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Published e sion
K upchyk, Ka ya; Salo, Mikko; Uhlmann, Gun he ; Wang, Jenn-Nan
K upchyk, K., Salo, M., Uhlmann, G., & Wang, J.-N. (2022). P e ace. In e se P oblems and
Imaging, 16(6), i-iii. h ps://doi.o g/10.3934/ipi.2022056
2022
In e se P oblems and Imaging
Vol. 16, No. 6, Decembe 2022, pp. i–iii
doi:10.3934/ipi.2022056
PREFACE
Ou es eemed colleague Vic o Isako passed away on May 14, 2021 a e a sho
illness. Vic o was an edi o o In e se P oblems and Imaging since i s incep ion
in 2007 and made many con ibu ions o he success o he jou nal. He also made
undamen al con ibu ions o he ield as indica ed below in he se e al a icles
w i en by his colleagues and iends. This issue is a ibu e o his memo y. He will
be so ely missed.
We shall now p oceed o desc ibe b ie ly he con en s o each o he 11 a icles
comp ising he special issue.
“On he scien i ic wo k o Vic o Isako ” by he gues edi o s begins wi h b ie
biog aphical in o ma ion and hen p oceeds o desc ibe in mo e de ail selec ed un-
damen al con ibu ions o Vic o Isako o he ield o in e se p oblems. The pape
concludes wi h he ull lis o publica ions o Vic o Isako oge he wi h a lis o
his Ph.D. s uden s.
“New no ions and cons uc ions o he bounda y con ol me hod” by Mikhail Bel-
ishe p esen s a su ey o he bounda y con ol me hod, in oduced by he au ho
back in 1988, wi h applica ions o in e se p oblems. Among he speci ic appli-
ca ions discussed in he pape a e in e se p oblems o he eco e y o a mani old
and a po en ial om he knowledge o he hype bolic Di ichle – o–Neumann map,
analogous in e se p oblems in he se ing o Maxwell’s sys em, in e se p oblems
o econs uc ing a Riemann su ace om he ellip ic Di ichle – o–Neumann map,
some esul s dealing wi h eikonal algeb as, he wa e spec um, and he so called
s-poin s in in e se sca e ing.
“A spec al a ge signa u e o hin su aces wi h highe o de jump condi ions”
by Fio alba Cakoni, Heejin Lee, Pe e Monk, and Yangwen Zhang s udies he in e se
p oblem o he eco e y o s uc u al p ope ies o a hin aniso opic and dissipa i e
inhomogenei y in he Euclidean space om he knowledge o he sca e ing da a a a
ixed equency. In he limi as he hickness ends o ze o, he hin inhomogenei y
is modeled by a co-dimension one submani old, called he sc een, and he ield
inside degene a es o jump condi ions along he sc een in ol ing a second o de
su ace di e en ial ope a o . The au ho s show ha he h ee sc een coe icien s,
o which one may be possibly ma ix alued, can be de e mined uniquely by he
ixed equency sca e ing da a. The in e sion me hod is based on a a ge signa u e
cha ac e ized by a no el eigen alue p oblem such ha he co esponding eigen alues
can be eco e ed om he measu ed sca e ing da a. Some p elimina y nume ical
esul s a e p esen ed as well.
“Two single–measu emen uniqueness esul s o in e se sca e ing p oblems wi hin
polyhed al geome ies” by Xinlin Cao, Diao Huai-An, Hongyu Liu, and Jun Zou
deals wi h an in e se obs acle sca e ing p oblem in he case o an impene able
obs acle wi h he impedance bounda y condi ion. Speci ically, in he se ing o
polyhed al geome ies, he au ho s ocus on he p oblem o he eco e y o he
i
ii PREFACE
shape o he obs acle as well as o he impedance pa ame e using only a single a -
ield measu emen a he han he a - ield ope a o . An in e se di ac ion g a ing
p oblem wi h single measu emen is also add essed in his pape .
In he pape “Global unique con inua ion om he bounda y o a sys em o is-
coelas ici y wi h analy ic coe icien s and a memo y e m”, Ma hias Elle , Nao umi
Honda, Ching-Lung Lin, and Gen Nakamu a es ablish a global unique con inua ion
p ope y om he bounda y o solu ions o a iscoelas ic sys em wi h analy ic co-
e icien s and a memo y e m. The global unique con inua ion p ope y is gi en in
e ms o he a el ime o he slowes wa e o he iscoelas ic sys em.
“Mic olocal analysis o bo ehole seismic da a” by Raluca Felea, Romina Gabu o,
Allan G eenlea , and Cli o d Nolan p o ides a gene al app oach o he analysis o
bo ehole seismic da a, using echniques o mic olocal analysis which ha e al eady
p o en o be ex emely powe ul o con en ional seismic da a. Bo ehole seismic
da a is collec ed by ecei e s loca ed in a well wi h sou ces loca ed on he su ace o
ano he well. The main ocus o he pape is on possible app oxima e econs uc ion
ia linea ized, il e ed backp ojec ion o an iso opic sound speed in he subsu ace
o he ollowing h ee ypes o da a se s: (i) he sou ces o m a dense a ay on he
su ace, (ii) he sou ces a e loca ed along a line on he su ace (walkaway geome y),
(ii) he sou ces a e in ano he bo ehole (c osswell).
“A uniqueness heo em o in e se p oblems in quasilinea aniso opic media”
by Md. Ib ahim Kholil and Ziqi Sun s udies he Calde ´on p oblem o impedance
omog aphy o quasilinea aniso opic conduc i i y equa ions wi h conduc i i ies
in he o m o a scala unc ion, depending on he spa ial a iable and he solu ion,
imes a ixed me ic ha depends only on he spa ial a iable. The au ho s p o e
ha he knowledge o he Di ichle – o–Neumann map o quasilinea conduc i i ies
de e mines he scala unc ion uniquely in he 2D case, eco e ing he esul o Sun–
Uhlmann (1997), as well as in he 3D case, assuming ha he ollowing, s ill open
conjec u e in 3D, holds: wo aniso opic conduc i i ies o he linea impedance
omog aphy p oblem wi h he same Di ichle – o–Neumann map a e pullbacks o
each o he ia a di eomo phism ha ixes he bounda y.
“Con exi ica ion-based globally con e gen nume ical me hod o a 1D coe i-
cien in e se p oblem wi h expe imen al da a” by Michael Klibano , Thuy Le, Loc
Nguyen, Ande s Sulli an, and Lam Nguyen de elops a new e sion o he con exi i-
ca ion me hod o sol ing nume ically coe icien in e se p oblems o 1D hype bolic
equa ions. In doing so he au ho s p o e a new e sion o he Ca leman es ima es
and use hese es ima es o cons uc a globally s ic ly con ex cos unc ional. The
desi ed nume ical solu ion o he coe icien in e se p oblem is ob ained by minimiz-
ing he cons uc ed cos unc ional by he g adien descen me hod. The au ho s’
con exi ica ion me hod p o ides a good app oxima ion o he exac solu ion wi h-
ou equi ing a good ini ial guess. Nume ical s udy o bo h expe imen ally collec ed
and compu a ionally simula ed da a a e gi en.
“Re ined ins abili y es ima es o some in e se p oblems” by Pu-Zhao Kow and
Jenn-Nan Wang es ablishes ins abili y es ima es o wo in e se p oblems: (i) in-
e se inclusion p oblem in he elec ical impedance omog aphy, (ii) in e se acous ic
sca e ing p oblem. Fo he i s in e se p oblem, he au ho s analyze how he in-
s abili y depends on he dep h o he hidden inclusion and he conduc i i y o he
backg ound medium, and show ha he exponen ial ins abili y becomes wo se when
he inclusion is hidden deepe inside he conduc o o he conduc i i y is la ge . Fo
PREFACE iii
he second in e se p oblem, he au ho s in es iga e how he exponen ial ins abil-
i y o eco e ing he nea - ield o a adia ing solu ion o he Helmhol z equa ion
om he a - ield pa e n is a ec ed by he equency and p o e ha he ins abili y
changes om an exponen ial ype o a H¨olde ype when he equency inc eases.
“Kan o o ich-Rubins ein me ic based le el-se me hods o in e ing modulus o
g a i y- o ce da a” by Wenbin Li and Jianliang Qian p oposes o use he Kan o o ich-
Rubins ein me ic as a no el mis i unc ion o he le el-se based app oach o in-
e se g a i y p oblems. The al e na ing di ec ion me hod o mul iplie s (ADMM)
algo i hm is used o he esul ing op imiza ion p oblem. Nume ical examples a e
gi en o demons a e he e ec i eness and pe o mance o he p oposed algo i hms.
“Linea ized in e se Sch ¨odinge po en ial p oblem wi h pa ial da a and i s deep
neu al ne wo k in e sion” by Sen Zou, Shuai Lu, and Boxi Xu s udies he linea ized
in e se bounda y p oblem o Sch ¨odinge –Helmhol z equa ions wi h pa ial da a.
Speci ically, i deals wi h he si ua ion when he Di ichle bounda y da a is sup-
po ed in a subse o he bounda y o he domain while he inaccessible pa o he
bounda y is a pa o a hype plane. H¨olde ype inc easing s abili y es ima es a e
ob ained o la ge equencies, and a deep neu al ne wo k app oach is applied o
nume ically sol ing his linea ized in e se p oblem.
We would like o exp ess ou since e g a i ude o all he au ho s o hei con-
ibu ions o his special issue. We would also like o hank Ziqi Sun o p o iding
use ul ma e ial ela ed o he wo k o Vic o Isako .
Gues Edi o s:
Ka ya K upchyk
Uni e si y o Cali o nia, I ine, USA
ka ya.k upc[email p o ec ed]
Mikko Salo
Uni e si y o Jy ¨askyl¨a, Finland
mikk[email p o ec ed]
Gun he Uhlmann
Uni e si y o Washing on / HKUST, USA
gun[email p o ec ed]ashing on.edu
Jenn-Nan Wang
Na ional Taiwan Uni e si y, Taiwan
jnw[email p o ec ed] u.edu. w