Paper id 26201425

International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637

Satellite Colour Image Compressions Using Hybrid Method: SPIHT & DWT Chandrashekhar Kamargaonkar1, Linta Ann George2 Associate Professor, Faculty of Engineering1 Student, M.E.(Communication) 2 Shri Shankaracharya Group of Institution, Bhilai, India Email: amol_kamar@rediffmail.com1 , Email: linta.geo89@gmail.com2

Abstract- In today’s era, people work on multimedia application where most of the images are coloured images which require a lot of space for storage because colour images are more redundant compared to grey-scale images. Redundancy of the images can be reduced by compressing the images. Hence the compression techniques are broadly classified as lossy compression and lossless compression. But when question arises of a satellite image, loss of any information is not acceptable. Hence in this paper, SPIHT (Set Partitioning In Hierarchical Trees ) algorithm using DWT(discrete wavelet transform) has been introduced. SPIHT is a lossless image compression technique used especially for satellite images. This algorithm further takes Human Visual System, PSNR value, MSE, spectral Frequency Measure(SFM), Spectral Activity Measure(SAM) and the extend to which the image has been compressed into consideration. In this, a coloured image which consists of RGB components are taken which is then converted into YCbCr component where Y is luminance component; Cb and Cr are chrominance components of the image. In each of the Y, Cb and Cr components we apply wavelet transform and then it is compressed using the mentioned algorithm. Different coloured images are taken into considerdation and PSNR value and extend of compression is compared in each case. Hence it is found that the tested images gives a PSNR value of about 38-45dB and the image gets compressed upto 85-95% with neither any loss of information nor any loss in image quality.

Index terms: SPIHT; DWT; YcbCr; lossless compression; SAM; SFM.

1. INTRODUCTION In digital true colour image, each colour component that is R, G, B components, each contains 8 bit data[3]. Also colour image contains lots of redundancy which will make it difficult to store and transmit. Hence, RGB model is not suited for image processing as well as compression purpose. For compression, a luminance-chrominance representation is considered as it is superior to the RGB representation. Therefore, RGB images are transformed to one of the luminancechrominance models, performing the compression process, and then transform back to RGB model because displays are most often provided output image with direct RGB model. Luminance chrominance component is known as YCbCr representation. YCbCr and Y′CbCr are a practical approximation to colour processing and perceptual uniformity, where the primary colours corresponding roughly to red, green and blue are processed into perceptually meaningful information. By doing this, subsequent image/video processing, transmission and storage can do operations and introduce errors in perceptually meaningful ways. Y′CbCr is used to separate out a luma signal (Y′) that can be stored with

high resolution or transmitted at high bandwidth, and two chroma components (CB and CR) that can be bandwidth-reduced, subsampled, compressed, or otherwise treated separately for improved system efficiency. The chrominance components represent the colour information in the image. The rest of the paper is organized as follows: Wavelets are explained in section 2, Wavelet Transformation of Image is described in section 3. SPIHT coding & algorithm is explained in section 4. Modelling is explained in section 5, results is given in section 6. Conclusion and Future work is explained in section 7.

2. WAVELETS A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. . Wavelets can be combined, using a "reverse, shift, multiply and integrate" technique called convolution, with portions of a known signal to extract information from the unknown signal. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including audio signals and images.

Sets of wavelets are generally needed to analyse data fully. A set of. Thus, sets of complementary" wavelets

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 will decompose data without gaps or overlap so that the decomposition process is mathematically reversible complementary wavelets are useful in wavelet based compression/decompression algorithms where it is desirable to recover the original information with minimal loss.[Wikipedia]. When wavelets and sinusoids are compared, it is observed that wavelets have limited duration whereas sinusoids extend from minus infinity to plus infinity. Secondly, sinusoids are smooth and predictable, and wavelets are irregular and symmetric.

3.

WAVELET TRANSFORMATION

4. SPIHT In the SPIHT algorithm, the image is first decomposed into a number of subbands using subband filtering . Low pass and high pass filter is used for filtering purpose. The resultant subband coefficients are then grouped into sets of coefficients known as spatial-orientation trees, which efficiently exploit the correlation between the frequency bands. The coefficients in each spatial orientation tree are then progressively coded using the lossless compression technique from the most significant bit-planes (MSB) to the least significant bit-planes (LSB). The coding is started with the coefficients with the highest magnitude and at the lowest pyramid levels. The SPIHT multistage encoding process employs three lists and sets: 1. The list of insignificant pixels (LIP) contains individual coefficients that have magnitudes smaller than the threshold(2n ).

2. The list of insignificant sets (LIS) contains sets of wavelet coefficients that are defined by tree structures and are found to have magnitudes smaller than the threshold (insignificant). The sets exclude the coefficients corresponding to the tree and all subtree roots and they have at least four elements.

3. The list of significant pixels (LSP) is a list of pixels found to have magnitudes larger than the threshold (significant) The above partition(i.e, test for significance and insignificance) is based on following equation:

Figure 1 The wavelet transformation tool which is used for decomposition. The wavelet transform is identical to a hierarchical sub band filtering system, in sub-band filtering, the sub bands are logarithmically spaced in frequency. The above diagram shows the sub-band filtering of 2-D image which is explained as follows.

An image is first decomposed into four parts based on frequency sub bands, by critically sub sampling horizontal and vertical channels using sub-band filters such as lowpass filter and high pass filter and the subbands are named as Low-Low (LL), Low-High (LH), High-Low (HL), and High- High (HH) sub bands as shown in figure 1. To obtain the next coarser scaled wavelet coefficients, the sub-band LL is further decomposed and critically sub sampled using the same filters. This process is repeated several times, which is determined by the application at hand. The diagram of this process is shown in figure 1. Each level has various bands information such as low–low, low–high, high–low, and high–high frequency bands.

Furthermore, from these DWT coefficients, the original image can be reconstructed. This reconstruction process is called the inverse DWT (IDWT).

……. Eq.(1) Where Sn(T), is the significance of a set of coordinates T, and c(i,j) is the coefficient value at coordinate (i,j) .

After the initialization, the algorithm takes two stages for each level of threshold – the sorting pass and the refinement pass . In the refinement pass actual progressive transmission is done and in the sorting pass lists are organised. The result is in the form of a bit stream. It is capable of recovering the image perfectly (every single bit of it) by coding all bits of the transform. However, the wavelet transform yields perfect reconstruction only if its numbers are stored as infinite imprecision numbers. Peak signal-to noise ratio (PSNR) is one of the quantitative measure for image quality evaluation which is based on the mean square error (MSE) of the reconstructed image. The MSE for N x M size image is given by:

……………Eq.(2) Where I(i,j) is the original image value and K(i,j) is the compressed image value. The PSNR value is given by:

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637

…….Eq.(3) 4.1 SPIHT Coding The set of offspring (direct descendants) of a tree node, O(i, j), in the tree structures is defined by pixel location (i, j). The set of descendants, D(i, j), of a node is defined by pixel location (i, j). L(i, j) is defined as L(i, j) = D(i, j) – O(i, j). The threshold, Sn (T), for the first bit-plane is equal to 2n, where n = [log2(max(i, j){|c(i, j)|}] where c(i, j) represents the (i, j)th wavelet coefficient.

The process is as follows. First of all, discrete wavelet transform is applied. Then the wavelet coefficients are searched in order to obtain the maximum c(i, j) after executing the discrete wavelet transform. After the operations in the subsequent bit-planes of threshold Sn (T) , n is reduced by 1. For each pixel in the LIP, one bit is used to describe its significance. If it is not significant, the pixel remains in the LIP and no more bits are generated; otherwise, a sign bit is produced and the pixel is moved to the LSP. Similarly, each set in the LIS requires one bit for the significance information. The insignificant sets remain in the LIS; the significant sets are partitioned into subsets, which are processed in the same manner and at the same resolution until each significant subset has exactly one coefficient. Finally, each pixel in the LSP is refined with one bit. The above mentioned procedure is then repeated for the subsequent resolution. The bit rate can be controlled precisely in the SPIHT[1] algorithm because the output produced is in single bits and the algorithm can be terminated at any time. The decoding process follows the encoding exactly and is almost symmetrical in terms of processing time.

Send Sn(D(i,j)) If Sn(D(i,j))=1 for each (k,l)∈ O(i,j) output Sn(k,l) if Sn(k,l)=1, then add (k,l) to the LSP and output sign of coeff: 0/1 = -/+ if Sn(k,l)=0, then add (k,l) to the end of the LIP end for end if else (type L ) Send Sn(L(i,j)) If Sn(L(i,j))=1 add each (k,l) ∈ O(i,j) to the end of the LIS as an entry of type D remove (i,j) from the LIS end if on type End loop over LIS Step II Refinement Pass Process LSP for each element (i,j) in LSP – except those just added above Output the nth most significant bit of coefficient End loop over LSP Update Decrement n by 1 Go to step I Where, O(i,j)- set of coordinates of all offspring of node(i,j).

D(i,j)- set of coordinates of all descendents of node(i,j).

H(i,j)- set of all tree nodes.

L(i,j)=D(i,j)-O(i,j)- all descendents except offspring.

ALGORITHMInitialization n = [log2 (max |coeff|)] LIP = All elements in H LSP = Empty LIS = D’s of Roots Step I Sorting Pass Process LIP for each coeff (i,j) in LIP Output Sn(i,j) If Sn(i,j)=1 Output sign of coeff(i,j): 0/1 = -/+ Move (i,j) to the LSP Endif End loop over LIP

5. Modelling Figure 2 shows the model used for compressing coloured satellite images. Matlab software has been used for simulation. In our analysis we have used true colour satellite image (RGB 24 bit).

Image is converted to YCbCr format. After converting wavelet analysis is done for Y, CB, CR. Then the data is compressed using SPIHT[1] algorithm. Along with the compression, PSNR value, spectral activity measure as well as spatial frequency domain has been calculated.

Process LIS for each set (i,j) in LIS if type D

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International Journal of Research in Advent Technology, Vol.2, No.6, June 2014 E-ISSN: 2321-9637 6. RESULTS The following data shows the results of various satellite images taken:

S.N o.

1.

2

3.

4.

Sat.image 1 5.

Imag es Sat. imag e1 Sat. imag e2 Sat. imag e3 Sat. imag e 4 Sat. imag e5

PSN R 42 dB

Compressio n(%) 98

SAM

SFM

0.184 9

0

41.4 5 dB

97.3664

0.156 8

0.00 78

40.1 dB

95.67

0.232 7

0.21 37

37.2 6 dB

93.36

9.227 8e004

0

38 dB

97.4963

0.486 5

0

Table 1

Sat.image 2

Sat.image 3

Sat.image 4

Sat.image 5

7. CONCLUSION & FUTURE WORK From the above results of 5 data taken, it can be concluded that the above mentioned algorithm gives a very high PSNR value as well as compression ratio. It is also concluded that it gives very low value of SAM and SFM. For sat.image 1,4 & 5, the SFM =0.this shows that the input & output imagees are exactly same. In future this work can be extended for video compression.

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AUTHOR PROFILE:

Chandrashekhar Kamargaonkar is an Associate Professor in the department of Electronics & Communication Engineering at Shri Shankarcharya Group of Institution,.Bhilai, India. He is M.E. Coordinator in the Department of Electronics & Communication Engineering at S.S.G.I. Bhilai, India. He has more than 10 year experience in teaching. He has received Master Degree (M.E.) in digital electronics from S.S.G.M. College of Engineering, Shegaon, India. His current area of research includes Image Processing, Digital Communication and Microcontroller & Embedded System.

Linta Ann George is a student of Shri Shankarcharya Group of Institution,.Bhilai, India. She is pursuing her Master Degree (M.E.) in Communication, Electronic & Communication Engineering. Her current area of research is on image processing.

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