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 
Automatic Spatially Dependent Parameter Selection for TV De-
noising of MR Images with Non-Uniform Noise Distribution
Florian Knoll, Yiqiu Dong, Michael HintermüllerRudolf Stollberger
Graz University of Technology, Institute of Medical Engineering, Graz, Austria
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Humboldt-University of Berlin, Department of Mathematics, Berlin, Germany
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Abstract
The Total Variation is a popular image model for denoising of MR images. The key problem in the application of the
method is often the determination of a proper regularization parameter. This work presents an automatic strategy to
determine a spatially dependent regularization parameter. It is shown that the method can be applied in cases where the
distribution of the noise is uniform over the whole image, as well as in situations when this assumption cannot be made.
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1 Introduction
The Total Variation (TV) is a popular regularization model
in image processing [1]. It was also recently introduced
for various applications in MR research. Examples include
denoising and constrained image reconstruction [2]. In
all TV based methods, a constrained optimization problem
has to be solved that consists of two terms. A penalty term
which enforces a low TV norm of the solution and a data
ÀGHOLW\ WHUP ZKLFK HQVXUHV WKDW WKH VROXWLRQ LV FRQVLVWHQW
with the original data. A regularization parameter controls
the tradeoff between the noise elimination and preserva-
tion of image details. Determination of the regularization
parameter is often performed based on visual inspection of
the reconstruction. This is a cumbersome and time con-
suming task and the results are always biased towards the
personal preference of the user. Additionally, MR images
are comprised of multiple details. In homogenous regions,
a higher regularization can be performed than in regions
ZKLFK LQFOXGH PXOWLSOH ÀQH GHWDLOV 7KLV LQGLFDWHV WKDW LW
is desireable to apply different amounts of regularization
EDVHG RQ WKH OHYHO RI GHWDLO LQ D VSHFLÀF UHJLRQ ,Q WKLV ZRUN
spatially dependent regularization parameter selection for
TV based denoising of MR images is introduced. With
this technique, the regularization parameter is adapted au-
tomatically based on the details in the images. This im-
proves the reconstruction of details while still providing
adequate smoothing for the homogeneous parts. It is also
demonstrated that this method can be used successfully in
situations where the distribution of the noise is not uniform
throughout the image, as it often occurs in combination
with parallel imaging reconstruction of undersampled data
sets [3, 4].
2 Theory
In order to enhance regions containing details while still
VXIÀFLHQWO\ VPRRWKLQJ KRPRJHQHRXV SDUWV ZH LPSURYH WKH
TV-model by using a spatially dependent regularization pa-
rameter instead of a scalar value only, i.e. we consider,





	
# ! % #  ! (1)
where % is the noisy image, ! is the restored image, and
 ! is the conventional TV penalty term [1]. In this
model,  is localized at image features. For small features,
large  leads to little smoothing so that details are usually
preserved well. On the other hand, for large features, small
 leads to smoothing so that noise is removed consider-
ably. Referring to [5], it can be shown that the minimiza-
tion problem (1) is related to a constrained optimization
problem of the type:


 ! (2)
 

	
! % #   !
for all windows ! with window size  in !. Here,  is
the noise variance, estimated from the image. Compared
with the common TV-model, the constraint in (2) is con-
ÀQHG WR HDFK ORFDO UHJLRQ ! instead of the whole image.
Considering a restored image ! from the TV-model with
a relatively small , the residual   %  ! will include
noise as well as details. Then, the violation of the local
FRQVWUDLQW LQ  UHÁHFWV WKH GLVWULEXWLRQ RI GHWDLOV LQ WKH
LPDJH %DVHG RQ WKLV ZH GHÀQH D VWDWLVWLF ´ORFDO YDULDQFH
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  
estimator”, as
 



	
%  ! (3)
where  is the window size. In general, whenever 
is less than  LH WKH FRQVWUDLQW LQ  LV VDWLVÀHG LW LV DV
sumed that in ! the residual primarily consists of noise.
2WKHUZLVH VLJQLÀFDQW LPDJH GHWDLOV DUH OHIW LQ WKH UHVLGXDl,
and  needs to be increased in order to preserve the details
in the reconstruction. This adjustment depends on a robust
upper bound for the (local) constraint. For this purpose,
WKH FRQÀGHQFH LQWHUYDO WHFKQLTXH IURP VWDWLVWLFV >@ LV LQ
troduced to automatically adjust  based on the size of the
windows ! . This yields a parameter-free method, i.e.,
without necessity of manually tuning parameters. More-
over, the minimization problem in (2) is solved by a su-
perlinearly convergent algorithm based on Fenchel-duality
and inexact semismooth Newton techniques [5, 7].
a) b) c)
d) e) f)
Figure 1: A numerical example of spatially variant regu-
larization. (a) A numerical test image. (b) Noisy test im-
age. (c) TV denoising with   . (d) TV denoising with
  . (e)  map:    (dark region) and   
(bright region). (f) TV denoising with spatially variant 
from subplot (e).
The concept of spatially variant regularization is illustrated
in Fig. 1 which shows the effect of different regularization
parameters for a numerical test image. If the amount of
regularization is too small, residual noise remains in the
image. With higher regularization, noise is eliminated, but
small image features start to disappear. The use of two dif-
ferent regularization parameters for the same image yields
a result where noise is eliminated, and small features are
preserved.
One limitation of this parameter estimation strategy is that
it assumes that noise is uniformly distributed over the
whole image. In reconstructions from undersampled data
with parallel imaging [3, 4] which are nowdays widely
used in daily clinical practice due to the pronounced reduc-
tion of scanning time, this assumption is violated. Recon-
VWUXFWHG LPDJHV VKRZ VLJQLÀFDQW ORFDO QRLVH DPSOLÀFDWLRQV
ZKLFK GHSHQG RQ WKH FRQÀJXUDWLRQ RI WKH XVHG FRLO DUUD\V
and their ability to separate pixels which are superimposed
due to aliasing. This decrease of SNR due to noise ampli-
ÀFDWLRQ FDQ EH TXDQWLÀHG E\  
	



[3]. The
factor

 only depends on the acceleration rate  and is
the same for each pixel in an image. In contrast, , the
so called geometry (g)-factor, strongly depends on the coil
geometry and takes different values for each pixel - in the
image. If the method from equation (2) is now directly ap-
plied to these data sets, the algorithm will interpret these
ORFDO QRLVH DPSOLÀFDWLRQV DV DGGLWLRQDO GHWDLOV LQ WKH LP
age. This means that the regularization will be decreased
in regions where the corruption with noise is higher. In
order to prevent this, information about the spatial distri-
EXWLRQ RI WKH QRLVH DPSOLÀFDWLRQ QHHG EH LQFOXGHG LQ WKH
parameter estimation process.
Since  VKRZV WKH QRLVH DPSOLÀFDWLRQV LQ UHFRQVWUXFWHG
parallel images, the noise variance can be estimated as a
multiple of , i.e., 
  , where  is the noise variance
in the background. Then, we restore the image iteratively
by adjusting  according to the following rule:


  



  -

     


 



	


  (4)
where -  					 
  in order to keep the new
 at the same scale as . Initially, we assign a small
positive value to  in order to keep most of the details in
the residual. After that, we restore the image iteratively,
and keep increasing  in the regions where the constraint
LQ  LV YLRODWHG XQWLO WKH FRQVWUDLQW LV VDWLVÀHG LQ DOO ! .
3 Methods and Results
3.1 Restoration of MR images with uniform
noise distribution
,Q D ÀUVW H[SHULPHQW GHQRLVLQJ ZDV SHUIRUPHG RQ D GDWD
set where the assumption of uniform noise distribution is
valid, and the parameter estimation strategy from equa-
tion (2) can be applied directly. MR measurements of the
brain of a healthy volunteer were performed on a clinical
3T scanner (Siemens Magnetom TIM Trio, Erlangen, Ger-
many) using a 4 channel head coil. Written informed con-
sent was obtained prior to the examination. A fully sam-
pled  weighted turbo spin echo scan was used. Sequence
parameters were repetition time TR=5000ms, echo time
TE=99ms, turbo factor 10, matrix size (x,y)=(256,256), 10
slices with a slice thickness of 4mm and an in plane resolu-
tion of 0.86mm  0.86mm. The raw data set was exported
from the scanner and complex Gaussian noise was added to
the original -space data of each individual coil. The stan-
dard deviation of the added noise was chosen such that the
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
ratio to the norm of the data was 1/40, 1/30 and 1/20. After-
wards, individual coil images were reconstructed with an
inverse FFT and a sum of squares combination of the coils
was performed. TV denoising was then performed with the
proposed spatially variant parameter selection method (2).
Fig. 2 displays noisy images, TV denoising results and
the corresponding  parameters from the experiments with
uniform noise distribution.
Noisy image TV denoised result L  map
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is
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Figure 2: TV restoration results from MR brain data with
uniform noise distribution. The images with noise (left col-
umn), the TV restorations and the regularization parameter
maps are displayed for three different levels of SNR.
3.2 Restoration of parallel imaging recon-
structions with non-uniform noise distri-
bution
In the second experiment, parallel imaging reconstructions
of the same dataset as in section 3.1 were investigated.
Noise was again added to the original -space data with
a standard deviation of 1/50 with respect to the ratio to
the norm of the data. Retrospective subsampling was per-
formed by including only every second (R=2) and every
third (R=3) line in row direction. 2D acceleration was
simulated by performing factor 2 subsampling in both row
and column direction, leading to total acceleration factor
of   . Coil sensitivity maps were obtained by divid-
ing each individual coil image of the fully sampled data
set by the sum of squares combination. Parallel imaging
reconstruction was performed with a SENSE [3] based al-
gorithm. This experiment was repeated ~~ times. Noise
DPSOLÀFDWLRQ PDSV ZHUH REWDLQHG E\ FDOFXODWLQJ WKH VWDQ
dard deviation in each pixel over all ~~ experiments. This
was done for both unaccelerated and accelerated images.
R = 2 R = 3 R = 4
N
o
is
y
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I 
re
c
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Figure 3: TV restoration results from undersampled par-
allel imaging MR data sets. Noisy images, parallel imag-
LQJ QRLVH DPSOLÀFDWLRQ PDSV 79 UHVWRUDWLRQ DQG WKH UHJX
larization parameter maps are displayed for three different
levels of acceleration.
Denoised result L  map
(a
)
(b
)
Figure 4: Comparison of denoising results for R=3 ac-
celerated parallel imaging reconstructions. Results with
the proposed method (4) (a) and with the original formula-
tion (2) (b) are shown.
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
The ratio of these two noise maps was used as an estima-
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denoising results and the corresponding  parameters are
shown in Fig. 3.
Fig. 4 shows a comparison of the proposed method which
includes information about the noise distribution with a di-
rect application of (2), which assumes that the noise distri-
bution is uniform for the case    of Fig. 3.
4 Discussion
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JDWHG H[SHULPHQWV ZKLOH SUHVHUYLQJ ÀQH LPDJH IHDWXUHV
Bright values in the regularization parameter maps of
Figs. 2, 3 and 4 correspond to high values of . This means
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LQÁXHQFH RQ WKH VROXWLRQ DQG WKHUHIRUH WKH 79 UHJXODUL]D
tion is reduced. As expected, the algorithm decreases reg-
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Additionally, the overall brightness of the parameter map
is higher in images with less noise corruption (top row in
Fig. 2, cases    and    in Fig. 3). This means that
the overall amout of regularization is lower in these cases
and illustrates, that the algorithm automatically adapts to
the noise level in a particular image.
,W LV HYLGHQW IURP WKH QRLV\ LPDJHV DQG WKH QRLVH DPSOLÀFD
tion maps in Fig. 3, that the assumption of a uniform noise
distribution is violated in this case. Pronounced noise am-
SOLÀFDWLRQ RFFXUV LQ VSHFLÀF UHJLRQV RI WKH LPDJHV 7KH
reason is, that the receive coils that were used during the
SDUDOOHO LPDJLQJ UHFRQVWUXFWLRQ GR QRW GHOLYHU VXIÀFLHQWOy
independent information in these regions. This is also the
UHDVRQ ZK\ QRLVH DPSOLÀFDWLRQ LV KLJKHU IRU    than
for two dimensional    acceleration because the sen-
sitivities of the receive coils deliver equal amounts of in-
dependet information in the row and column direction. It
can also be seen from the regularization parameter maps
WKDW WKH DOJRULWKP FRUUHFWO\ LGHQWLÀHV UHJLRQV ZLWK D KLJK
amount of detail and reduces the regularization in these
UHJLRQV ZLWKRXW EHLQJ LQÁXHQFHG E\ ORFDO QRLVH DPSOLÀFD
tion.
The parameter maps in Fig. 4 demonstrate that the orig-
inal method (equation 2) decreases regularization in re-
JLRQV ZLWK KLJK QRLVH DPSOLÀFDWLRQ WKH SDUDPHWHU PDSV
are brighter in these regions) because it is not able to seper-
ate them from locations in the image with a high amount
RI ÀQH GHWDLOV 7KHUHIRUH VLJQLÀFDQW DPRXQWV RI UHVLGXDO
noise remain in the TV restoration. This problem does
not occur with the proposed parameter selection strategy
(equation 4).
While our experimental setup of repeating parallel imaging
reconstruction  times is of course not suitable for prac-
tical application, this approach was chosen because it is
the only established gold standard to estimate noise in par-
allel imaging. The SENSE theory [3] also allows to make
WKHRUHWLFDO SUHGLFWLRQV DERXW QRLVH DPSOLÀFDWLRQV EDVHG Rn
the used coil geometry. The use of such g-factor maps in
the proposed method is the subject of current investiga-
tions. Future work will also include the extension of the
proposed method to the problem of constrained image re-
construction [2].
One of the most important features of the proposed param-
eter selection strategy is that it is completely independent
RI DQ\ XVHU GHÀQHG SDUDPHWHUV :KLOH UHJXODUL]HG LPDJH
reconstruction and image denoising have been very active
ÀHOGV LQ 05, UHVHDUFK GXULQJ WKH ODVW \HDUV VHOHFWLRQ RI
the regularization parameter is still based on visual inspec-
tion of the results in many cases, and surprisingly little
work has been done as regards this subject. Our results
have shown that automatic estimation of spatially depen-
dent regularization parameters leads to excellent results in
MR image denoising and that the algorithm automatically
adapts to data sets with different amounts of noise level
DQG ÀQH GHWDLOV
Acknowledgements
This work was supported through project SFB F3209
granted by the Austrian Science Fund.
References
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tal variation based noise removal algorithms,” Phys.
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radial MRI with multiple coils. Iterative image recon-
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[3] K. P. Pruessmann, M. Weiger, M. B. Scheidegger,
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Nov 1999.
[4] M. A. Griswold, P. M. Jakob, R. M. Heidemann,
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tions (GRAPPA).” Magn Reson Med, vol. 47, no. 6,
pp. 1202–1210, Jun 2002.
[5] Y. Dong, M. Hintermüller, and M. Rincon-Camacho,
“Automated parameter selection in a multi-scale total
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versity of Graz.
[6] A.Mood, Introduction to the Theory of Statistics. Mc-
Graw Hill, 1974.
[7] M. Hintermüller and G. Stadler, “An infeasible primal-
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6FLHQWLÀF &RPSXWLQJ, vol. 28, no. 1, pp. 1–23, 2006.
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Automatic Spatially Dependent Parameter Selection for TV De- noising of MR Images with Non-Uniform Noise Distribution

Aistleitner, Christoph

Berkes, István

Seip, Kristian

GCD sums from Poisson integrals and systems of dilated functions

Müller-Putz, Gernot R.

Ofner, Patrick

Schwarz, Andreas

Pereira, Joana

Pinegger, Andreas

Dias, Catarina Lopes

Hehenberger, Lea

Kobler, Reinmar J.

Sburlea, Andreea Ioana

Towards Non-Invasive EEG-based Arm/Hand­
Control in Users with Spinal Cord Injury 
Gemüt R. Müller-Putz, Patrick Ofner, Andreas Schwarz, Jüana Pereira, Andreas Pinegger, Catarina Lüpes Dias, 
Lea Hehenberger, Reinmar Kübler, Andreea Tüana Sburlea 
Institute ofNeural Engineering, BCI Lab 
Graz University of Technology 
Graz, Austria 
gernot.mueller@tugraz.at 
Abstract - Restodng the ability to reach and gmsp can 
dramatically improve quality of life for people with ce,"Vical spinal 
cord injury (SCI)" The main challenge in restoring independent 
,"eaching and gmsping in patients is to develop assistive 
technologies with intuitive and non-invasive user inte,"faces. We 
believe that this challenge can be met by directly translating 
movement-related brain activity into control signals" During the 
last decade, we have conducted ,"esea,"ch on EEG-based brain­
computer interfaces (BCIs) for the decoding of movement 
parameters, such as trajectories and targets" Although our 
findings are promising, the control is still unnatural. Therefore, 
we sUl"mise that natural and intuitive control of neu,"opl"Ostheses 
could be achieved by developing a novel control framework that 
incorporates detection of goal directed movement intention, 
movement decoding, identifying the type of grasp, error potentials 
detection and delivery of feedback. 
Keywords - EEG, brain-computer interface, natural movement 
control, spinal cord injury 
1. INTRODUCTION 
Grasping an apple, brushing teeth, or simply playing around 
with the fingers is not possible for people who received a 
cervical spinal cord injury. Depending on the damaged area, 
motor commands from the brain to the periphery (efferent) or 
sensory signals from the periphery to the brain (afferent) 
cannot bypass the interruption in the spinal cord. One approach 
to provide help for this group of people is to detect the 
intention of their movement and to reproduce the movement of 
their paralyzed arm/hand with the help of a motor 
neuroprosthesis or artificial anno 
In the past we have shown that it is possible to combine 
brain-computer interfaces with motor neuroprostheses [1]. We 
used classical motor imagery of sustained feet or hand 
movement in a single class BCI to switch between predefined 
grasp phases [2], [3]. Later, we applied our methodology for 
elbow movements in healthy subjects and in end-users with 
SCI [4], [5], [6]. 
The introduction of hybrid BCIs [7], [8], known as the 
fusion of a BCI with a second input modality (e.g., shoulder­
controlled joystick), allowed the user to benefit from the 
advantages of both technologies [9]. Various studies showed 
the benefits of the hybrid BCI concept over classical BCI [10], 
[11]. However, these strategies have the drawback of not 
reflecting the natural way of planning a movement. To achieve 
an ecological and intuitive control, the movements decoded by 
the BCI need to be closely related to the user's intention. 
11. METHODS & RESULTS 
In the following section we describe the results of first 
experiments which are the basis of our research towards a 
natural neuroprosthesis control based on non-invasive EEG 
signals. 
A. Goal directed movement detection 
Movement-related cortical potentials (MRCPs) are EEG 
neural correlates of movement which have been used for 
movement intention detection and are known to be modulated 
by several movement-related parameters [12]. We study 
MRCPs during goal-directed movement tasks to assess whether 
goal-directed strategies should be preferred in the context of 
BCI control [13]. Our first results on healthy subjects suggest 
that movement detection is significantly improved in goal­
directed movement execution when compared to the same task 
(i.e. same movement kinematics) without a specific target. 
These differences are particularly visible during movement 
planning. Such performance improvements can lead to a 
reliable and natural response of the BCI-controlled system to 
the user's intention. By estimating the brain sources of the 
discriminative spatial patterns, we further concluded that the 
differences between the two motor tasks were associated to 
motor areas and the posterior parietal lobule. 
B. Movement decoding from executed and 
imagined arm movements 
We showed in [14] the decoding of executed hand 
movements with a linear decoding model from low-frequency 
EEG signals. The Pearson correlation coefficients between the 
decoded and measured hand positions were 0.70, 0.78 and 
- 63-
0.62 for the x, y, and z dimension, respectively. Based on this 
decoder, we discriminated between imagined horizontal and 
vertical hand movements with astatistically significant 
cIassification accuracy of 64% [15]. 
c. Decoding o/movement target/direction 
In a preliminary study employing a center-out reaching 
task to 4 targets displayed on a computer screen, all 3 subjects 
reached a statistically significantly classification accuracy of 
42%, 47% and 73% [16]. 
D. Single joint movement classifzcation 
Based on EEG signals from 0.3 to 3 Hz, we found 6 
different upper-limb movements to be discriminable with a 
cIassification accuracy of 37% in a group of 15 healthy 
subjects [17]. The cIassifier sources originated mainly on 
premotor and primary motor areas. 
E. Classifzcation 0/ different types 0/ grasp 
Despite the high number of degrees of freedom of the 
human hand, most actions of daily life can be executed using 
just palmar, pinch or lateral grasp [18]. Therefore we 
conducted an EEG-based study in 15 healthy users to find out 
whether these grasps can be discriminated from each other and 
from a no-movement condition. Using a cue-guided paradigm, 
we recorded 72 trials of executed reach and grasp actions for 
each condition. Our results show that time-domain features 
located in the low frequency range (0.3-3 Hz) provide 
sufficient information for meaningful classification [19]. 
TTT. DISCUSSION 
With the presented work we laid the basis for a series of 
several studies in these specific areas, with the final aim of 
developing a new decoder system. Using the new system end 
users with SCI will be able to control neuroprosthethic arm 
movements in 3D space with the goal to grasp and manipulate 
objects. However, several aspects need to be addressed further. 
When the user controls a robotic arm or neuroprosthesis, 
visual feedback is inherent. Without experimental restrictions, 
the eyes would track points of interest (e.g. end-effector and 
target object). lt is therefore imperative to remove the resulting 
electroocular artifacts in order to obtain reliable control based 
on EEG brain activity. 
In addition, we aim to incorporate a classifier of error­
related potentials, as a backup system. When the main cIassifier 
fails, and the prosthesis's movement does not correspond to the 
user's intent, the user will perceive this action as an error and 
therefore generate an error-related potential. By detecting error­
related potentials during the continuous movement of the 
prosthesis, its trajectory can be automatically corrected or 
interrupted, allowing a smoother and faster interaction between 
the user and the prosthesis. 
Intuitive control of a neuroprosthesis necessitates artificial 
feedback to compensate for the absence of the comprehensive 
feedback provided to a healthy person via intact afferent 
pathways, such as the sense of touch, proprioception or grasp 
force. 
IV. CONCLUSION 
In conclusion, our findings highlight the growing interest 
for non-invasive EEG-based BCI and its potential for the 
recovery of upper limb lost functions in individuals with 
spinal cord injury. The results of our studies based on the 
detection of goal directed movement intention, movement 
decoding, identifYing the type of grasp, error potentials 
detection and deIivery of feedback, show a promising 
perspective towards achieving a natural and intuitive control 
of neuroprostheses. 
ACKNOWLEDGMENT 
This work was supported by the Horizon 2020 RlA project 
MoreGrasp (643955) and the ERC Consolidator Grant FeeI 
Y our Reach (681231 ). 
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- 65-


English

Towards Non-Invasive EEG-based Arm/Hand­ Control in Users with Spinal Cord Injury

Arsanjani, Arash

Sarbandifarahani, Hossein

Rezaee, Behrooz

Teschl, Reinhard

Bösch, Wolfgang

A Compact Slow-Wave Filter with Double-sided
Selectivity and Wide Out-of-Band Rejection
Arash Arsanjani1, Hossein Sarbandi Farahani2, Behrooz Rezaee, Reinhard Teschl, and Wolfgang Bösch
Institute of Microwave and Photonic Engineering, Graz University of Technology, Graz, Austria
1 arash.arsanjani@tugraz.at, 2 sarbandifarahani@tugraz.at
Abstract—In this paper, a miniaturized filter with double-sided
selectivity and wide out-of-band rejection is presented. The
slow-wave and negative cross-coupling structures are effectively
adopted to realize an ultra-compact K-band filter with two
symmetric transmission zeros. Starting from a bandpass filter
configured for a center frequency of 18.5 GHz and the main-line
couplings that only exhibits a good out-of-band rejection of 30
dB up to 30 GHz, the two proposed negative cross-couplings
enable the steep roll-off out-of-band rejections as well as low
in-band insertion losses of 1.7 dB and 2.4 dB. The designed
structures are utilizing both the additive manufacturing
and PCB-based technology which in turn, provide a simple,
low-profile, and cost-effective fabrication process for highly
integrated RF systems, particularly in satellite applications.
Index Terms—K-band filter, negative coupling, slow-wave,
transmission zero.
I. INTRODUCTION
Future generations of telecommunication systems will
exhibit a deeper integration – or even convergence – of
fixed and mobile services. Scenarios have been identified
were satellite systems and in particular LEO satellite mega-
constellations, can support 5G architectures to improve
the connectivity of IoT devices in remote areas. Besides
managing the intersystem handover and security issues, other
challenges have been identified. One of which is associated
with the economic utilization of the limited spectrum and the
use of higher frequencies. For that purpose filters are essential
building blocks which demand low-profile, lower losses, strict
passband performance, and good out-of-band rejection [1].
Slow-wave microwave components are a branch of metama-
terials that provide good performance in terms of out-of-band
rejection and size reduction, making them a good candidate to
address the strict requirement of satellites. Many investigations
have been made to exploit the benefits of slow-wave structures
in implementing microwave and mm-wave components [2],
[3]. One of the worthy mentions is the implementation of slow-
wave substrate integrated waveguide (SW-SIW) [2], where the
slow-wave effect inside the SIW was created by an array of
periodic blind vias inside the propagation medium. The SW-
SIW reported in [2] achieved a longitudinal size reduction
of better than 40% compared to a conventional SIW. There is
also a recent study of a slow-wave filter implementation in the
SIW platform [4], [5], where the implementation of inductive
post and iris coupling has been investigated. Both of the filters
exhibit a significant size reduction. However, it is shown in the
results that the insertion loss is high due to the dielectric losses.
In some other literature, a type of slow-wave structure is intro-
duced, where it is referred to as meta-substrate structure. These
meta-substrate structures also show significant improvement
in miniaturization of microwave components such as patch
antennas [6] or SIW cavities [7]. All of these components are
designed for the lower spectrum of microwave frequencies.
Despite the compactness of these planar solutions, one sig-
nificant setback in the implementation of slow-wave structures
in a planar solution were the increased losses, especially at
higher frequencies. One method of reducing losses at higher
frequencies was to remove the dielectric substrate to eliminate
the dielectric losses [8], [9]. Reference [9] proposes a semi-
planar structure which has the advantage of compactness and
high quality factor performance. Additionally, having a PCB
layer as the top layer provides opportunities to create paths
for waves through the PCB layer to create negative coupling.
Moreover, the filter component can be used as surface mount-
able component which can be interesting in some applications.
The implementation of a semi-planar air-filled SW filter has
challenges of its own and requires further investigation. This
paper investigates two different methods for implementing
a negative coupling in the proposed SW filter configuration.
All three proposed structures show low losses due to
the elimination of dielectric loss from the structure. The
two proposed negative couplings created symmetrical
transmission zeroes around the passband, thus improving
the filter’s frequency selectivity. Furthermore, the slow-wave
filters show improved out-of-band rejection because of the
SW’s frequency selective characteristic, which is a desirable
factor in practical filter design. In the end, a comparison
between the three filter configuration is made and a conclusion
based on the achieved results is drawn.
II. SLOW-WAVE FILTER DESIGN
A. Slow-wave Unit-cell and resonator
The working principle of slow-wave structures is based
on reducing the group velocity of the transmission line
by creating an array of periodic structures in the wave
propagation path. The unit cell design is decided based on
the upper out-of-band rejection specification and the required
miniaturization. The stop-band of the unit cell can be utilized
to achieve an even better out-of-band rejection. The dispersion
diagram of the proposed unit cell is shown in Fig. 1. The
stopband of the proposed unit cell is in the frequency band
of 62 to 95 GHz, while the designated slow-wave passband
is from 17 to 20 GHz. Therefore, an excellent out-of-band
rejection can be achieved with a careful design of unit-cell
resonators and input and output coupling.
This manuscript is a reproduction of the accepted version of the paper with the full citation:
A. Arsanjani, H. S. Farahani, B. Rezaee, R. Teschl and W. Bösch, "A Compact Slow-Wave Filter with Double-sided Selectivity and Wide Out-of-Band Rejection,"
2021 IEEE Asia-Pacific Microwave Conference (APMC), 2021, pp. 256-258, doi: 10.1109/APMC52720.2021.9661651.
https://ieeexplore.ieee.org/document/9661651, Copyright © 2021, IEEE
Fig. 1: Dispersion diagram of the slow-wave structure over the
irreducible Brillouin zone (Γ−X−M−Γ).
Additionally, to demonstrate the slow-wave effect of the
proposed structure, the phase velocity was plotted versus the
frequency for different values of pin’s height. It is shown
in Fig. 2 that the bigger the height of the pins are with
respect to the cavity, the slower is the phase velocity of the
proposed structure. The resonator created with the proposed
unit-cell shows a size reduction of equal to 41% compared to
a conventional resonator of the same shape without the pins.
B. Inline filter and negative coupling implementation
A four-pole inline filter was designed using the proposed
slow-wave resonators, with an insertion loss of 1.7 dB at
the center frequency of 18.5 GHz and a bandwidth of 400
MHz. The proposed filter has a lower roll-off factor of
6.1 dB/100 MHz, an upper roll-off factor of 7.9 dB/100 MHz
and an out-of-band rejection of better than 30 dB up to
30 GHz. The substrate used for the proposed structure is
from the Rogers company (RO4350B), with a thickness of
0.508 mm, dielectric constant of εr = 3.66 and dissipation
factor of tanδ=0.0037. The frequency response of the filter,
as shown in Fig. 3c, has an acceptable performance in terms
of loss and out-of-band rejection.
As a complementary, the filter selectivity was improved by
implementing transmission zeros around the passband. Two
possible solutions for achieving a negative coupling were
simulated: either through the substrate integrated waveguide
on top or from a GCPW coupling through the top conductor
of the resonator. The non-zero elements of the coupling
matrix of the proposed filter have the following values:
MS1 = M4L = 0.91, M12 = M34 = 0.79, M23 = 0.676,
M14 = −0.071. The aforementioned couplings and external
quality factor and corresponding physical dimensions of the
filter can then be calculated through the following expressions:
K=
f2High−f2low
f2High+f
2
low
, Qext =
2f0
BW−3 dB
, (1)
The two possible solutions along with the frequency
responses are shown in Fig. 4a and Fig. 5a, respectively. These
filters were simulated through the frequency domain engine
10 20 30 40 50 60 70
Frequency (GHz)
0.5
1
1.5
2
2.5
/c
0
h2/h3=0
h2/h3=0.4
h2/h3=0.6
h2/h3=0.8
Fig. 2: Normalized phase velocity (νφ/c0) versus frequency
for different relative heights of pins (h2) to the height of the
cavity (h3).
(a) (b)
𝑺
MS1
R1
R2 R3
R4 𝑳
M23
M12 M34
M4L
(c)
Fig. 3: (a) 4-pole filter inline filter, (b) top view of filter, and
(c) out-of-band rejection performance of filter.
of CST 2020, and the results were confirmed using the HFSS
software. The Fig. 4a solution provides the filter response
with a roll-off factor of 13.8 dB/100 MHz and upper roll-off
factor of 18.9 dB/100 MHz, which provides better selectivity
compared to the inline configuration. The second solution also
provides a good roll-off factor of 13.9 dB/100 MHz and upper
roll-off factor of 15.7 dB/100 MHz. The negative coupling
(a) (b)
M14
𝑺
MS1
R1
R2 R3
R4 𝑳
M23
M12 M34
M4L
(c)
Fig. 4: First proposed filter (a) negative coupling structure-1,
(b) top view, (c) filter response inset with topology.
provided in both solutions are realized by transferring the
peak of electrical fields of the first resonators to that of the
fourth resonator. The first solution shows a filter response with
lower insertion loss than the second solution because the slots
on top of the resonator can cause an increased leakage loss.
III. CONCLUSION
In this communication, we described the implementation
of two negative coupling solutions which can effectively
improve the frequency selectivity, in-band insertion loss,
and overall size of an inline slow-wave filter with the
same filtering specifications but more number of resonators.
The two proposed filters feature a lower roll-off factor of
13.8 dB/100 MHz and 13.9 dB/100 MHz and an upper roll-off
factor of 18.9 dB/100 MHz and 15.7 dB/100 MHz, respec-
tively. The proposed filter has the advantages of low-loss,
high selectivity, good out-of-band rejection, and low-profile.
ACKNOWLEDGEMENT
“This project has received funding from the European
Union’s Horizon 2020 research and innovation pro-
gramme under the Marie Skłodowska-Curie grant agreement
No 811232”.
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M14
𝑺
MS1
R1
R2 R3
R4 𝑳
M23
M12 M34
M4L
(c)
Fig. 5: Second proposed filter (a) negative coupling structure-
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A Compact Slow-Wave Filter with Double-sided Selectivity and Wide Out-of-Band Rejection

Graz University of Technology

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