Novel Approach for Image Restoration and Transmission

Rabab Abdul Rasool
International Journal of Image Processing (IJIP), Volume (8) : Issue (5) : 2014 220
Novel Approach for Image Restoration and Transmission
Rabab Abdul Rasool rabab_rassol@yahoo.com
Computer and Software Engineering
Al-Mustansirya University
Baghdad, Iraq
Abstract
This paper develops a new technique in image restoration and transmission process, where the
image size is halved after transforming it to the frequency domain by applying discrete Fourier
transform. The conjugate symmetry and mirror property of transformed image spectrums could be
utilized by deleting the redundant spectrums from second half image after tracking and keeping
the conjugated locations. Those redundant locations are kept using one- to- one relationship.
Depending on the halving procedure, the new image size will be divided by two. A reconstructed
procedure is created to redistribute the deleted spectrum with their associated locations. The
reconstructed image is ready now for restoring again by applying the inverse discrete Fourier
transform back to the spatial domain. The restored image is qualified using Peak Signal to Noise
Ratio measurement and the result was very satisfied. The advantages of this technique appear in
the storage cost, where the memory locations will be reduced to the half. Also, from
communication side, this work approved that the image transmission time needs to transmit the
halved image is half of the original one.
Keywords: DFT, Conjugate Symmetry, Mirror, One to one.
1. INTRODUCTION
Most of digital image processing methods concern how to process image details in spatial
domain. Image details might be color intensity or pixel coordinates (locations). The second
domain that digital image could be processed in is the frequency domain. The transformation
from spatial domain to the frequency one could be implemented by applying the Two Dimension
Discrete Fourier Transform (2D-DFT) or Fast Fourier Transform (FFT) [1] [2]. The transformed
image details are spectrums. These spectrums are distributed in a manner that has many
properties like: DC coefficients; conjugate symmetry; shifting; and mirror. Transforming from
spatial to the frequency domain will still provide same operation and even better because it is an
alternative method for low pass and high pass filtering. Also, it could process some particular
frequencies efficiency. The convolution in time or spatial domain could be intercepted into
multiplication in frequency domain, and for this reason image will be processed as a whole block.
This work adopts and develops new technique of considering the half image size in storing and
network communication. This technique applies the mirror and conjugate symmetry property in
implementing the tracking, mapping, and reconstructing procedure. Image restoration in [1] has
different procedure which is based on the intensities of the nearest neighbor of pixel in spatial
domain [3][4] . This paper is organized as follows: section 1 is an introduction. Section 2 provides
a preview about the 2D DFT and its properties. The tracking, mapping and reconstructing
procedure is explained in section 3. Section 4 produces an example of five restored images. The
transmitting time for different image size over different networks types is compared in section 5.
The final section is the conclusion in section 6.
2. THE TWO DIMENSION DISCRETE FOURIER TRANSFORM
Image with M rows and N columns can be transforming from spatial domain to the frequency
domain by applying formula 1. While the inverse Fourier transform could be obtained from
applying formula 2.

Rabab Abdul Rasool
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Where f(x,y) is the two dimensional image in the spatial domain and F(u,v) is the transformed
image in the frequency domain.
Many properties could be obtained from that transformation to the frequency domain, it includes:
• Similarity
• Seprability
• DC Coefficient
• Shifting
• Conjugate Symmetry or Mirror
The two DFT properties, the DC coefficient and Mirror property is explained in figure 1. This figure
clearly explained that the upper half image is the mirror or complex conjugate to the down half
and vise versa. Also, the left half side of image is a mirror to right half side and vise versa. Next
section will explain how tracking, mapping is, and reconstruction procedure will utilize these
properties to obtain a new image with half size, which means half rows or columns [5][6][7].
FIGURE 1: Conjugate Symmetry in 2D DFT.
3. ONE - TO - ONE MAP PROCEDURE
A powerful tracking and mapping procedure is applied to track the redundant spectrum locations
in the lower half image, keep those 1 to 1 relations, and then delete them. The transformed image
size is approximately halved, i.e.; (rows/2 +1) or (columns/2 +1). Now, the new image could be
stored or transmitted. The restored or received image should be inversed back to the spatial
domain after applying the mapping or reconstructing procedure. The restored image is qualified
using Peak Signal to Noise Ratio measurement and the result is shown in figure 2.
(a) original image (b) 2D DFT Spectrums (c) mirror deleting (d) half size image
FIGURE 2: Mapping Procedure Sequence State.
a a*
b* B* d* A*
C DC C*
b B d A

Rabab Abdul Rasool
FIGURE 3: Five original and restored images, (a) origin images, (b) restored images.
4. THE TRANSMISSION TIME ESTIMATION
The new image file size has been evaluated over data transmission system. Five different images
with different file size have been transmitted and the delivery time is calculated as in formula 3.
Packet transmission time = Packet size / Bit rate (3)
(a) Original images (b) Restored images

Rabab Abdul Rasool
Those five images are transformed to the frequency domain by applying the 2D-DFT. Then the
redundant (mirror) information is cut-out. The new image size would be approximately halved of
the original one. These new images are transmitted again over data transmission system. The file
transmission time is re-calculated. Figure 4 represents the wired computer network with bit rate
equals to 250 Mb/s.
FIGURE 4: Wired Computer Network.
Clearly, the time need to transmit the original size is approximately twice, where the difference for
image size 150 Kbyte is 0.3 m sec, while for image size 1.8 M Byte the difference time would be
3.6 m sec and so on as the image file size becomes large the differences time would be larger.
Figure 5 belongs to the wireless network with bit rate equals to 600 M b/s. With image file size
equals to 150 Kbyte, the difference of the delivery time between the two transmissions is
approximately 0.125 msec. for image size 1.8 M Byte the differences time would be 1.5 msec.
FIGURE 5: Wireless Computer Network.
This result approved that, transmitting half image size will eventually reduce the transmission time
to the half under same circumstances like network type, distance, and bit rate.
0
1
2
3
4
5
6
7
8
0 1000000 2000000
Transmission-Time(ms)
Size (Mb)
Wired-Network
Transmission
Time of Image
with original size
Transmission
Time of Image
with half size
0
0.5
1
1.5
2
2.5
3
3.5
0 1000000 2000000
Transmission-Time(ms)
Size (Mb)
Wireless-Network
Transmission
Time of Image
with original size
Transmission
Time of Image
with half size

Rabab Abdul Rasool
5. CONCLUSION
A new and novel approach has been considered and implemented. This approach is depending
on the two properties of the Two-Dimensional Discrete Fourier Transform, the mirror and the
conjugate symmetry. A one -to- one map frequency domain procedure is developed and
implemented to half image file and to restore or reconstruct the spatial domain image file again.
Five images have been transformed, halved, stored, and restored again. The appearance of
those images was very good and the transmission time needed for network delivery is reduced to
the half of the original one.
6. REFERENCES
[1] JAGADISH H. PUJARA. “ Novel Approach for Image Restoration via Nearest Neighbor
Method, Journal of Theoretical and Applied Information Technology, pp. 76-79, 2010.
[2] Muthana Hamd. "RGB Image Reconstruction Using Two-Separated Band Reject Filters",
Advances in Image and Video Processing, Vol. 2, No. 2, pp.1-7, 2014.
[3] M. Andrew. An Introduction to Digital Image Processing with Matlab. Victoria University of
Technology, 2004, pp. 85-115.
[4] W. K. PRATT. Digital Image Processing. New York: John Wiley and Sons, 2001, pp. 185-
319.
[5] M. Goparaju and S Mohan. "Design & Implementation of DWT – IDWT Algorithm for Image
Compression by using FPGA", International Journal of Scientific and Research Publications,
Vol. 3, pp. 1-4, March 2013.
[6] T. R. Jeyalakshmi and K. Ramar. "A Modified Method for Speckle Noise Removal in
Ultrasound Medical Images", International Journal of Computer and Electrical Engineering,
Vol. 2, No. 1, pp. 54-58, February, 2010.
[7] Muthana Hamd and Rabab Rassol. "Quality Measurement for Reconstructed RGB Image via
Noisy Environments", Advances in Image and Video Processing, Vol. 2, No.1, pp. 1-8, 2014.

Novel Approach for Image Restoration and Transmission

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