48th International Symposium ELMAR-2006, 07-09 June 2006, Zadar, Croatia

Lossy Compression Approach to Transmultiplexed Images

Przemyslaw Sypka I, Mariusz Ziolko I, Bartosz Ziolko 21 Department of Electronics,

2 Faculty of Electrical Engineering, Automatics, Computer Science and ElectronicsAGH University of Science and Technology al. Mickiewicza 30, 30-059 Krakow, Poland

phone: + (48-12) 6173048, fax: + (48-12) 6332398,E-mail: tsypka, ziolko, bziolko} ,&agh.edu.pl

Abstract - The application ofimage compression methods in transmultiplexer systems is presented. The specificenergy distribution in the combined image spectrum makes the standard compression methods, especially thesethat base on frequency decomposition not efficient. Two cases are described and compared. the compression ofcombined image and the preliminary compression of input images before transmultiplexing. Wavelet packetdecomposition was used to obtain the frequency decomposition of images. Multirate processing involves digitalfilters that may be used to process images continuously. The results ofconducted experiments are presented. Theluminance of the transmitted image is calculated using formulae, which include both, upsampling and digitalfiltering. The combined image can be sent over a single transmission channel.

Keywords - image transmultiplexer, compression, wavelet packet, JPEG, filter bank

1. INTRODUCTION

Multimedia content is more and more popular inmany different types of telecommunications. That iswhy new and efficient methods of sending severalimages through a single transmission line areneeded. The transmultiplexer is a structure thatcombines suitably upsampled and filtered signals forthe transmission by a single channel. The spectrumof each user's signal is spread over the wholechannel bandwidth. It can be only intercepted by areceiver programmed with the same code.Transmultiplexing is easy to apply because it needsonly simple digital processing: upsampling, filteringand summing. All operations used intransmultiplexer are linear and time-invariant. Itgives important advantages. The z-transform can beused to build the mathematical model and thefrequency approach can be applied to analyze ordesign the considered system. A crucial point foroverall performance of such systems is the quality ofimages delivered to the end user. The separation ofimages should be perfect and the recovery of eachimage should be performed without distortion. Themain problem in transmultiplexers is preventingimage distortion caused by the change of amplitudeand phase as well as image leakage from onechannel into another. This aim can be achieved by aselection of appropriate filters that ensure a perfectimage reconstruction in the receiver [1] [2]. Anotheradvantage is that combined signal may be treatedand processed still as an image. Integer-to-integeroperations provide an efficient system - images areprocessed in finite-precision arithmetic and mappedintegers to integers. In other words, it is possible toprovide all calculations without divisions to omit the

rounding errors. Systems equipped with integerfilters can be used not only to transmit images butalso for encrypted data, lossless compressed signals,computer software data or other data where a changein even one single bit is inadmissible. In this contextthere is no reduction of quality due to fulfilling theperfect reconstruction conditions.

In a compression algorithm the number of bitsneeded to represent the image or its spectrum isminimized. Our fundamental concept ofcompression is to split up the frequency band of theimage and then quantizied each subband using a bitrate accurately matched to compromise between thetwo opposite criteria: minimize distortions andmaximize the compression rate.

Over the past several years, the wavelet methodshave gained widespread acceptance in signalprocessing in general, and in the signal compressionresearch in particular. Multirate processing is relatedto signal transformation using wavelets. Waveletpackets are a way to analyze a signal using basefunctions which are well localized both in time andin frequency. The properties of wavelet transformmake it useful in compression standards. Itsfrequency character enables us to exploit theknowledge connected with the frequency propertiesof human vision system. Moreover the localcharacter of wavelet transform does not introducethe block effects and makes it possible to conductthe compression in real time systems. Thiscontinuous type of processing is the main advantagein lossy compression which reduces the imagespectrum by eliminating redundant information.Lossy compression is generally used where a loss ofa certain amount of information will not be detectedby most users.

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48th International Symposium ELMAR-2006, 07-09 June 2006, Zadar, Croatia

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Fig. 1. Scheme of 4-channel image transmultiplexer

2. IMAGE TRANSMULTIPLEXING

Fig. 1 shows the classical structure of the four-channel image transmultiplexer. The input imagesare upsampled and filtered vertically and summed toobtain two combined images. These combinedimages are then upsampled and filtered horizontallyand summed to obtain the final version of combinedimage [2]. In presented system the combined imageconsists of four times more pixels than each inputimage. At the receiver end, the signal is relayed firstto two channels of the detransmultiplexation part,where the signals are filtered and downsampledhorizontally. Then these signals are relayed to fourchannels where images are filtered anddownsampled vertically to recover the originalimages.

3. COMPRESSION

The wavelet transform belongs to the group offrequency transforms, and that is why the propernonuniform quantization is easy to find. TheWavelet Packet Transform (WPT) gives a tool thatcan be used to analyze the combined images. Thewavelet packet algorithm generates a set oforthogonal subimages that are derived from a single

i{T

Fig. 2. 2-D WPT structure

combined image. The wavelet spectra are producedby cascading filtering and downsampling operationsin a tree-structure. Wavelet packets were introducedfor splitting images into its frequency components sothat to compress the image by non-uniformquantization.

The 2-D WPT can be viewed as a decompositionsystem shown in Fig. 2 for three levels. The basisdata are the coefficients of wavelet series of theoriginal image. The next level results of one step ofthe 2-D wavelet discrete transform. Subsequentlevels are constructed by recursively applying the 2-D wavelet transform step to the low (A -

approximation) and high (D - detail) frequencysubbands of the previous wavelet transform step.The higher level component have two timesnarrower frequency bands when compare with thesubsequent lower frequency components. Multirateprocessing involves the application of filtering anddown-sampling. The main subject lies in the designof lowpass and highpass filters which gives usefultransformations and allow to recover the transnittedimages.

4. EXAMPLE

To verify the frequency properties of transmittedimages and the efficiency of compression method,some examples were analyzed. One of them ispresented below. Four test images (boats, F-16, Lenaand baboon) with 512x512 pixels resolution in 256grayscale levels were selected for the analysis. Thecombined image has 1024x 1024 pixel resolution. Itsluminance values are integer numbers from -1088 to1884. The combining filters Hic and the separationfilters Hs were designed by algorithm presented in[3]. The obtained coefficient values are presented inTab. 1. Transmultiplexing does not provide

Table 1. Coefficient of transmultiplexer filters

__Hc_____Hs__1 0 O O1 -1 O -12 1 1 1-2 1_______I_-1 -20 0 -1 -2

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48th International Symposium ELMAR-2006, 07-09 June 2006, Zadar, Croatia

Sim _JE .-0t t4 1-E H1| g ! > tz M t~~1-D-- - | f -- 1~~~~~~~~~~---D t1010 ~<

.. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~00010~~~~~~~ ; Ne=m4 --- -----

EL-X+<F-E3-~~~~----101Fig. 3. Amplitude [dB] of spectrum of combined

image

distortions because digital filters have integercoefficients which satisfy the requirements ofperfect reconstruction.

Linearity of the transmultiplexer system enablesto split the combined image into its frequencycomponents. The periodicity of spectrum of thecombined image, presented in Fig. 3 especially atcorners, results from the periodicity of Fourierspectra ofupsampled signals. The sampling densitiesin the frequency domain for all levels are the same

but the amounts of samples are different. Thespectrum of the upsampled signal consists of theoriginal spectrum and moreover its components,shifted in frequency, are added. It makes that theimage in transmission line has some similarities withthe original images (see Fig. 1).

The three level 2-D wavelet packet decompo-sition was provided by means of discrete Meyerwavelets. The absolute values of coefficients ofwavelet packet decomposition nodes are presentedin Fig. 4. The main part of energy (96.6%) of thesignal is localized in last four subbands of thenetwork AAA (2.5%), HAA (13.3%), VAA (10.4%)and DAA (70.4%). The compression with factor 16were obtained by omitting information from otherbands. The reconstructed output images are

presented in Table 2 (second row). Even though the

Fig. 4. 2-D WPT coefficients

Fig. 5. Alternative structure for lossy compression intransmultiplexer system

large part of the signal energy was sent and thecompression was not very high, some distortions are

visible. The obtained PSNR values below 30 dB are

unacceptable. The important observation is that thedecreasing of compression coefficient degradates thequality of transmultiplexer output images (Table 2,third row). In the presented example data from bandswith the energy higher than 0.2% of the wholeenergy was transmitted. Rejecting other valuescaused compression with rate equals to 8. The lossof the image quality is connected with proliferationof signal spectra after upsampling. This is why, incontradiction to expectations, transmitting data fromonly four nodes of WPT network (AAA, HAA,VAA, DAA) gives good results.

Another possible solution is the preliminarycompression of the input images, e.g. using JPEGalgorithm [4], and applying the 1-D transmultiplexerafter converting of the bit streams into integer 1-Dsignal (Fig. 5). In such a system the rate ofcompression can be adapted to each of the imageseparately depending on needs. The compressionwith factor 16 using the JPEG algorithm on the eachof input images allows to gain the better quality ofimages than in case of the compression of thecombined image. However such a method requirescareful and precise design of filters. Any change ofthe signal value on the transmultiplexer outputbefore decompression will cause the total loss of theimages. Methods of designing integer filters for 1-Dtransmultiplexers are presented in [5].

5. CONCLUSION

The important role of high frequencies in thecombined image makes impossible the applicationof standard lossless compression methods. Thesealgorithms, based on reduction of high frequency

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48th International Symposium ELMAR-2006, 07-09 June 2006, Zadar, Croatia

Table 2. Comparison of input and output images

24.27/ cdB

30.96 dB

21.42 cdB

32.84 dB

23.79 dB

35.59 dB

components, cause major errors in output images ofthe transmultiplexer. The transmultiplexing ofalready compressed images seems to be moreefficient solution. The preliminary compression ofthe input images applying JPEG 2000 [6] or othermethod allows to gain the higher compression ratewith the better quality of output images. In this casethe very precise design of filters is necessary, as theyhave to fulfill the perfect reconstruction conditions.In the other case any change of the signal in thetransmultiplexer system destroys the imagescompletely.

ACKNOWLEDGEMENT

This work was supported by MEiN under Grant3 TIlD 01027.

REFERENCES

[1] M. Vetterli, "A theory of multirate filter banks",IEEE Trans. Accoust. Speech Signal Process,vol. 35, pp. 356-372, 1987.

[2] P. Sypka, B. Ziolko, and M. Ziolko, "Integer-to-integer filters in image transmultiplexers",IEEE International Symposium onCommunications, Control and Signals,Marrakech, Morocco, March 13-15. 2006,accepted for publication.

[3] P. Sypka, M. Zio6ko, and B. Zio6ko, "LosslessJPEG-Base Compression of TransmultiplexedImages", IEEE 14-th European SignalProcessing Conference, Florence 2006,submitted for publication.

[4] ISO/JEC IS 10918-1 / ITU-T Rec. T.81,Information technology- digital compressionand coding of continuous still images.requirements and guideline.

[5] M. Zio6ko and M. Nowak, "Design of IntegerFilters for Transmultiplexer Systems", IEEETrans. on Signal Processing, under review.

[6] D. Taubman, M. Marcellin, JPEG2000 imagecompression fundamentals, standards andpractice, Kluwer Academic Publisher, 2002.

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