ECE380_Midterm1_Solution

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Electrical Engineering

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Dec 6, 2023

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I/' ECE/BIOE 380 (Fall 2023) Biomedical Imaging Midterm Exam October 19, 2021 7:00 - 10:00 pm Closed book, closed notes, no formula sheets, conventional calculators allowed (not on a smart P.hone/tablet/comP.u~ ~~u:e_nt_N_am_e=~~ ~S::==o=~L::~u~~ = T:=1::0:,:~=: / ===- Problem 1 (40 points): Problem 2 (30 points): Problem 3 (20 points): Problem 4 (10 points): Problem 5 (10 points): Problem 6 (10 points): Problem 7 (12 points): Problem 8 (18 points): Total ( 150 points): I '

1. Circle the b t 1 ) (T e ~~ swer._ (2pts each question, 40 pts total) . ~e or~ A high k 0 _ 1 value indicates a wide point-spread-function and hence poorer spatial resolution. 2 ) (True o@ Fine details of an image tend to cluster near the center of the 2-D Fourier transform of the image. 3) ~ or False) In an x-ray tube , if the applied voltage is less than the k-shell binding energy of the target, then ka characteristic x-rays would not be generated. 4) ~ or False) Deeper tissues (with respect t_o x-ray source) are more susceptible to Comp ton scattering because of the beam hardenmg. 5) S or False) We inject iodine-based contrast for coro~ary arte~ exams because iodine increases x-ray attenuation and thus decrease the x-ray signal received by the detector. 6) Which of the following processes (select all that apply) involve ejection of electrons from the target atoms? a. Bremsstrahlung radiation @= haracteristic radiation c. Rayleigh scattering @): ompton scattering ("E)Photoelectric effect Y Pair production 7) (True or~ The overall system spatial resolution (or point spread function) 1s determine~e system component that has the narrowest/best PSF. 8) ~ or False) Increasing source x-ray energy is helpful for obese patients in the context of signal-to-noise-ratio because it compensates for the increased x-ray attenuation and casts more photons on the detector. 9) (True o~ To properly capture an image object with sinusoidal patterns (e.g., sine or cosine waves) and the smallest wavelength being 1 mm, the pixel or detector size of the imaging system should be at least I mm to avoid aliasing. 10) Which of the following factors influence the photoelectric effect? (select all that apply) @ Atomic number of tissue {3) X-ray energy c. Tissue density d. Electron density e. Mass attenuation coefficient 11) (True o~ Characteristic radiation only occurs when the K-shell electrons are ejected. 12) (True _or Q A higher density_ material or tissue always produces more Compton scattermg ~ hat of a lower density material. 13) fr~ r False) The reason why bone appears brighter than air in x-ray imaging is because ~ s higher x-ray attenuation. 2

14 ) O. r False) s ft · . . . ~ 0 tissue trans1t1ons from predominantly photoelectric effect to Compton hi h enng fa st er than does the bone with increased x-ray energy because soft tissue has g er electron density than bone. lS) ~ r False) The lower the HVL (half-layer value) of an x-ray source, the lower the x- ray energy. 16 ) (True o~ For screen film-based x-ray imaging systems, a thicker screen provides better spatial resolution because it converts more x-ray photons into visible ones. 17) The following factors result in a slower helical CT scan (select all that apply): (i) Low pitch number b. Large number of detector arrays (in z-axis) c. Large slice thickness ( or detector size in z-axis) d. Small field-of-view (FOV) in z-axis e. None of the above 18) (True ~ The fan-beam geometry requires less projections to be collected than does the par~m geometry because each projection angle encompasses a range of angles instead of only one. 19) (True o@ In CT, to avoid aliasing, one needs to reduce the step angle ti0 and increase the number of projections. 20) G r False) Backprojection generates blurred CT images because it under-samples the high-frequency range of the Fourier k-space. 2. Short answers (10 pts each, 30 pts total) 1) In two to three sentences, describe the tradeoff between x-ray energy and x-ray imaging quality. X-Y~ <?A'<?tr9~ t --;?.> qt. pJwio,._J A~eo( 1-> SNR. t x-~ (?,f\~~ t ~ Cr..r1n,. ~ieri"J 1 ➔ kb~ t J,es"~~ \I; , __ ifAj ~IK9'J t -> pl,-6,elec, t>.c. ~~~ ~ i 3

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2) As shown below . artifacts A .' an image of the face of a clown (left) was contaminated by some stripe · certain type of i · th" · d · remove th . . . mage processing was performed on 1s contaminate image to this mi ht eb st npe artifact (right). In two-three sentences. describe what kind of processing g e a nd how was the stripes removed? Contaminated Processed TJ..e ~,es~ be Y'f Y~ ~ ~ bctN>(-f;.,...ie,,( ~ <eJ . c.. ;(),~ of Oetta. ~) M ~ Le ea.~1fJ ,{iUer${ (JIM)' ~ a • ,w iJ.. f Uer- •· ( e-5., c... 1,o,,.rA. - stvp frUer) w ~ s~l' po,t"fill>\td o:/J -IJ..e Velta f-t,/})\. i~~s: J 3) Describe the process of filtered backprojection in CT image reconstruction . I. I() n 1 pwij-w;i'lh-.r },, Ul.) -tis Jet 60 ((') ;;_. FiUe-r 619 (f) e,.,c ·t~ ftU~ IP/ 3. ZFT fiUer-erJ G,cp) CeJ /Pl U"cf)) 'O) 5e:t r -~ pwJedillh. g9 I ( ~) 'f. M. f >o J t4i Jo '< rl) tJ Je:ft 4< c Xtj) 4

3. For the spatial im corresponding im ag~s and the 2-0 Fourier Transfonns shown belo w. sketch th e missing age m the other domain . (10 pts each, 20 pts total) 4. X-ray Generation and Spectrum. Below is a set of x-ray spectra for a tungsten anode at a tube voltage of 80, 100, 120, and 140 keV. (5 pts each question, 10 pts total) 70 , 000 T""-------r----------, .J eo . ooo • I 50, ooo ; f 40 , 000 0 a 30. ooo .: i 20,000 ,f 10 , 000 a: A o 10 20 30 40 50 eo 10 eo 90 100 110 120 130 140 Energy (ktV) I) On the graph, label each radiation curve with the corresponding x-ray tube voltage. 2) What are the names of the types of radiation for the two regions marked A and B? Explain how the x-ray radiation is generated in these two regions (in 2-3 sentences). A: ~ert rti, ya,,t,~ : 9&~ 'J IMJV~ of e(A6,,,.s• p.r,.. DlrM.r kD. 1:P (hi.er~ , uk,e AIU/"¢ efu4-,,,.s are tje,,,ted. l:,;J , 4~ ~J' . i · B~s-t r~ raPU~ : g&-6,Q)«J 'J c.ower.n · r-. 'ef- k..Wi<. ~J 1 1 ka'dev6 ~s J.ece~ '.J l~MdeuJ,. tru;v6 ~~~

r 5. Based on the attached F . functions: rect(x) o(ur)ier transform tables, calculate the convolution between two reel • . , * rect x (10 pts) F { )'w(i ( '<) * te..tl ( >c) J = F { J,ec;,t (K) j . Ff te.<,tc ,c) j :=, S-,1' (.. ( S ) • S'1J\ ' ( .f ) - ~i~~(SJ {:7-i { ~I~ a G ( J) J 1:n~Ul. (x) - - 6. 100 trillion (lx10 14 ) x-ray photons with energy of 62.4 keV were emitted to a small area of tissue (2 cm 2 ) with an exposure time of 0.5 second: (5 pts each question, 10 pts total) I) What is the initial intensity of the x-ray in unit ofWatts/cm 2 ? (lJ = 6.24 x 10 18 eV) 62 -4' kev . Ix,.,•"==- 6°. l,'fJ x , " ' a -e v = I J ( J o.SS - - I w/"'" ~ 2) The tissue has a mass attenuation coefficient of0.5 cm 2 /g, and a density of2 g/cm 3 • Based on answer in 1), what is the intensity of the x-ray after passing through 20 cm of the tissue? vi.A.= o, 5 e,t,,i .. / i J . 2 JI {At4 =- I ~-I 1 ' == 1 _ -44,c I \,v - I~-• . 2,1>v~ e - - .e - ~a.. - - I • e -20 w

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7 · Match the objects on t he left with thei r corresponding sinograms on the right. (l pts each, 12 pts total) a 1 I .. • .. • - ... ... • ■ • • • ~ m ~ ~ b \2 .. + ... "' • • • • • m ,. ,. ,a C 13 .. J ... ,.. • ■ - ■ - - - - - d z 3 ... "' lO ~ m C Q 1» ,. IW 1m e Js ·~ 2 ... "' " .. .. - "" llO UO 1• I ■ f 0 ~ ·~ :00 0 "' ... "' " ■ " ., llDBIU O ltoU D ·- 7

V 8 ' i~S pts total) A patient is prescribed for a liver CT exam. The desired FOY size is 20 cm x d . cm ~ 2 0 cm (FOVx X FOVy x FOVz). with a spatial resolution of I mm x. y. and z 1mens1on. 8 - 1 How many projections do you need to accurately reconstruct a single slice of the image? (6 pts) ~0~ 2o~ .2.Xf fllM 0. c) J r-a.ol -==- - t-> - 2ovm - # P"'J~.r::: 7C . .. ~ dlS °'oJrao( 8.2 If the CT system is a 16-slice scanner with a detector size (or slice thickness) of 1 mm, how long does it take to scan the patient's liver if each slice (as in a single-slice system) takes Is to scan? ( 6 pts) 16~ T.,ta). J~ tlh-..t. ~ f 3 X. I J' == 13 S. 8.3 If the set of x-ray projections in the spatial frequency domain is represented by P(k,0), and the filter to be applied to the filtered backprojections is represented by H(k) = lkl , then write the expression for the filtered backprojections in the spatial frequency (k 1 0) domain and in the spatial (r,0) domain. (6 pts) ~ r lR, t')) x l k, 8