PERFORMANCE ANALYSIS OF ROLE OF WAVELET IN CCSDS IMAGE DATA COMPRESSION
ALGORITHM
1
RINA JANI,
2DR.G.R.KULKARNI
1
PG student ,Department of Electronics & Communication Engineering C.U.Shah College of Engineering and Technology Wadhwan city, Gujarat, India
2
Principal , C.U.Shah Engineering College,
C.U.Shah College of Engineering and Technology – Wadhvan city - Gujarat, India [email protected],[email protected]
ABSTRACT :With the increase in spatial resolution and in corporation with hyperspectral bands in electro- optical payloads, large volume of data at high data rate will be generated. To handle this situation in the available data bandwidth, use of data compression is inevitable. CCSDS (Consulative Committee for Space Data System) recommendation specifies image data compression that is based on DWT (Discrete wavelet transform)and bit plane encoding. Objective of the paper is to observe the effect of discrete wavelet transform used in CCSDS image data compression algorithm. Algorithm suitable for the lossy and lossless both type of compression. The Recommendation supports two choices of DWT: an integer and a floating point DWT. The integer DWT requires only integer arithmetic, is capable of providing lossless compression, and has lower implementation complexity. The floating point DWT provides improved compression effectiveness at low bit rates, but requires floating point calculations and cannot provide lossless compression. paper describe the integer and floating point equations. CCSDS given the test set of images. Simulation is performed on the 8,10,12 bit.
Keywords— Discrete Wavelet transform, Image compression, CCSDS, Wavelets, Wavelet transform.
I.
INTRODUCTIONCommon characteristic of most images is that the neighbouring pixels are correlated and therefore contain redundant information. The foremost task then is to find less correlated representation of the image. Two fundamental components of compression are redundancy and irrelevancy reduction-
Redundancy Reduction: aims at removing duplication from image source.
Spatial - Between neighboring pixel values.
Spectral - Between different color pans or spectral bands
Temporal - Between adjacent frames in a sequence of image (not for still image compression).
Irrelevancy reduction- aims at omitting parts of signal that will not be noticed by Human Visual System. Image compression aims at reducing spatial and spectral redundancies as much as possible to reduce number of bits representing the image. Initialy DCT based image compression is used. which represent an image as a superposition of cosine functions with different discrete frequencies. The transformed signal is a function of two spatial dimensions and its components are called DCT coefficients or spatial frequencies. DCT coefficients measure the contribution of the cosine functions at different discrete frequencies. DCT provides excellent energy compaction and a number of fast
algorithms exist for calculating the DCT. Most existing compression systems use square DCT blocks of regular size. The image isdivided into blocks of samples and each block is transformed independently to give coefficients. To achieve the compression, DCT coefficients should be quantized. The quantization results in loss of information, but also in compression. Increasing the quantizer scale leads to coarser quantization, gives high compression and poor decoded image quality. The block-based segmentation of source image is a fundamental limitation of the DCT-based compression system.
The degradation is known as the "blocking effect"
and depends on block size. A wavelet image compression system can be consists of wavelet function,quantizer and an encoder.
II.
OVERVIEWOF IMAGE COMPRESSION
Number of methods are present to provide image compression. This methods can be classified into 2 general categories
(i) Based on Tolarability
Lossless
Lossy
(ii) Method of Preprocessing
Predictive
Transform
3. CCSDS ALGORITHM DESCRIPTION
The recommended algorithm consists of two functional modules as depicted in Figure 2, a Discrete Wavelet Transform (DWT) module that performs decorrelation, and a Bit-Plane-Encoder (BPE) that encodes the decorrelated data. The wavelets Transforms can be interpreted in two ways. Vector space decomposition and Filter bank approach. The former one describes the wavelet transform as a projection of a signal onto a series of basis functions called the wavelet basis. Just like the Fourier series, where the signal is decomposed into trigonometric sine & cosine basis functions, the wavelet transform decomposes the signal into a basis called the wavelet.
Fig-1 Algorithm
There are different family of wavelet basis available, namely Haar, Dabauchies, coiflets, biorthogonal and more. The filter bank approach describes the wavelet transform as a set of filter band which filters the input signal into different sub-bands. Discrete Wavelet transform (DWT) represents image as sum of wave functions. So, the basis of wavelet transform can be composed of function that satisfies requirements of multi-resolution analysis. Due to presence of these large variety of wavelets I tested daubchies, biorthogonal and coieflet wavelet and their effect on the image.
III.
ADVANTAGES OF WAVELETTRANSFORM
Often signals we wish to process are in the time- domain, but in order to process them more easily other information, such as frequency, is required.
Mathematical transforms translate the information of signals into different representations. For example as shown in Fig 2, the Fourier transform converts a signal between the time and frequency domains, such that the frequencies of a signal can be seen.
However the Fourier transform cannot provide information on which frequencies occur at specific times in the signal as time and frequency are viewed independently. To solve this problem the Short Term Fourier Transform (STFT) introduced the idea of windows through which different parts of a signal are viewed. For a given window in time the frequencies can be viewed. However Heisenberg’s Uncertainty Principle states that as the resolution of the signal improves in the time domain, by zooming on different sections, the frequency resolution gets worse. Ideally, a method of multiresolution is needed, which allows certain parts of the signal to be resolved well in time, and other parts to be resolved well in frequency. It is a
basic wave which can be defined by following properties
It is irregular compared to a simple wave.
It is compactly supported.
Its average value is zero.
It is a prototype for generating various window functions.
Their irregular shape lends them to analyze signals with discontinuity's or sharp changes, while their compactly supported nature enables temporal localization of a signal’s features.
Two of its constructing features are scale and translation.
Scale – It is technically the reciprocal of frequency but it defines the width of the analyzing wavelet.
Translation – It defines the position of the analyzing wavelet.
This kind of multi-resolution transform gives –
At low frequencies – It gives high frequency resolution and low time resolution.
At high frequencies – It gives high time resolution and low frequency resolution.
Figure 2: STFT and DWT
This approach is especially useful when we are processing signal.
This approach has low durations of high frequency components and high durations of low frequency components. Fortunately, the signals that are encountered .
First thing to notice is that although the widths and heights of the boxes change, the area is constant. That is each box represents an equal portion of the time- frequency plane, but giving different proportions to time and frequency. Note that at low frequencies, the height of the boxes are shorter (which corresponds to better frequency resolutions, since there is less ambiguity regarding the value of the exact frequency), but their widths are longer (which correspond to poor time resolution, since there is more ambiguity regarding the value of the exact time). At higher frequencies the width of the boxes decreases, i.e., the time resolution gets better, and the heights of the boxes increase, i.e., the frequency resolution gets poorer.
4. FORMULATION
For preprocessing required by lossy and lossless compression, different methods and formulae are applied. For lossless compression Integer Discrete Wavelet Transform is applies whereas in Lossy
applied. Also for this recommendation a three level transform of coefficients is done. These are explained as following. Both are done using 9/7 tap filters.
(i) Integer discrete wavelet transform (for lossless compression) forward dwt
In this case we do a non-linear approximation of 9/7 tap Integer DWT. Data is fed into the program in a row-wise fashion first then column-wise. A 1- dimentional wavelet transform maps a vector to a set of wavelet coefficients, one high pass set, Dj, and one low pass set Cj. This completes a one level forward Integer Discrete Wavelet Transform. This process is repeated two more times to achieve the required three-level wavelet transform of the image. The equations used to compute this transform are as follows. Here we have considered a row size of N and a row containing elements from 0 to N-1.
Eq (1) Eq (2)
Eq (3) Eq (4)
Eq (5)
Eq (6)
Now because of the rounding procedure, the recommended transform is, strictly speaking, non- linear and hence not truly a DWT. Nevertheless, a non-linear strict inverse transform exists.
Figure 3 Stepwise the forward Integer DWT
Figure 3 shows the intermediate result for this process. This process is repeated three times to achieve the required result which looks like figure 4.
Figure 4: 3 level forward DWT
.From the figure 5 we can notice various segments depicting the image in various bands. These bands can be identified in the following simple manner shown in figure 3.3-4. In this figure we have Low- Low (LL) band, High-High (HH) band, High-Low (HL) band and Low-High(LH) band with their respective levels of transforms depicted in subscript.
Figure 5: Subband formation
(ii) Floating discrete wavelet transform (for lossy compression) forward (analysis)
In this case we do 9/7 tap Floating DWT. Similar to the case of Integer DWT data is fed into the program in a row-wise fashion first then column-wise. A 1- dimentional wavelet transform maps a vector to a set of wavelet coefficients, one high pass set, Dj, and one low pass set Cj. This completes a one level forward Integer Discrete Wavelet Transform. This process is repeated two more times to achieve the required three-level wavelet transform of the image. The equations used to compute this transform are similar to those of convolution of the input signal with the filter. Hence the filter coefficients are to be specified as well. The coefficients for forward transform are known as analysis filter coefficients and are stated in table 1
Analysis Filter Coefficients
i Lowpass Filter hi Highpass Filter gi
0 0.852698679009 -0.788485616406
±1 0.377402855613 0.418092273222
±2 -0.110624404418 0.040689417609
Analysis Filter Coefficients
i Lowpass Filter hi Highpass Filter gi
±3 -0.023849465020 -0.064538882629
±4 0.037828455507 Table -1: Filter coefficient
And the equations used are as follows
Eq (7)
Eq(8) In the above equations is the set of low pass filter coefficients and are the set of high pass coefficients.
The steps and bands’ positions are similar to those of the forward Integer DWT. The can be referred form the previous section.
5. RESULTS
Original image: Marstest (512 512), 8 bit
Marstest:Lossless integer DWT 3 level
Marstest:Lossy float DWT 3 level Table 2 CCSDS Test images
Original image: India_2kb1 (2048x2048), 10 bit CCSDS Test Images used
Image
Name Source–
Copyright
Size(col. rows)
Bits/pi xel marstest Mars Pathfinder
(Sojourner) - NASA
512 512
8
india_2kb 1
NOAA Polar Orbiter
(AVHRR) – NOAA
2048
2048 10
Foc Hubble Space
Telescope -
NASA
1024 512
12
India_2kb1:Lossless Integer DWT 3level
India_2kb1: Lossy float DWT 3level
Original image: Foc (1024 X 512), 12 bit
Foc : Lossless Integer DWT 3level
Foc : Lossy Float DWT 3level
6. CONCLUSION
Paper demostrate the implementation of DWT for the CCSDS image data compression.DWT is better transformation than DCT becaurse it has no blocking artifacts .This implementation of DWT is specialy for the CCSDS image data compression application.
CCSDS alogorithm is suitable for the on board payload and it gives both losssy and lossless compression.Paper give the equation and values of the coefficient for the lossless and lossy compression.
Float DWT is used for lossy while Integer used for Lossless compression. Simulation represents the results for the lossy and lossless DWT which can be further applied to the Bit plane encoder for the compression purpose. Quality of lossless DWT is better than the Lossy DWT.
7. REFERENCES
[1] Pen-shu Yeh, Phillippe Armbruster, Aaron Kiely, Bart Massschelein, Gilles Moury, Christoph Schaefer, Carole Thiebaut, “The new CCSDS image compression recommendation ”Proc. Of the IEEE Aerospace Conference, pp,1-7 big Sky, MT, March 2005.
[2] Pen-shu Yeh , Jack Venbrux, “High Performance Image data compression Technique for Space application. in: NASA Earth Science Technology Conference, Maryland, USA, 2003.
[3] M. Carbal, R. Trautner, R. Vitulli, C.Monteleone, ”Efficient Data Compression for
Space craft including Planetary probes”, IPPW-7 S/C incl. PP – 2010.
[4] Michael W. Marcellin, Michael J. Gormish, Ali Bilgin, Martin P. Boliek,” An Overview of JPEG- 2000”, Proc. of IEEE Data Compression Conference, 2000.
[5] C.Chysafis and A.Orgeta. “Line based.
Reduced memory, Wavelet image compression.”
IEEE Transaction on image processing 9,march 2000,issue-3.
[6] Consulative committee for space Data Systems, Image Data compression, nov-2005, ser, Blue Book CCSDS 122.0-B-1.
[7] Consulative committee for space Data Systems, Image Data compression CCSDS120.1-G-1, 2007, Washington DC:CCSDS. USA .Green book.
