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UID:submissions.pasc-conference.org_PASC19_sess180_pap_jan119@linklings.co
 m
SUMMARY:Joint Inverse Medium and Optimal Control Problems for Acoustic Wav
 es
DESCRIPTION:Paper\nComputer Science and Applied Mathematics, Life Sciences
 \n\nJoint Inverse Medium and Optimal Control Problems for Acoustic Waves\n
 \nNahum, Seppi, Cattin\n\nBackground: Ever since endoscopes were invented,
  surgeons try to widen their field of usage by developing novel surgical a
 pproaches. An obvious advantage of the endoscope is the minimal invasivene
 ss, but this comes at a price of reduced dexterity, loss of tactile feedba
 ck and difficulty in orientation. One of the challenges is to acquire the 
 data of the neighborhood to find the relative position of the endoscope to
  the surrounding tissues.<br />Methods & Results: In this paper, we pr
 esent a mathematical approach to reconstruct unknown source(s) position(s)
  (e.g. endoscope, which produces a signal in different frequencies) and a 
 medium (e.g. tissue surrounding the endoscope). We solve the joint Inverse
  Medium and Optimal Control on the Helmholtz equation, where both source(s
 ) and medium velocity are unknown. The use of the Adaptive Eigenspace Inve
 rsion (AEI) in combination with frequency stepping, proofs itself to be a 
 good solution. We underline our claim, with two-dimensional numerical expe
 riments.<br />Conclusion: The application of this method together with its
  promising results can potentially aid to navigate an endoscope through th
 e body while collecting information on the surrounding tissue. These resul
 ts may also find their application in geophysics.<br /><br />https://doi.o
 rg/10.1145/3324989.3325718
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