1458 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 5, MAY 2011
IMAGE Resolution Enhancement by Using Discrete and
Stationary Wavelet Decomposition
Hasan Demirel and Gholamreza Anbarjafari
Abstract—In this correspondence, the authors propose an image resolu-
tion enhancement technique based on interpolation of the high frequency
subband images obtained by discrete wavelet transform (DWT) and the
input image. The edges are enhanced by introducing an intermediate stage
by using stationary wavelet transform (SWT). DWT is applied in order
to decompose an input image into different subbands. Then the high fre-
quency subbands as well as the input image are interpolated. The estimated
high frequency subbands are being modified by using high frequency sub-
band obtained through SWT. Then all these subbands are combined to
generate a new high resolution image by using inverse DWT (IDWT). The
quantitative and visual results are showing the superiority of the proposed
technique over the conventional and state-of-art image resolution enhance-
ment techniques.
Index Terms—Discrete wavelet transform, image super resolution, sta-
tionary wavelet transform.
I. INTRODUCTION
Resolution has been frequently referred as an important aspect of an
image. Images are being processed in order to obtain more enhanced
resolution. One of the commonly used techniques for image resolution
enhancement is Interpolation. Interpolation has been widely used in
many image processing applications such as facial reconstruction [1],
multiple description coding [2], and super resolution [3]–[6]. There are
three well known interpolation techniques, namely nearest neighbor
interpolation, bilinear interpolation, and bicubic interpolation.
Image resolution enhancement in the wavelet domain is a relatively
new research topic and recently many new algorithms have been pro-
posed [4]–[7]. Discrete wavelet transform (DWT) [8] is one of the re-
cent wavelet transforms used in image processing. DWT decomposes
an image into different subband images, namely low-low (LL), low-
high (LH), high-low (HL), and high-high (HH). Another recent wavelet
transform which has been used in several image processing applica-
tions is stationary wavelet transform (SWT) [9]. In short, SWT is sim-
ilar to DWT but it does not use down-sampling, hence the subbands
will have the same size as the input image.
In this work, we are proposing an image resolution enhancement
technique which generates sharper high resolution image. The pro-
posed technique uses DWT to decompose a low resolution image into
different subbands. Then the three high frequency subband images have
been interpolated using bicubic interpolation. The high frequency sub-
bands obtained by SWT of the input image are being incremented into
the interpolated high frequency subbands in order to correct the esti-
mated coefficients. In parallel, the input image is also interpolated sep-
arately. Finally, corrected interpolated high frequency subbands and
interpolated input image are combined by using inverse DWT (IDWT)
to achieve a high resolution output image. The proposed technique
has been compared with conventional and state-of-art image resolu-
Manuscript received May 28, 2010; revised August 09, 2010; accepted Oc-
tober 05, 2010. Date of publication October 18, 2010; date of current version
April 15, 2011. The associate editor coordinating the review of this manuscript
and approving it for publication was Dr. Rafael Molina.
H. Demirel is with the Department of Electrical and Electronic Engi-
neering, Eastern Mediterranean University, Mersin 10, Turkey (e-mail:
hasan.demirel@emu.edu.tr).
G. Anbarjafari is with the Department of Information Systems Engineering,
Cyprus International University, Mersin 10, Turkey (e-mail: sjafari@ciu.edu.tr).
Digital Object Identifier 10.1109/TIP.2010.2087767
tion enhancement techniques. The conventional techniques used are the
following:
— interpolation techniques: bilinear interpolation and bicubic
interpolation;
— wavelet zero padding (WZP).
The state-of-art techniques used for comparison purposes are the
following:
— regularity-preserving image interpolation [7];
— new edge-directed interpolation (NEDI) [10];
— hidden Markov model (HMM) [11];
— HMM-based image super resolution (HMM SR) [12];
— WZP and cycle-spinning (WZP-CS) [13];
— WZP, CS, and edge rectification (WZP-CS-ER) [14];
— DWT based super resolution (DWT SR) [15];
— complex wavelet transform based super resolution (CWT SR) [5].
According to the quantitative and qualitative experimental results, the
proposed technique over performs the aforementioned conventional
and state-of-art techniques for image resolution enhancement.
II. P
ROPOSED IMAGE RESOLUTION
ENHANCEMENT
In image resolution enhancement by using interpolation the main
loss is on its high frequency components (i.e., edges), which is due to
the smoothing caused by interpolation. In order to increase the quality
of the super resolved image, preserving the edges is essential. In this
work, DWT has been employed in order to preserve the high frequency
components of the image. The redundancy and shift invariance of the
DWT mean that DWT coefficients are inherently interpolable [9].
In this correspondence, one level DWT (with Daubechies 9/7 as
wavelet function) is used to decompose an input image into different
subband images. Three high frequency subbands (LH, HL, and HH)
contain the high frequency components of the input image. In the pro-
posed technique, bicubic interpolation with enlargement factor of 2 is
applied to high frequency subband images. Downsampling in each of
the DWT subbands causes information loss in the respective subbands.
That is why SWT is employed to minimize this loss.
The interpolated high frequency subbands and the SWT high fre-
quency subbands have the same size which means they can be added
with each other. The new corrected high frequency subbands can be
interpolated further for higher enlargement. Also it is known that in the
wavelet domain, the low resolution image is obtained by lowpass fil-
tering of the high resolution image [16]. In other words, low frequency
subband is the low resolution of the original image. Therefore, instead
of using low frequency subband, which contains less information than
the original high resolution image, we are using the input image for
the interpolation of low frequency subband image. Using input image
instead of low frequency subband increases the quality of the super
resolved image. Fig. 1 illustrates the block diagram of the proposed
image resolution enhancement technique.
By interpolating input image by
=
2
, and high frequency subbands
by 2 and
in the intermediate and final interpolation stages respec-
tively, and then by applying IDWT, as illustrated in Fig. 1, the output
image will contain sharper edges than the interpolated image obtained
by interpolation of the input image directly. This is due to the fact that,
the interpolation of isolated high frequency components in high fre-
quency subbands and using the corrections obtained by adding high
frequency subbands of SWT of the input image, will preserve more
high frequency components after the interpolation than interpolating
input image directly.
III. R
ESULTS AND DISCUSSIONS
Fig. 2 shows that super resolved image of Baboon’s picture using
proposed technique in (d) are much better than the low resolution
1057-7149/$26.00 © 2010 IEEE
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 5, MAY 2011 1459
Fig. 1. Block diagram of the proposed super resolution algorithm.
image in (a), super resolved image by using the interpolation (b),
and WZP (c). Note that the input low resolution images have been
obtained by down-sampling the original high resolution images. In
order to show the effectiveness of the proposed method over the
conventional and state-of-art image resolution enhancement tech-
niques, four well-known test images (Lena, Elaine, Baboon, and
Peppers) with different features are used for comparison. Table I
compares the PSNR performance of the proposed technique using
bicubic interpolation with conventional and state-of-art resolution
enhancement techniques: bilinear, bicubic, WZP, NEDI, HMM, HMM
SR, WZP-CS, WZP-CS-ER, DWT SR, CWT SR, and regularity-pre-
serving image interpolation. Additionally, in order to have more
comprehensive comparison, the performance of the super resolved
image by using SWT only (SWT-SR) is also included in the table. The
results in Table I indicate that the proposed technique over-performs
the aforementioned conventional and state-of-art image resolution
enhancement techniques. Table I also indicates that the proposed tech-
nique over-performs the aforementioned conventional and state-of-art
image resolution enhancement techniques.
IV. C
ONCLUSION
This work proposed an image resolution enhancement technique
based on the interpolation of the high frequency subbands obtained
by DWT, correcting the high frequency subband estimation by using
Fig. 2. (a) Original low resolution Baboon’s image. (b) Bicubic interpolated
image. (c) Super resolved image using WZP. (d) Proposed technique.
1460 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 5, MAY 2011
TABLE I
PSNR (
DB) R
ESULTS FOR
RESOLUTION ENHANCEMENT
FROM
128
2
128 TO
512
2
512
OF THE
PROPOSED TECHNIQUE
COMPARED
WITH THE
CONVENTIONAL AND
STATE-OF-ART
IMAGE
RESOLUTION ENHANCEMENT
TECHNIQUES
SWT high frequency subbands, and the input image. The proposed
technique uses DWT to decompose an image into different subbands,
and then the high frequency subband images have been interpolated.
The interpolated high frequency subband coefficients have been cor-
rected by using the high frequency subbands achieved by SWT of the
input image. An original image is interpolated with half of the interpo-
lation factor used for interpolation the high frequency subbands. After-
wards all these images have been combined using IDWT to generate
a super resolved imaged. The proposed technique has been tested on
well-known benchmark images, where their PSNR and visual results
show the superiority of proposed technique over the conventional and
state-of-art image resolution enhancement techniques.
A
CKNOWLEDGMENT
The authors would like to thank Dr. I. Selesnick from Polytechnic
University for providing the DWT and SWT codes in MATLAB.
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