Concu en ocal-plane gene a ion o comp essed
samples om ime-encoded pixel alues
M. T e isi(1) , H. C. Bandala(2), J. Fe nández-Be ni(1), R. Ca mona-Galán(1), Á. Rod íguez-Vázquez (1)
(1) Ins i u o de Mic oelec ónica de Se illa (IMSE-CNM), CSIC-Uni e sidad de Se illa, Spain
(2) Ins i u o Nacional de As o ísica, Óp ica y Elec ónica (INAOE), Puebla, Mexico
e [email protected]
Abs ac — Comp essi e sampling allows w apping he
ele an con en o an image in a educed se o da a. I exploi s
he spa si y o na u al images. This p inciple can be employed o
deli e images o e a ne wo k unde a es ic ed da a a e and
s ill ecei e enough meaning ul in o ma ion. An e icien
implemen a ion o his p inciple lies in he gene a ion o he
comp essed samples igh a he image . O he wise, i. e.
digi izing he comple e image and hen composing he
comp essed samples in he digi al plane, he equi ed memo y
and p ocessing esou ces can se iously comp omise he budge o
an au onomous came a node. In his pape we p esen he design
o a pixel a chi ec u e ha encodes ligh in ensi y in o ime,
ollowed by a global s a egy o pseudo- andomly combine pixel
alues and gene a e, on-chip and on-line, he comp essed
samples.
Keywo ds— comp essi e sampling; cellula au oma on; ime-
encoded pixels;
I. INTRODUCTION
Spa si y in na u al images can be exploi ed o comp ess he
signal and hen eco e he con en om a numbe o samples
ha is below he limi de e mined by Nyquis ’s heo em [1] [2].
In o de o implemen his comp essing mechanism, a pai o
ma ices is applied o he coe icien s o he o iginal signal,
image pixel alues in ou case. These ma ices a e he
comp essi e s a egy, Φ, and he spa si ying dic iona y, Ψ.
Each comp essed sample is a linea combina ion o he
elemen s o he o iginal image. Then, om a se o comp essed
samples much smalle han he o iginal image, con ex
op imiza ion can lead o a unique solu ion. In o de o achie e
his, he p oduc o Φ and Ψ mus hold he es ic ed isome y
p ope y (RIP) [3].
Building a comp essi e s a egy on-chip is no i ial. The
mos common app oach is o ob ain he elemen s o Φ om a
andom dis ibu ion. I has been implemen ed by using op ical
elemen s [4] and also by employing dedica ed ci cui y [5]. The
simples implemen a ion consis s in using a sub-Gaussian
dis ibu ion, i. e. he elemen s o Φ a e ob ained om a no mal
dis ibu ion ha is h esholded so hey a e ei he one o ze o. In
his way each comp essed sample esul s di ec ly om he
addi ion o all he pixels selec ed by Φ. In p ac ice, he e a e
wo majo limi a ions o implemen hese echniques a senso
le el. Fi s o all, he comp essi e s a egy mus be known a
bo h ex emes o he communica ion channel. This is, no only
he senso mus know which he comp essi e s a egy is in
o de o gene a e he co esponding comp essed samples, bu i
mus be p esen also a he end o he channel, in o de o
econs uc he o iginal image. The e o e, ei he he
comp essi e s a egy is gene a ed a he senso and ansmi ed
o he image econs uc ion sys em o i needs o be s o ed a
bo h ends. This ep esen s an impo an bu den as hese op ions
will in oduce s ong equi emen s on he ansmission
bandwid h and/o he in-senso memo y. The second ques ion
is dynamic ange. The numbe o bi s equi ed o desc ibe he
linea combina ion o 𝑁 pixels is log2𝑁 in addi ion o he bi s
equi ed o desc ibe one single pixel. This is a majo limi a ion
o an implemen a ion o his addi ion in he analog plane, as
dynamic ange in analog ci cui s is limi ed by he a ailable
ou pu ange and noise le el.
These wo limi a ions can be alle ia ed wi h a widely
ex ended app oach: block-based comp essi e sampling [6] [7]
[8]. The pixels o he comple e image a e di ided in o mac o-
blocks o which he comp essi e s a egy is applied. This
ep esen s a conside able educ ion o Φ and he in as uc u e
equi ed o i s gene a ion, ansmission and/o s o age. A he
same ime, he equi ed dynamic ange o ep esen he
comp essed samples is no iceably educed. In exchange o
his, econs uc ion depa s om ideal and may equi e
addi ional samples o achie e a p esc ibed accu acy.
Ou app oach is he on-chip gene a ion o a ull- ame
comp essi e s a egy [9] by means o a 1D cellula au oma on
(CA) o he pseudo- andom selec ion o pixels [10]. This
solu ion a oids bo h ansmi ing and s o ing he comp essi e
s a egy as i can be e o - ee econs uc ed om he ini ial
seed wi h an analogous CA implemen a ion. In addi ion o his,
pixel alues need o be ep esen ed in a o m ha does no
exhaus he a ailable dynamic ange when being added up. In
o de o do his, we a e encoding pixel alues in ime. Addi ion
is ealized in he digi al domain by asynch onously agging
e en s in a pe -column basis. In his pape we a e displaying
he de ails o he design o he chip, s a ing wi h he indi idual
pixel, and ollowing wi h he pseudo- andom selec ion o
pixels, he ime o digi al con e sion o he pixel alue, he
column addi ion and he inal gene a ion o he comp essed
sample.
II. PIXEL ARCHITECTURE
The ou pu o a comp essi e sampling image is gi en in
he o m o linea combina ions o andomly selec ed pixel
con ibu ions. These linea combina ions a e he comp essed
samples [1]. As we ha e al eady e e ed, he gene a ion o he
andom pa e n o he selec ion o pixels has been le o a
one-dimensional cellula au oma on ha will be desc ibed la e
on. As o now, jus conside ha a se o de ices deli e ing
andom logic ze oes and ones a e employed o gene a e
selec ion signals o he ows and columns o he pixel a ay.
Apa om he gene a ion o andom selec ion signals, he
majo di icul y on implemen ing a ull- ame comp essi e
s a egy is p o iding enough dynamic ange o accommoda e
comp essed samples. Conside ha each pixel alue, ei he
o iginally a ol age o a cu en , is ep esen ed by 𝑁𝑏 bi s. Fo
an image o 𝑀 × 𝑁 pixels ha can be chosen a andom o
compose a comp essed sample, he numbe o bi s equi ed o
a oid any kind o clipping in he gene a ion o comp essed
samples is:
𝑁𝐵= 𝑁𝑏+ log2(𝑀𝑁) (1)
Fu he mo e, e en in block-based comp essi e sampling [11],
whe e images a e di ided in o small blocks o educe 𝑁𝐵,
comp essi e samples a e gene a ed using blocks ha ha e a
minimum p ac ical size o 8 × 8 pixels. Smalle blocks would
no be e y spa se and as such one o he undamen al p emises
behind comp essi e sampling would all. To p ese e
esolu ion, i each pixel alue is encoded in 8b, we would s ill
need 14b o esolu ion in o de o p ope ly encode comp essed
samples. Ou app oach o p o ide he numbe o bi s p esc ibed
by Eq. (1) is o ime-encode he pixel alues and employ ime-
o-digi al con e sion. The summa ion o pixels is hen ealized
in he digi al domain, a oiding he equi emen o a wide
dynamic ange in he analog domain.
A. Time-encoding o ligh in ensi y
The elemen a y pixel (Fig. 1) con ains an in eg a ing
pho odiode ha discha ges node 𝑉
𝑝𝑖𝑥 a a a e de e mined by
he pho ocu en . This is depic ed inside he ‘Time-encoding o
ligh in ensi y’ box in Fig. 1. When 𝑉
𝑝𝑖𝑥 c osses a e e ence
ol age 𝑉
𝑟𝑒𝑓, a ol age compa a o lips i s ou pu , 𝑉
1. I ime-
encodes he magni ude o he ligh in ensi y, wha is desc ibed
as pulse-modula ion imaging [12]. The pixel alue is hen
con ained in he pe iod o ime sepa a ing he ese o node 𝑉
𝑝𝑖𝑥
and he momen in which 𝑉
1 u ns om low o high. The lowe
(highe ) he ligh in ensi y on he diode is, he longe (sho e )
i akes o he compa a o o swi ch. In his chip, bo h 𝑉
𝑟𝑠𝑡 and
𝑉𝑟𝑒𝑓 can be adjus ed on-line in o de o adap o di e en
illumina ion condi ions in eal- ime.
B. Pixel selec ion ci cui
As p e iously men ioned, he con ibu ion o each pixel o a
pa icula comp essed sample is de e mined by a combina ion
o ow and column selec ion signals, 𝑆𝑖 and 𝑆
𝑗, ha a e
gene a ed wi h he help o a one-dimensional cellula
au oma on posi ioned a ound he senso a ay (Fig. 2). These
wo signals a e combined by a XOR ga e, implemen ed by 6
ansis o s in Fig. 1. The ol age 𝑉
2 is s uck a 𝑉
𝑑𝑑 i selec ion
signals 𝑆𝑖 and 𝑆𝑗 a e equal. I no , 𝑉
2 is he in e se logic alue
o 𝑉
1. Using a XOR ga e gua an ees ha he pixel con ibu es
o he linea combina ion ha cons i u es a comp essed sample
in jus hal o he possible combina ions o 𝑆𝑖 and 𝑆
𝑗. I is
impo an o no ice ha his pixel selec ion uni is alloca ed
igh a e he compa a o because his helps educing powe
consump ion. I a pixel is no con ibu ing o he comp essed
sample he e is no eason o le he pixel ac i a ion on
p opaga e, inducing changes in he subsequen nodes ha a e
going o be disca ded la e .
C. P opaga ion o he ac i a ion edge
Signal 𝑉
2 is ac i e in low, elici ing a ising edge in 𝑉
3 i his
signal has no been ac i a ed be o e. I i has, he eedback o
𝑉3
 locks 𝑉
3 o logic ‘1’ un il he pixel is ese again. Now
conside ha signal 𝑄′ is high. La e we will wha makes 𝑄′
changes o e ime. I 𝑄′ is in logic ‘1’, hen 𝑉
4 is he in e se o
𝑉3, i. e. i he pixel is ac i a ed and is selec ed o con ibu e o
he comp essed sample, 𝑉
3 goes om logic ‘0’ o ‘1’ and 𝑉
4
goes om ‘1’ o ‘0’. I signal 𝐶𝑖𝑛 is low, his alling edge in 𝑉
4
induces a ising edge in 𝑉
5 which is he signal con olling
d i ing ansis o M2. The column bus, whose ol age 𝑉
𝑜 is
pulled up o 𝑉
𝑑𝑑 by de aul , expe iences a pull down d i en by
M2. 𝑉
𝑜 will emain low i i was no o he e en e mina ion
ci cui .
D. E en e mina ion ci cui
The ising edge in 𝑉
5 is eedback o he e en e mina ion
ci cui , whe e i is in e ed as long as 𝑄, which is a global
signal, is high. This causes 𝑄′ o all o logic ‘0’, swi ching
Fig. 1 Schema ics o he elemen a y pixel
back 𝑉
4 o logic ‘1’ and hen 𝑉
5 o logic ‘0’, e mina ing he
pulse ha s a ed be o e a e a sho delay.
The mo i a ion o use a global pulse e mina ion signal o
es ablish he du a ion o he e en s ins ead o a local delay uni
is o p o ide global con ol wi hou in oducing a ea and/o
powe consuming elemen s in he pixel. In pa icula , 𝑄 is a
signal p o ided by a con ol uni in each column o he pixel
a ay. This uni senses he column bus and de ec s i i is being
pulled down. Once he alling edge is de ec ed, and a e a use -
con ollable delay, 𝑄 ises enabling he e mina ion o he pulse
only in he pixel ha has al eady u ned M2 on. This is e i ied
by he NAND ga e in he ‘E en e mina ion ci cui ’ box
(Fig. 1).
E. Pixel ou pu con ol
As depic ed in Fig. 1, all pixels in he same column o he
a ay sha e he same column bus o ansmi i s ou pu pulse.
As will be explained la e , he ime-encoding o he pixel alue
will be con e ed o digi al by means o a ime- o-digi al
con e e , which in his case will be buil wi h a clock and a
coun e . O cou se, he e is no a p io i knowledge on he
p oximi y o he alues o he pixels and, he e o e, how close
in ime will be he pulses emi ed by he pixels. Wha is clea is
ha each one o hem needs o be aken in o accoun i we do
no wan o in oduce addi ional e o s in he image
econs uc ion om i s comp essed samples. In o de no o
skip any o he pulses, a oken p o ocol is es ablished so pixels
ha a e being igge ed close in ime a e only allowed o emi
hei pulse one a e he o he . This blocking mechanism needs
o be pa allel o all pixels so ha he i s pixel ha deli e s i s
e en pu s all o he pixels on hold un il i s e en is o e . The
elease mechanism on he con a y has o be sequen ial so ha ,
i he e is mo e han one pixel in queue wai ing o deli e i s
pulse, i will be impossible o ha e mo e han one o hem
ac i e a he same ime. In o de o do so, each pixel ecei es a
signal 𝐶𝑖𝑛 om he pixel immedia ely abo e (Fig. 1), and sends
a signal 𝐶𝑜𝑢𝑡 o he pixel immedia ely below i . I he e is no
p eceding pixel wai ing o deli e a pulse h ough he column
bus, 𝐶𝑖𝑛 will be low. This enables he p opaga ion o a alling
edge in 𝑉
4 when i occu s in o a ising edge in 𝑉
5. I 𝐶𝑖𝑛 is high,
howe e , his p opaga ion is e ained.
One pixel’s 𝐶𝑖𝑛 co esponds o i s uppe neighbo 𝐶𝑜𝑢𝑡. In
o de o be ‘0’, h ee di e en condi ions mus hold, namely: i s
𝐶𝑖𝑛 is low, wha means ha he e is no pixel abo e i ha wan s
o deli e a pulse; 𝑉
4 is high, wha means ha ei he he pixel
has no been ac i a ed o i has al eady deli e ed a pulse; and
𝑉
𝑜 is high, wha means ha he column bus is a ailable. I any
o hese h ee condi ions is no ue 𝐶𝑜𝑢𝑡 will be s uck a he
logic ‘1’, hus p e en ing any o he pixels below i emi ing a
pulse h ough he column bus. A 3-inpu NAND ga e is
employed o combine he le el a 𝐶𝑖𝑛, he pixel eadiness o
pull down he column bus and he eedback on he ac ual s a e
o his column bus. This agg ega ed in o ma ion is hen sen as
𝐶𝑜𝑢𝑡 o he pixels below. Using his logic each pixel will know
ha i 𝑉
𝑜= 𝑉𝑑𝑑 and no pixel abo e is wai ing o pull i down i
is allowed o elease i s own e en . Since 𝑉
𝑜 is ed back o his
con ol block, when a pull down occu s, each pixel will
simul aneously block he pixel immedia ely below h ough
𝐶𝑜𝑢𝑡. The blocking mechanism is pa allel. On he con a y,
when an e en is o e , i s 𝐶𝑜𝑢𝑡 u ns o ‘0’, so he pixels will be
eleased sequen ially in a op down ashion.
III. SENSOR ARCHITECTURE
The pixel al eady desc ibed is pa o an image senso ha
implemen s a ull- ame comp essi e s a egy. The a chi ec u e
o he chip is depic ed in Fig. 2. The cen al elemen o he
a chi ec u e is an a ay o 64 ×64 pixels. The pe iphe al
ci cui needs o implemen he ollowing unc ionali ies:
pseudo- andom column and ow selec ion, ime- o-digi al
con e sion o he pixel alues, addi ion o he pixel alues o
he selec ed pixels. Le us desc ibe he ci cui s implemen ing
hese unc ionali ies one by one.
Fig. 2 Concep ual loo plan o he senso chip
A. Pseudo- andom gene a ion o selec ion signals
The gene a ion o pseudo- andom pa e ns s a ing om a
seed can be ealized using di e en me hods. Some o hem
ha e been employed be o e in he con ex o comp essi e
sampling, like Hadama d ec o s [13] o linea eedback shi
egis e s [14]. As al eady men ioned, ou app oach consis s in a
1-D cellula au oma on, which has he ad an age o being
easily implemen ed in CMOS echnology and i s scalabili y, as
he e olu ion o i s cells only depends on hei own s a e and
hose o hei closes neighbo s. Typically a linea CA wi h
adius-1 in e ac ions be ween i s cells is de ined by a u h able
de ined on he cell s a e (S) and he s a es o he le (L) and
igh neighbo (R). Table I shows he u h able o Rule 30,
which has been demons a ed o display ape iodic (class III)
beha io [10]. The ci cui employed o implemen a cell o his
cellula au oma on is depic ed in Fig. 3. The cell s a e is
p ecisely he selec ion signal ha is deli e ed o a ows o a
column, depending on he posi ion o he CA cell (Fig. 2).
Table I T u h able o Rule 30
L
S
R
NS
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
Fig. 3 Implemen a ion o a Rule 30 cell o a cellula au oma on
B. Column-wise ime- o-digi al con e sion
E en s gene a ed a he pixels and ansmi ed h ough he
column bus a i e o block ‘Sample & Add’ in (Fig. 2). These
pulses encode he pixel alue in he pe iod o ime ha has
passed be ween he pixels ese and he a i al o he ‘Sample
& Add’. A s aigh o wa d me hod o ansla e all his pulses
in o digi al codes is o use he pulses o ac i a e he sampling o
a global ime coun e (Fig. 2) ac i a ed by a clock signal and
s a ed wi h he global pixel ese —alloca ing some ini ial
delay o allow he pulses o each he bo om o he a ay. Each
ime a pixel ac i a ion pulse a i es, he 8b o he coun e a e
sampled and added o he al eady s o ed sum. A e 256 clock
pe iods, he pixel alues ha e been accumula ed a he ‘Sample
& Add’, which deli e s a 14b wo d con aining his sum, as i is
he esul o adding up o 64 pixel alues. A e ha , he 64
column sums a e added up in o a comp essed sample o 20b.
Comp essed samples need o be encoded in a much la ge
digi al wo d, he e o e he e is an amoun o comp essed
samples beyond which i is be e o jus deli e he
uncomp essed image. In ou case, as pixel alues a e encoded
by 8b and, and comp essed samples in 20b, he comp ession
a io (𝑅), i. e. he numbe o samples deli e ed di ided by he
o al numbe o pixels in he image, needs o be below 0.4. This
means ha o a 𝑀 × 𝑁-pixel image, we will be always
conside ing less han 0.4𝑀𝑁 comp essed samples.
In addi ion, as comp essed samples a e gene a ed
sequen ially, i is necessa y o ope a e he image a a ame
a e (𝑓
𝑐𝑠) —conside ing ha i is e e ed o he ime i akes o
deli e one single comp essed sampling— ha is a maximum
0.4𝑀𝑁 imes he o iginal ame a e (𝑓
𝑠)
𝑓
𝑐𝑠 = 𝑅 ∙ 𝑀𝑁𝑓
𝑠 (2)
Fo 𝑓
𝑠=30 ps, 𝑅 = 0.4 and an image o 64 ×64 pixels,
comp essed samples can be gene a ed a ≈50kHz a
maximum. This is 20s pe comp essed sample. I he du a ion
o e en s is, o ins ance, 5ns, and he 64 pixels in a column a e
selec ed, he e is a 6.25% chance ha wo e en s will andomly
o e lap. In o de o a oid missing any pulses, we a e deli e ing
hem one by one so ha , i he e is mo e han one pixel in
queue wai ing o deli e i s e en , i is impossible o ha e mo e
han one o hem ac i e a he same ime. As he ime- o-digi al
con e sion clock need o ick 256 imes in he 20s, i is
possible ha some pulses a e de ec ed in he ollowing clock
pe iod, wha will in oduce a 1LSB e o in he 20b
comp essed sample. Ve i ica ion on he negligible in luence o
his e o has been pe o med a sys em le el.
IV. CHIP PROTOTYPE
A p o o ype chip has been designed in a CMOS 0.18m
echnology ollowing he al eady desc ibed me hodology. The
die size including pads is 3.17 × 2.23 sq. mm (Fig. 4). I has
84 pads, o which one hi d is dedica ed o powe supply and
g ound connec ions. Table II con ains a summa y o he
ea u es o he p o o ype ha is al eady in ab ica ion.
Fig. 4 Layou o he p o o ype senso chip
Table II Summa y o chip ea u es
Technology
CMOS 0.18m 1P6M
Die size (w. pads)
3174μm × 2227μm
Pixel size
22μm × 22μm
Fill ac o
9.2%
Resolu ion
64 ×64
Pho odiode ype
n-well/p-subs a e
Powe supply
3.3V-1.8V
P edic ed powe consump ion
<100mW
F ame a e
30 ps
Max. comp essed sample a e
50kHz
Clock F eq.
24MHz
The cen al pa o he chip is he a ay o 64 ×64 pixels.
Fig. 5 depic s he layou o he elemen a y pixel. The blocks
desc ibed in Sec . II can be iden i ied. In o de o educe he
in luence o he o se o he compa a o , an au o-ze oing
scheme has been implemen ed using a MiM capaci o on he
op me al laye s (no showing in he pic u e). Fo mal
e i ica ion o he chip pe o mance has been ealized wi h
pos -layou simula ion.
Fig. 5 Layou o he elemen a y pixel
V. CONCLUSIONS
The design o comp essi e sampling image senso
p o o ype based on he on-chip gene a ion o a ull- ame
comp essi e s a egy has been comple ed. Majo design ade-
o s a e ela ed wi h accu acy o he econs uc ion and ame
a e, because o comp essed samples being oo ew o
inaccu a e. Time-encoding o he pixel alues and agging o
asynch onous pulses coming om a collec ion o pulses is he
me hodology employed o o e come dynamic ange limi a ions
in he cons uc ion o he comp essed samples. Expe imen al
cha ac e iza ion o he p o o ype will allow e i ying he
ad an ages o ull- ame comp essi e s a egies e sus block-
based comp essed sampling.
ACKNOWLEDGMENT
This wo k has been unded by he Spanish Go e nmen
h ough p ojec s TEC2015-66878-C3-1-R MINECO (Eu opean
Region De elopmen Fund, ERDF/FEDER), by Jun a de
Andalucía h ough p ojec TIC 2338-2013 CEICE and by he
O ice o Na al Resea ch (USA) h ough g an
N000141410355 and CONACYT (Mexico) h ough g an
MZO-2017-291062.
REFERENCES
[1] Candès. “Comp essi e sampling”. In . Cong ess o Ma hema ics, pp.
1433-1452. Mad id, Spain. Augus , 2006.
[2] J. Rombe g. “Imaging ia Comp essi e Sampling”. IEEE Signal
P ocessing Magazine, Vol. 25, No. 2, pp. 15-20. Ma ch, 2008.
[3] R. G. Ba aniuk, V. Ce he , M. B. Wakin. “Low-Dimensional Models o
Dimensionali y Reduc ion and Signal Reco e y: A Geome ic
Pe spec i e”. P oc. o he IEEE, Vol. 98, No. 6, pp. 959-971. Jun 2010.
[4] M. B. Wakin, J. N. Laska, M. F. Dua e, D. Ba on S. Sa o ham, D.
Takha , K. F. Kelly, R. G. Ba aniuk. “An A chi ec u e o Comp essi e
Imaging”. IEEE In e na ional Con e ence on Image P ocessing,
pp. 1273 – 1276. A lan a, USA. Oc obe , 2006.
[5] V. Majidzadeh, L. Jacques, A. Schmid, P. Vande gheyns and Y.
Leblebici. “A (256x256) Pixel 76.7mW CMOS Image /Comp esso
Based on Real-Time In-Pixel Comp essi e Sensing”. P oceedings o
2010 IEEE In e na ional Symposium on Ci cui s and Sys ems (ISCAS),
pp. 2956 – 2959. Pa is, F ance. May, 2010.
[6] Y. Oike, A. El Gamal. “CMOS Image Senso Wi h Pe -Column ΣΔ
ADC and P og ammable Comp essed Sensing”. IEEE Jou nal o Solid-
S a e Ci cui s, Vol. 48, No. 1, pp. 318 - 328, Janua y. 2013.
[7] B. Kaliannan, V S. Rao Pasupu eddi. “A Low Powe CMOS Image
Based on Dis ibu ed Comp essed Sensing”. 27 h In e na ional
Con e ence on VLSI Design and 13 h In e na ional Con e ence on
Embedded Sys ems, pp. 534 – 538. Mumbai, India. Janua y. 2014.
[8] M. Dadkhah, M. Jamal Deen, S. Shi ani. “CMOS Image Senso Wi h
A ea-E icien Block-Based Comp essi e Sensing”. IEEE Senso
Jou nal, Vol. 15 No. 7, pp 3699-3710, July, 2015.
[9] M. T e isi, R. Ca mona-Galán, Á. Rod íguez-Vázquez, "Comp essi e
Image Senso A chi ec u e wi h On-Chip Measu emen Ma ix
Gene a ion". IEEE In . Con . PhD Resea ch in Mic oel. and Elec onics
(PRIME 2017), pp. 25-28, Tao mina, Sicily (I aly), June 2017.
[10] E. Jen. “Ape iodici y in one-dimensional cellula au oma a”. Physica D:
Nonlinea Phenomena, Vol. 45 No. 1-3, pp 3-18. Sep embe , 1990.
[11] Lu Gan "Block Comp essed Sensing o Na u al Images", 15 h
In e na ional Con e ence on Digi al Signal P ocessing, pp. 403-406.
Singapo e, Republic o Singapo e. July, 2007.
[12] D. G. Chen, D. Ma olin, A. Be mak, C. Posch, “Pulse-Modula ion
Imaging—Re iew and Pe o mance Analysis”. IEEE T ans. on
Biomedical CAS, Vol. 5, No. 1, pp. 64-82, Feb ua y 2011.
[13] G. Sudhish, P. Deep hi. “A Secu e LFSR Based Random Measu emen
Ma ix o Comp essi e Sensing”. Sensing and Imaging, New Yo k,
Sp inge , 2014, Vol. 15 No. 1.
[14] L. Wang, Y. Zhao Z. Dai. “A Random Sequence Gene a ion Me hod o
Random Demodula ion Based Comp essi e Sampling Sys em”.
In e na ional Jou nal o Signal P ocessing, Image P ocessing and
Pa e n Recogni ion, Vol. 8 No. 1, pp 105-114, 2015.