denoiSpli : a me hod o join mic oscopy
image spli ing and unsupe ised denoising
Ashesh Ashesh and Flo ian Jug
Fondazione Human Technopole, Viale Ri a Le i-Mon alcini 1, 20157 Milan, I aly
[email p o ec ed], [email p o ec ed]
Abs ac . In his wo k, we p esen denoiSpli , a me hod o ackle a
new analysis ask, i.e. he challenge o join seman ic image spli ing
and unsupe ised denoising. This dual app oach has impo an appli-
ca ions in luo escence mic oscopy, whe e seman ic image spli ing has
impo an applica ions bu noise does gene ally hinde he downs eam
analysis o image con en . Image spli ing in ol es dissec ing an image
in o i s dis inguishable seman ic s uc u es. We show ha he cu en
s a e-o - he-a me hod o his ask s uggles in he p esence o im-
age noise, inad e en ly also dis ibu ing he noise ac oss he p edic ed
ou pu s. The me hod we p esen he e can deal wi h image noise by in-
eg a ing an unsupe ised denoising sub ask. This in eg a ion esul s in
imp o ed seman ic image unmixing, e en in he p esence o no able and
ealis ic le els o imaging noise. A key inno a ion in denoiSpli is he
use o speci ically o mula ed noise models and he sui able adjus men
o KL-di e gence loss o he high-dimensional hie a chical la en space
we a e aining. We showcase he pe o mance o denoiSpli ac oss mul-
iple asks on eal-wo ld mic oscopy images. Addi ionally, we pe o m
quali a i e and quan i a i e e alua ions and compa e he esul s o ex-
is ing benchma ks, demons a ing he e ec i eness o using denoiSpli : a
single Va ia ional Spli ing Encode -Decode (VSE) Ne wo k using wo
sui able noise models o join ly pe o m seman ic spli ing and denoising.
1 In oduc ion
Fluo escence mic oscopy emains a co ne s one in he explo a ion o cellula
and sub-cellula s uc u es, enabling scien is s o isualize biological p ocesses
a a ema kable le el o de ail [9, 22]. Howe e , he abili y o dis inguish and
analyze mul iple s uc u es wi hin a single sample equi es a mul iplexed imaging
p o ocol ha equi es ex a ime and e o [22]. To add ess hese downsides and
enable o mo e e icien and new ypes o in es iga ion, a powe ul me hod o
seman ic image spli ing was ecen ly in oduced [1].
Building on his p e ious wo k [1], we add ess a key challenge ha pe sis ed:
noise in mic oscopy images and i s ad e se e ec on he quali y o image-spli ing
p edic ions. Recognizing he need o a me hod capable o handling noisy inpu
images while main aining he in eg i y o he seman ic spli ing ask, we in o-
duce a echnique ha no only builds on he s eng hs o µSpli [1] bu also
2 Ashesh, F. Jug
Fig. 1: Tease Figu e. In his wo k we use a a ia ional encode -decode ne wo k
o join ly sol e an usupe ised denoising and image spli ing ask and show ha ou
app oach ou pe o ms exis ing baselines.
inco po a es unsupe ised denoising capabili ies, o example as in [15, 19–21].
Figu e 1 ou lines he o e all app oach we a e p oposing.
Toge he , hese ing edien s lead o a new me hod denoiSpli . I e ines he
p ocess o image decomposi ion, ensu ing ha e en unde high le els o pixel
noises p esen in he en i e body o a ailable aining da a, he seman ic in-
eg i y o he seman ically spli image componen s ( he p edic ions) is well p e-
se ed. Addi ionally, denoiSpli can assess da a unce ain y by sampling om
he lea ned pos e io o possible spli ing solu ions, ollowed by e alua ing he
in e -sample a iabili y. In Sec ion 4, we show how o use his possibili y o
p edic he expec ed e o denoiSpli makes on a gi en inpu .
In summa y, we belie e ha his wo k will open new a enues o he e icien
and de ailed analysis o complex biological samples, o example, in he con ex
o luo escen mic oscopy.
2 Rela ed Wo k
2.1 Image Denoising
Image denoising is a ask ha has a long and exci ing his o y. Classical me hods,
such as Non-Local Means [5] o BM3D [6], we e equen ly and e y success ully
used be o e neu al ne wo k based app oaches ha e been in oduced owa ds he
end o he las decade [14,25–27].
The ad en o deep lea ning saw people exploi di e en aspec s o noise
and he way ne wo ks lea n o enable denoising. Noise, while usually unde-
si ed, is simul aneously much ha de o p edic , as was elegan ly demons a ed
in [24], leading o a ze o-sho denoise . In he case speci ic o pixel noises, i.e.
all o ms o noise ha a e independen pe image pixel (gi en he signal a ha
pixel) [22], he impossibili y o p edic he noise was exploi ed in a ious ways,
leading o impo an con ibu ions such as Noise2Void [14], Noise2Sel [3], o
Sel 2Sel [13]. Ano he well known app oach close o his amily o app oaches
is Noise2Noise [16], capable o denoising e en mo e complex noises ha can
co ela e beyond he con ines o single pixels.
To u he imp o e denoising pe o mance, P obabilis ic Noise2Void [15,21]
in oduced, and Di Noising [20] and Hie a chical Di Noising (HDN) [19] eused
denoiSpli 3
he idea o sui ably measu ed o ained pixel noise models. Such noise models
a e, in essence, a collec ion o p obabili y dis ibu ions mapping om a ue pixel
in ensi y o obse ed noisy pixel measu emen s (and ice e sa).
2.2 Image Decomposi ion
Image decomposi ion is he in e se p oblem o spli ing a gi en inpu image ha
is he supe posi ion (i.e. he pixel-wise sum) o wo cons i uen image channels.
While he sum o wo alues is no uniquely in e ible, i o each summand
a p io on i s alue exis s, e en a unique solu ion can exis . In a simila ein,
ha ing lea ned s uc u al p io s o he appea ance o he wo cons i uen image
channels, an inpu image (a g id o obse ed pixels ha a e each a sum o wo
alues) can be spli in o wo pixel g ids such ha each one sa is ies he espec i e
s uc u al p io . In compu e ision, e lec ion emo al, dehazing, de aining e c.
a e some o he applica ions [2,4,7,8] o which image spli ing can be used.
Mo e ecen ly, image spli ing in luo escence mic oscopy was ecei ing heigh -
ened a en ion, p obably because o he di ec applicabili y and po en ial u il-
i y ha a well-wo king app oach can b ing o his mic oscopy modali y, which
inds wide-sp ead use in biological in es iga ions. In pa icula , a me hod called
µSpli [1] demons a ed imp essi e image spli ing pe o mance on se e al da ase s,
sugges ing ha i is eady o be used in biological esea ch p ojec s.
Howe e , µSpli equi es ela i ely noise- ee da a o aining and p edic ion,
which limi s i s po en ial u ili y (see also Sec ion 5 o Figu e 2).
2.3 Unce ain y Calib a ion
The abili y o co ec ly assess he quali y o p edic ions is na u ally use ul. Ide-
ally, a p edic i e sys em capable o co-p edic ing a con idence alue has he
p ope y ha he p edic ed con idence scales wi h he a e age e o o he p e-
dic ion. I he ela ionship be ween e o and con idence is close o he iden i y,
we call he unce ain y p edic ions o his sys em calib a ed.
Ea ly wo ks ied o use he de ia ion o he p edic ion as a p oxy o he ne -
wo k’s con idence in he p edic ion [26]. O he wo ks ied o calib a e he p e-
dic ed s anda d de ia ion wi h he expec ed e o (i.e. he RMSE) [17]. Ea lie
calib a ion wo ks we e mainly conce ned wi h classi ica ion asks [18]. Howe e ,
in [17], hese app oaches we e e o mula ed in he con ex o eg ession.
In [17], he au ho s p opose a way o e alua e calib a ion. They ain a
sepa a e b anch o p edic a s anda d de ia ion pe pixel ha exp esses i s p e-
dic ion unce ain y. Fo e alua ing he calib a ion quali y, he au ho s clus e ed
examples on he basis o he p edic ed s anda d de ia ion alues. Wi hin each
clus e , he p edic ed unce ain y is hen compa ed wi h he empi ical unce -
ain y (RMSE loss). To u he imp o e he calib a ion, he au ho s p opose
a simple, ye e ec i e scaling me hodology whe ein hey lea n a scala pa am-
e e on e-calib a ion da a, i.e. a subse o da a no included in he aining
da a. (In ou expe imen s, we use he alida ion da a o his pu pose.) This
4 Ashesh, F. Jug
scala ge s mul iplied o he p edic ed unce ain y alues, which hen educes
he calib a ion e o .
3 P oblem Fo mula ion
Le s deno e a noise ee da ase con aining npai s o images as D= (C1, C2),
wi h each Cicon aining nimages Ci= (ci,j |1≤j≤n). Le s de ine a co e-
sponding se o images X= (xj|1≤j≤n), such ha all xj=c1,j +c2,j a e he
pixel-wise sum o he wo co esponding channel images.
Al hough Dis ypically no a ailable (o e en obse able), in p ac ice we
can only obse e noisy da a, deno ed he e by DN= (CN
1, CN
2). Analogously o
be o e, we de ine XN= (xN
j|1≤j≤n), such ha xN
j=cN
1,j +cN
2,j a e he
pixel-wise sum o he noisy channel obse a ions.
Gi en one xN
j∈XNo DN, he ask a hand is o p edic he noise ee and
unmixed uple (c1,j, c2,j). We shall deno e he p edic ions made by a ained
denoiSpli ne wo k by (ˆc1,j,ˆc2,j).
Whene e abo e no ions a e used in a con ex ha makes he jin he sub-
sc ip edundan , we allow ou sel es o omi hem o b e i y and eadabili y.
Fo e alua ion pu poses, we will in la e sec ions use high-quali y mic oscopy
da ase s ha con ain minimal le els o noise as su oga es o D,X,C1, and
C2, bu we ne e use hem du ing aining, and only hei noisy coun e pa s
a e used.
4 Ou App oach
In he ollowing sec ions we desc ibe he main ing edien s o denoiSpli , namely
he hie a chical ne wo k s uc u e we use (Sec ion 4.1), he changed loss e m o
a ia ional aining o he spli ing ask (Sec ion 4.2), he noise models we em-
ploy o enable he join unsupe ised denoising (Sec ion 4.3), and an unce ain y
calib a ion me hodology allowing us o es ima e he p edic ion e o in oduced
by alea o ic unce ain y in a gi en inpu image (Sec ion 4.4).
4.1 Ne wo k A chi ec u e and T aining Objec i e
In his wo k, we employ an al e ed Hie a chical VAE (HVAE) ne wo k a chi-
ec u e. HVAEs we e o iginally desc ibed in [23] and la e adap ed o image
denoising in [19] and o image spli ing in [1]. In gene al e ms, HVAEs lea n a
hie a chical la en space, wi h he lowes hie a chy le el encoding de ailed pixel-
le el s uc u e, while highe hie a chy le els cap u e inc easingly la ge scale
s uc u es in he aining da a.
Fo denoiSpli , we modi y he HVAE a chi ec u e so ha i no longe e-
mains an au oencode . Ins ead, ou ou pu s a e he wo unmixed channel images
(ˆc1,ˆc2), mo i a ing us o call he esul ing a chi ec u e a Va ia ional Spli ing
Encode -Decode (VSE) Ne wo k (see Fig. 1).
denoiSpli 5
Ou objec i e is o maximize he likelihood o e he noisy wo channel da ase
we ain on, i.e., inding decode pa ame e s θsuch ha
θ= a g max
θX
1≤j≤n
log P(cN
1,j, cN
2,j;θ).(1)
Using he modi ied e idence lowe bound (ELBO), as p oposed in [1] and
assuming condi ional independence o he wo p edic ions (ˆc1,ˆc2)gi en he la en
space embedding, we maximize
Eq(z|x;ϕ)[log P(cN
1|z;θ) + log P(cN
2|z;θ)] −KL(q(z|x;ϕ), P (z)),(2)
whe e q(z|x;ϕ)is he dis ibu ion pa ame e ized by he ou pu o he encode
ne wo k Encϕ(x),P(cN
i|z;ϕ)is he dis ibu ion pa ame e ized by he ou pu o
he decode ne wo k Decθ(z)and KL() deno es he Kullback-Leible di e gence
loss. As in [1], P(z) ac o izes o e he di e en hie a chy le els in he ne wo k.
De ails abou aining, hype pa ame e s, µSpli , and i s ela ionship wi h HDN
and denoiSpli can be ound in Supp. Sec. 2.
Simila o he way noise models had been employed in he con ex o denois-
ing [19], we model he wo log likelihood e ms log P(cN
1|z;θ)and log P(cN
2|z;θ)
using noise models which we desc ibe in de ail in Sec ion 4.3 and ou open code
eposi o y1.
4.2 Hie a chical KL Loss Weighing o Va ia ional T aining
In µSpli , he au ho s showed SOTA pe o mance on a mul i ude o spli ing
asks. Howe e , used da ase s we e close o noise- ee, making he ask a hand
simple hen he one we ou lined in Sec ion 3. When µSpli is ained on noisy
da ase s, he esul ing channel p edic ions a e hemsel es noisy. A e analyzing
his ma e , we concluded ha a modi ied KL loss can help educe he amoun
o noise econs uc ed by he decode .
In mo e echnical e ms, le Zbe a hie a chical la en space and Z[i]deno e
he la en space embedding a i- h hie a chy le el, ha ing shape (c, hi, wi), wi h
cbeing channel dimension, and hi,wi he heigh and wid h o he la en space
embedding. Now le KLideno e he KL-di e gence loss enso compu ed on Z[i],
which has he same shape as Z[i]i sel .
In µSpli , he co esponding scala loss e m kliis de ined as kli=α·
Pj,h,w
KLi[j,h,w]
hi·wi, wi h αbeing a sui able cons an . Obse e ha he denomi-
na o makes each klibe he a e age o all alues in KLi, making he espec i e
alues no scale wi h he size o Z[i], e en hough lowe hie a chy le els (Z[i]
o smalle i) ha e mo e en ies. Howe e , his also means ha he KL loss o
he indi idual pixels in hese lowe hie a chy le els is gi en less weigh . Hence,
smalle s uc u es, such as noise i sel , can mo e easily seep h ough such pixel-
nea hie a chy le els.
1h ps://gi hub.com/juglab/denoiSpli
6 Ashesh, F. Jug
In his wo k, we di e ge om his o mula ion and e u n o a mo e classical
se up whe e we compu e he scala loss e m o he i- h hie a chy le el Z[i]as
kli=α·X
j,h,w
KLi[j, h, w].(3)
The decisi e di e ence is ha his changed o mula ion gi es mo e weigh
o he KL loss a lowe hie a chy le els, leading o mo e s ongly en o cing he
Gaussian na u e he KL loss en o ces, and he e o e hinde ing noise om being as
easily ep esen ed du ing aining. We e e o his a chi ec u e as Al e ed µSpli
and show quali a i e and quan i a i e esul s in Sec ion 5 and Tables 1.
The nex sec ion ex ends on Al e ed µSpli by adding unsupe ised denoising,
adding he las ing edien o he denoiSpli app oach we p esen in his wo k.
4.3 Adding Sui able Pixel Noise Models
As b ie ly in oduced in Sec ion 2, pixel noise models a e a collec ion o p oba-
bili y dis ibu ions mapping om a ue pixel in ensi y o obse ed noisy pixel
measu emen s (and ice- e sa) [15]. They ha e p e iously been success ully used
in he con ex o unsupe ised denoising [19,20] and we in end o employ hem
o his pu pose also in he se up we a e p esen ing he e. We use he ac ha ,
gi en a measu ed (noisy) pixel in ensi y, a pixel noise model e u ns a dis i-
bu ion o e clean signal in ensi ies and hei espec i e p obabili y o being he
unde lying ue pixel alue.
We inco po a e his likelihood unc ion in o he loss o ou o e all se up,
encou aging denoiSpli o p edic pixel in ensi ies ha maximize his likelihood
and he eby alues ha a e consis en wi h he noise p ope ies o he gi en
aining da a.
Since denoiSpli , in con as o exis ing denoising applica ions, p edic s wo
images ( he wo unmixed channels), we employ wo noise models and add wo
likelihood e ms o ou o e all loss.
Mo e o mally, in VAEs [12] and HVAEs, he gene a i e dis ibu ion o e
pixel in ensi ies is modeled as a Gaussian dis ibu ion wi h i s a iance ei he
clamped o 1o also lea ned and p edic ed. We change ou VSE Ne wo k o
only p edic he ue pixel in ensi y and eplace he Gaussian dis ibu ion men-
ioned abo e by he dis ibu ions de ined in wo noise models Pnm
1(cN
1|c1)and
Pnm
2(cN
2|c2), one o each espec i e unmixed ou pu channel. These noise models
a e pixel-wise independen , i.e.,
Pinm(cN
i|ci) = Y
k
Pnm
i(cN
i[k]|ci[k]), i ∈ {1,2},(4)
whe e cN
i[k]is he noisy pixel in ensi y o he k- h pixel and ci[k] he co e-
sponding noise- ee in ensi y alue. This independence makes hem pa icula ly
sui able o mic oscopy da a whe e Poisson and Gaussian noise a e he p edom-
inan pixel noises one desi es o emo e.
denoiSpli 7
Since we now di ec ly p edic he noise- ee pixel alues, he ou pu o he
decode can di ec ly be in e p e ed as Decθ(z) = (ˆc1,ˆc2)and he o al loss o
denoiSpli now becomes
Eq(z|x;ϕ)[log Pnm(cN
1|ˆc1) + log Pnm(cN
2|ˆc2)] −KL(q(z|x;ϕ), P (z)).(5)
In [20], wo ways o he c ea ion o noise models a e desc ibed, and he
decision o pick which me hod depends upon whe he o no one has access o
he mic oscope om which da a was acqui ed. In Supp. Sec. 5, we desc ibe he
p ocess o noise model gene a ion and also compa e pe o mance be ween hese
wo me hodologies.
4.4 Compu ing Calib a ed Da a Unce ain ies
The idea o calib a ion is o hose ne wo k se ups ha p oduce bo h p edic ion
and a measu e o unce ain y o he p edic ion.
Ne wo ks ha can co-assess he unce ain y o hei p edic ions a e called
calib a ed, when he p edic ed unce ain ies a e in line wi h he measu ed p e-
dic ion e o . To imp o e he calib a ion o a gi en sys em, one can ind a sui -
able ans o ma ion om unce ain y p edic ions o measu ed e o s (e.g., he
RMSE). A e such a ans o ma ion is ound, an ideal calib a ed plo would be
igh ly i ing y=x, wi h y and x being he e o and es ima ed unce ain y,
espec i ely. See, o example, Figu e 3. Since VSE ne wo ks, simila o VAEs,
a e a ia ional in e ence sys ems, we can sample om hei la en encoding and
he eby sample om an app oxima e pos e io dis ibu ion o possible solu ions
gi ing us he da a unce ain y. In his sec ion, ou in en ion is o u ilize his
abili y o p edic a eliable unce ain y e m o ou esul s.
Fo his, we adap he calib a ion me hodology o [17]. In con as o he
app oach desc ibed he e, we p opose o use he a iabili y in pos e io samples
o es ima e a pixel-wise s anda d de ia ion. Mo e speci ically, we sample k= 50
p edic ions o each inpu image and compu e he pixel-wise s anda d de ia ions
σ1and σ2 o he wo p edic ed image channels ˆc1and ˆc2, espec i ely. This gi es
us unce ain y p edic ions.
Nex , we calib a e hese unce ain y p edic ions by scaling hem app op i-
a ely wi h he help o wo lea nable scala s, α1and α2. Following [17], we as-
sume ha pixel in ensi ies come om a Gaussian dis ibu ion. The mean and
s anda d de ia ion o his dis ibu ion a e he pixel in ensi ies o he MMSE
p edic ion, i.e. he image ob ained a e a e aging k= 50 p edic ions, and he
scaled σ, espec i ely. We lea n he scala s α1and α2by minimizing he neg-
a i e log-likelihood o e he ecalib a ion da ase . I is impo an o no e ha
he p esen ed calib a ion p ocedu e does no al e he o iginal p edic ions bu
ins ead lea ns a mapping ha bes p edic s he measu ed e o .
To e alua e he quali y o he esul ing calib a ion, we so he scaled s an-
da d de ia ions σi·si o each pixel in a p edic ed channel and build a his og am
o e l= 30 equally sized bins Bj
i. We hen compu e he oo mean a iance
(RMV) and RMSE o each bin jand channel ias
8 Ashesh, F. Jug
RMVi(j) =
u
u
1
|Bj
i|X
k∈Bj
i
(σk
i·αi)2RMSEi(j) =
u
u
1
|Bj
i|X
k∈Bj
i
(ci[k]−ˆci[k])2
As in Sec ion 3, ci[ ]and ˆci[ ]deno e he noise- ee pixel in ensi y and he co e-
sponding p edic ion o i- h channel. In Fig. 3, we plo he RMSE s. RMV o
mul iple asks, obse ing ha he plo s closely esemble he iden i y y=x. Fol-
lowing [17], we use he alida ion da ase o ecalib a ion and show calib a ion
plo s on he es da ase .
5 Expe imen s and Resul s
5.1 Da ase s
BioSR da ase We wo k p ima ily wi h BioSR da ase [11], a comp ehensi e
da ase comp ising luo escence mic oscopy images o mul iple cell s uc u es.
Fo ou expe imen s, we ha e picked ou s uc u es, namely cla h in-coa ed
pi s (CCPs), mic o ubules (MTs), endoplasmic e iculum (ER), and F-ac in.
Since he aw da a quali y is e y high and only a small amoun o image
noise is p esen in he indi idual mic og aphs, we add Gaussian noise and Poisson
noise o a ious le els o hese aw da a. The a i icially noisy images a e used
o ain denoiSpli , while he aw da a is shown o con ince he eade o he
alidi y o ou app oach and o compu e e alua ion me ics (see Figs. 2 and 4
and Tab. 1).
Hagen e al. Ac in-Mi ochond ia Da ase We picked he noisy Ac in and Mi-
ochond ia channels om Hagen e al. [10], channels ha ing eal mic oscopy
noise. Fo e alua ion, we use he co esponding high-SNR (noise- ee) channels
p o ided in he da ase .
Syn he ic Noise Le els We wo k wi h 4le els o ze o-mean Gaussian noise and
wo le els o Poisson noise. Fo Gaussian noise, we compu e he s anda d de-
ia ion o he inpu da a XN o each o he asks and scale he noise ela i e
o one s anda d de ia ion. Speci ically, he 4scaling ac o s a e {1,1.5,2,4}. In
cases whe e Poisson noise is added, and since i is al eady signal dependen , we
use a cons an ac o o 1000 o hi a ealis ic-looking le el o Poisson noise. We
also conside he case whe e Poisson noise is no added, which we deno e by he
Poisson le el o 0in Tab. 1. To emo e any emaining oom o misin e p e a-
ions, we p o ide a pseudo-code o he syn he ic noising p ocedu e in he Supp.
Sec. 2.
5.2 Baselines
We conduc ed all expe imen s wi h wo baseline se ups, µSpli and HDN⊕µSpli .
In he o iginal µSpli wo k [1], he au ho s in oduce h ee a chi ec u es, each
wi h a di e en ade-o be ween GPU e iciency, speed and pe o mance. We
denoiSpli 9
High SNRdenoiSpli µSpli GTInpu
A
B
C
D
c0
cN
0
c1
cN
1
c0
cN
0
c1
cN
1
c0
cN
0
c1
cN
1
c0
cN
0
c1
cN
1
Fig. 2: Quali a i e Resul s. We show examples o noisy inpu s, indi idual noisy
channel aining da a (GT), and p edic ions by one o he baselines (µSpli ) and ou
own esul s ob ained wi h denoiSpli o ou asks (A: MT s. CCPs, B: ER s. CCPs,
C: MT s. ER, and D: F-ac in s. ER). We show high SNR channel images (no
used du ing aining) and show PSNR alues w. . . hese images. Addi ionally, we plo
his og ams o a ious panels o compa ison (see legend on he igh ). The bo om
cell in he i s column o each panel shows he used noise models (see main ex o
de ails). The supe imposed plo s (g een) show he dis ibu ion o noisy obse a ions
(cN
i) o wo clean signal in ensi ies.
16 Ashesh, F. Jug
20. P akash, M., K ull, A., Jug, F.: Di Noising: Di e si y denoising wi h ully con o-
lu ional a ia ional au oencode s. ICLR 2020 (Jun 2020)
21. P akash, M., Lali , M., Tomancak, P., K ull, A., Jug, F.: Fully unsupe ised p ob-
abilis ic Noise2Void. a Xi eess.IV (No 2019)
22. Sh o , H., Tes a, I., Jug, F., Manley, S.: Li e-cell imaging powe ed by compu a ion.
Na . Re . Mol. Cell Biol. (Feb 2024)
23. Sønde by, C.K., Raiko, T., Maaløe, L., Sønde by, S.K., Win he , O.: Ladde a i-
a ional au oencode s. Ad . Neu al In . P ocess. Sys . 29, 3738–3746 (Jan 2016)
24. Ulyano , D., Vedaldi, A., Lempi sky, V.: Deep image p io . In . J. Compu . Vis.
128(7), 1867–1888 (Jul 2020)
25. Weige , M., Roye , L., Jug, F., Mye s, G.: Iso opic econs uc ion o 3D luo es-
cence mic oscopy images using con olu ional neu al ne wo ks. In: Medical Image
Compu ing and Compu e -Assis ed In e en ion - MICCAI 2017. pp. 126–134.
Sp inge In e na ional Publishing (2017)
26. Weige , M., Schmid , U., Boo he, T., Mülle , A., Dib o , A., Jain, A., Wilhelm,
B., Schmid , D., B oaddus, C., Culley, S., Rocha-Ma ins, M., Sego ia-Mi anda, F.,
No den, C., Hen iques, R., Ze ial, M., Solimena, M., Rink, J., Tomancak, P., Roye ,
L., Jug, F., Mye s, E.W.: Con en -awa e image es o a ion: pushing he limi s o
luo escence mic oscopy. Na u e Publishing G oup 15(12), 1090–1097 (Dec 2018)
27. Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a gaussian denoise :
Residual lea ning o deep CNN o image denoising. IEEE T ans. Image P ocess.
26(7), 3142–3155 (Jul 2017)
