The ray density estimation of a CT system by a supervised learning algorithm
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1 Te ray densty estaton of a CT syste by a suervsed learnng algort Nae : Jongduk Baek Student ID : 5459 Toc y toc s to fnd te ray densty of a new CT syste by usng te learnng algort Background Snce te develoent of te CT scanner te faster scan te was te gest rorty to aceve and terefore tere ave been a lot of efforts to reduce te scan te Te frst generaton CT scanner (Fgure (a)) uses one encl bea and te rojecton data were acqured by translatng te x-ray source and detector lnearly After te coleton of te lnear easureents te x-ray source and detector rotated to te next angular oston to acqure te next set of easureents A faster scan te could be aceved by usng ultle encl beas Snce ts second generaton CT scanner (Fgure (b)) used a sall fan bea te data acquston te was reduced by te sae factor of te ncreased detector nubers However a translaton-rotaton rncle was stll eloyed for data acquston Te trd generaton scanner (Fgure (c)) used a large nuber of detectors and a sngle source Snce te detector sze was suffcent to cover te entre object a translaton-rotaton rncle was not eloyed Te elnaton of te translaton ste reduced te scan te sgnfcantly and nearly all of te state-of-te-art scanners on te arket today are trd generaton Te otental roble of te trd generaton syste s te g detector cost and g scatter-to-rary rato In order to cobat tese robles a dfferent tye of CT geoetry can be agned as sown n Fgure (d) In ts syste nstead of usng one source and any detector cells t uses any sources and saller nuber of detector cells For exale f te trd generaton CT syste uses detector cells te new syste (Fgure (d)) ay eloy 5 detector cells and sources so tat te detector cost can be reduced by a factor of (a) Frst generaton CT (b) Second generaton CT
2 (c) Trd generaton CT Fgure Dfferent tyes of CT scanner (d) New CT syste Suervsed learnng and reconstructon Te reconstructon algort for te trd generaton CT syste was already develoed [] It uses te fltered backrojecton algort and te ray densty s coensated before te fltered backrojecton For exale te frst generaton CT syste as unfor ray densty because te ray sacng s unfor In contrast te ray densty of te trd generaton CT syste s non-unfor due to te dfferent data acquston geoetry and te analytcal exresson for te ray densty was develoed [] However t s very ard to fnd te analytcal exresson of te ray densty for te new syste So our goal s to estate te ray densty eurstcally Snce te fltered backrojecton can be exressed as one syste atrx we can exressed te reconstructon rocess as follows y A () were A s te syste atrx for te reconstructon y s te deal reconstructed value(or tranng data set) and s a ray densty vector tat we want to estate To fnd te ray densty for te new CT syste te reconstructon stes flterng and backrojecton are exressed as a atrx oeraton For a rojecton wt sales ray denstes and - reconstructon flter coeffcents are used As a tranng data set a centered-unfor-cylnder wc s large enoug for te ray densty estaton was used so tat te rojecton s te sae for all vews We wll ten verfy tat te sae ray densty works for oter objects Te ray densty ultlcaton and flterng for eac fan bea can be conducted by te followng atrx ultlcaton
3 A P H F ) ( () were F s te fltered rojecton for te t fan bea P s te rojecton data for te t fan bea s te ⅹ ray densty for te t fan bea and H s a (-)ⅹ atrx of flter coeffcents A s a (-)ⅹ atrx wose ters contan flter coeffcents and te t fan bea data Te fnal age s roduced by sung te backrojectons of eac fan bea Pxel-drven backrojecton of eac fltered rojecton usng lnear nterolaton [] can be descrbed by te followng equaton d v N N j j CT new A R _ () were N d s te nuber of detectors N v s te nuber of vews j contans te lnear nterolaton coeffcents of te t fan bea at te jt vew and R new_ct s te reconstructed age In equaton () j and A are known for tranng data set and s unknown By coarng R new_ct wt te deal tranng data set R tran te error vector E s defned as tran CT R new R E _ (4) Te ray densty wc nzes te nor of E was found by usng a conjugate-gradent etod [] usng T as te ntal guess Te root ean square (e rs) error was calculated as n eac teraton n E rs E (5) were n s te lengt of te error vector E 4 Result Te new CT syste as rays er vew and terefore needs a ray densty coosed of values Fgure (a) sows te rs error er teraton Te ntal rs error was 598 and after teratons t was reduced to 9 Fgure (b) sows te ray densty calculated usng te tranng data set after teratons
![Fgure (a) rs error er teraton and (b) ray densty for te new CT geoetry Te Se-ogan anto data [] was reconstructed by usng](/docs-images/90/103238400/images/4-1.jpg "te ray densty Fgures (a) and (b) sows te reconstructed ages wtout and wt alyng ray densty Fgures (c) and (d) lots te")
4 Fgure (a) rs error er teraton and (b) ray densty for te new CT geoetry Te Se-ogan anto data [] was reconstructed by usng te ray densty Fgures (a) and (b) sows te reconstructed ages wtout and wt alyng ray densty Fgures (c) and (d) lots te corresondng central rofles Coarson wt Fgures (a) and (b) sows tat te rngng artfacts were suressed sgnfcantly Ts result suorts te aroac of calculatng a ray densty for a unfor centered cylnder (eg tranng data set) and alyng t to an arbtrary object (a) (b)
5 (c) (d) Fgure Reconstructed ages and central rofles wt and wtout alyng te ray densty 5 Concluson For te ray densty estaton of a new CT syste suervsed-learnng algort was used Snce te ray densty of a new CT syste s very ard to derve analytcally eurstc etod (Newton etod by usng a suervsedlearnng) was leented Te estated ray densty fro te tranng data set works well for general object and te age qualty was sgnfcantly roved after usng te ray densty By addng soe constrants to te ray densty we ay exect te reduced varaton of te ray densty so tat te nose attern of a new CT syste can be unfor Reference [] A Kak and Slaney Prncles of Couterzed Toograc Iagng New York : IEEE Press 988 [] Jang Hse Couted Toogray Prncles Desgn Artfacts and Recent Advances Wasngton :SPIE Press [] cael T Healt Scentfc Coutng an Introductory survey cgraw-hll 5
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