 2. The model graph of Cartesan coordnates and polar coordnates. φ x r P(x,y ) V 2 V 3 () B. Radx-4 CORDIC Algorthm Mechansm Radx-4 CORDIC algorthm has two operaton modes: rotaton mode and vectorng mode [8], [9]. The sne and cosne of any angle can be calculated on rotaton mode whch realzed the converson of Cartesan coordnates to polar coordnate. The operaton of square root and the arctangent functon can be realzed on vector mode, whch realzed the converson of Cartesan coordnates to polar converson. In ths paper, we focus on the rotaton mode whch wll be dscussed as followed. The basc teratve equatons of Radx-4 Rotaton CORDIC algorthm [8] are: x+ = x σ 4 y y+ = y + σ 4 x z+ = z arctan( σ 4 ) where, σ { 2,,, +, + 2}, After n-teratons x and y wll have a gan of the scale factor K, whch can be expressed as formula (3). We defne a new varable: (2) n 2 2 /2 ( σ 4 ) (3) = K = + w The value of σ s determned by the convergence value of w. = 4 z 25

3 IACSIT Internatonal Journal of Engneerng and Technology, Vol. 7, No. 3, June 25 For = For > + 2 5/8 w + 3/8 w < 5/8 σ = /2 w < 3/8 7/8 w < /2 2 w 7/ /2 w + /2 w < 3/2 σ = /2 w < /2 3/8 w < /2 2 w 3/2 when x =,y =, z = ϕ,after n-teratons, w, the equaton wll be transformed as formula (6). xn+ = K yn+ = K zn+ = cosϕ snϕ Accordng to the teraton results of x n+ and y n+, the sne and cosne values of angle can be calculated as: cos sn ϕ = Kx+ ϕ Ky+ =. C. Radx-4 CORDIC Algorthm Realzaton on FPGA We used ppelnng archtecture on FPGA mplementaton. As the scale factor K s not a constant, the pretreatment technque s used. Accordng to the dfferent values of σ, we translated k and arctan( σ 4 ) nto constant by Lookup table. Thus the teratve process s translated nto add and shft operatons, whch the computng speed can be accelerated. If the angle s represented by 6 bt bnary number, the angle resoluton s expressed as 36 /(65536-)=.55. As the angle resoluton of CORDIC algorthm has not resolved after 7-teratve, so we use 7-level ppelne archtecture to realze algorthm on FPGA. The -level ppelne structure dagram on FPGA s shown n Fg. 3. x RX 4-2 MUX3 2 MUX4 y RW z RZ 4-4 Arctan Table w Compactor Module σ Calculate K (4) (5) (6) begn f(w[] > 35225) //w[]>3/2 begn //sgma <= 2 x[3]<=x[2] - {{{y[2][5]}},y[2][5 : ]}; y[3]<=y[2] + {{{x[2][5]}}, x[2][5 : ]}; z[3]<=z[2] - 88; Kx[2] <= 5867; // 65536*/sqrt[ + 4/6]; else f(w[] > 7342) ///2 begn //sgma <= x[3]<=x[2] - {{2{y[2][5]}}, y[2][5 : 2]}; y[3]<=y[2] + {{2{x[2][5]}}, x[2][5 : 2]}; z[3]<=z[2] ; Kx[2] <= 63579; End III. SIMULATION A. System Resource Usage Based on the Quartus II9., we have smulated on Cyclone II: EP2S5F484C6 FPGA to observe system resource usage. The system resource usage of algorthm usng ppelnng archtecture s lst at Table I. We can fnd that the system resources usage of algorthm s very low whch s only 78 logc elements, 282 logc regsters, 6 multplers and PLLs. TABLE I: THE SYSTEM RESOURCE USAGE OF ALGORITHM USING PIPELINING ARCHITECTURE Logc Logc elements regsters Multpler PLLs usage total rato 2% 2% 3% % TABLE II: COMPARISON TABLE ON THE ACCURATE AND CALCULATED VALUE OF COSINE AT ANY ANGLE angle accurate value calculated values φ( ) of cosne of cosne calculaton error x + y + z + Fg. 3. The -level ppelne structure dagram on FPGA. Here are some codes of the comparson and teratve process at the 2-level ppelne archtecture. // level ppelne assgn w[] = 4 z[2]; clk) k B. Calculaton Speed On the analyss of the algorthm, we selected the angle of degree as the object of observaton. The tmng smulaton waveform s shown n Fgure 4. If the system clock s T, the computng latency of sne and cosne functon s 7T. For an mage of 6 42 pxel under MHz FPGA, consderng the non-operatonal latency as 3T, the total converson tme of mage s t=6 42 7T+3T =.8ms. However, 25

4 IACSIT Internatonal Journal of Engneerng and Technology, Vol. 7, No. 3, June 25 the converson tme of same mage s 2 ms for B mode and 2.3 ms for color mode under 3 MHz by callng functon method on the MAP-CA processor []. So the scan converson rate of algorthm would mprove the effcency at least tmes than the tradtonal algorthm Fg. 4. The tmng smulaton waveform of any angle on FPGA. C. Error Analyss Based on the Modelsm6.5, we have smulated on Cyclone II: EP2S5F484C6 FPGA to analyze the precson of algorthm, where the clock frequency s MHz and the data wdth s 6 bt. In order to mprove the resoluton of data operatons, we expand 892 tmes to sample data. At Table II we gve the cosne values of part of angle on FPGA operaton, where the maxmum calculaton error s 3-4. The calculaton error of sne functon s shown n Fgure 5 when the angle s between -9 degrees and less than 9 degrees, where the maxmum calculaton error s.5-3. calculaton error converson, based on PA2 ultrasonc phased array nstrument made n Guangzhou Doppler Electronc Technology Co., Ltd., the S-scan orgnal mage data s sampled. S-scan data acquston parameters of ultrasonc phased array are lst n Table III. Respectvely usng the tradtonal method of callng functon and Radx-4 Rotaton CORDIC algorthm module to read the mage data, we would acheved the output mage by coordnate converson, and compare ther output effect based on Matlab. The comparson chart s shown n Fg. 6. The test results show that the magng qualty s bascally the same (the orgnal mage wth pxels changed to pxels after nterpolaton) n two ways conversaton. Thus, the method of usng Radx-4 Rotaton CORDIC algorthm module could effectvely replace the tradtonal method of callng functon n mage processng. TABLE III: S-SCAN DATA ACQUISITION PARAMETERS OF ULTRASONIC PHASED ARRAY focus rule number samplng data ponts scannng angle step angle range ~ angle φ( ) Fg. 5. The operaton error of sne functon at φ=[-9 ~9 ]. (a) tradtonal method of callng functon (b) Radx-4 Rotaton CORDIC algorthm. Fg. 6. Comparson effect chart of the output mage after coordnate converson. D. Output Effect To verfy the output effect of scannng mage coordnate IV. CONCLUSION In ths work, we used Radx-4 Rotaton CORDIC algorthm module to realze the ultrasonc S-scan mage coordnates converson, used the pretreatment technque to solve the non-constant problem of scale factor K. Snce the workload of mage data converson process s very huge, ncludng a large number of functonal operatons, ths work has very hgh applcaton value on mprovng the speed of computaton. The smulaton results show that the maxmum error of Radx-4 Rotaton CORDIC algorthm s.5-3 and the computng latency s only 7T at 6 bt data-wdth under MHz FPGA. Compared wth the tradtonal method of callng functon, the scan converson rate speed up at least tmes, and the output effect of the mage s bascally the same as the tradtonal method. ACKNOWLEDGMENT Ths work was partally supported by the natonal major scentfc nstrument and equpment development project of Chna n 23(No. 23YQ23575). 252

5 IACSIT Internatonal Journal of Engneerng and Technology, Vol. 7, No. 3, June 25 REFERENCES [] S. Skdar, R. Managul, T. Mtake, T. Hayash, and Y. Km, Programmable ultrasound scan converson on a meda processor-based system, n Proc. the Socety of Photo-optcal Instrumentaton Engneers(SPIE), vol. 439, pp , 2. [2] S. Wang, B. Wen, C. Wang, Z. Yan, K. L, and J. Yang, UHF surface dynamcs parameters radar desgn and experment, IEEE Mcrowave and Wreless Components Letters, vol. 24, no., pp , 24. [3] G. X. Lu, W. M. Tang, and D. J. Tan, Focusng tme delay technology of ultrasonc phased array based on multstage half-band flter, Optcs and Precson Engneerng, vol. 22, no. 3, 24. [4] Y. Y. Tan and Z. Nng, An mage processng system scheme n b mode ultrasonc ophthalmologcal scanner, n Proc. the 6th IEEE Symposum on Computer-Based Medcal Systems (CBMS 3), pp , 23. [5] P. Zeng, F. Lu, and X. Q. Zhao, The effcent realzaton of B mode ultrasonc dgtal scan converson based on radx-4 CORDIC algorthm, n Proc. 2 4th Internatonal Congress on Image and Sgnal Processng (CISP 2), 2, vol. 5, pp [6] G. X. Lu, L. Chou, and W. M. Tang, Synthetc focusng technology based on correlaton-delay n ultrasonc magng, Chna Measurement and Test, vol. 4, no., pp , 24. [7] R. B. Ln, G. X. Lu, and W. M. Tang, CORDIC algorthm on FPGA for general formula of sne and cosne based on complement method, Chna Measurement and Test, vol. 4, no. 4, 24 [8] E. Antelo, J. Vllalba, J. D. Bruguera et al., Hgh performance rotaton archtectures based on the radx-4 CORDIC algorthm, IEEE Trans. Computers, vol. 46, no. 8, pp , 997 [9] J. Vllalba, E. L. Zapata, and E. Antelo, Radx-4 Vectorng CORDIC Algorthm and Archtectures, Journal of VLSI Processng Systems for Sgnal Image and Vdeo Technology, vol.9, no. 2, pp.27-47, 998. Ruobo Ln was born n 974. He s currently an assocate professor, He receved a lecturer n Xdan Unversty, x an, Chna n 996. He receved hs master degree from Hunan Unversty, Changsha, Chna, n 29. He s a vstng scholar of South Chna Unversty of Technology now. Hs research nterests nclude electromechancal ntegraton technology, sgnal processng, nstrument, measurement and control technology. Guxong Lu was born n 968. He s currently a professor and as a doctoral supervsor n South Chna Unversty of Technology, Guangzhou, Chna. He receved hs doctor degree from Chongqng Unversty, Chongqng, Chna, n 995. Hs research nterests nclude modern detecton technology and networked control, ntellgent sensng theory and method, nformaton system modelng theory and applcaton. Wenmng Tang was born n 983. He s currently a assocate professor, He receved a lecturer n Harbn Unversty of Scence and Technology, Harbn, Chna n 25. He receved hs master degree n Harbn Unversty of Scence and Technology, Harbn, Chna n 28. He s currently pursung doctor degree at School of Mechancal and Automotve Engneerng n South Chna Unversty of Technology. Hs research nterests nclude ultrasonc nondestructve testng, sgnal processng. 253