Hybrid Image Compression Technique using Huffman Coding Algorithm

Technology Volume 1, Issue 2, October-December, 2013, pp. 37-45, IASTER 2013 www.iaster.com, Online: 2347-6109, Print: 2348-0017 ABSTRT Hybrid Image Compression Technique using Huffman Coding Algorithm Keerti Mishra 1, R.L.Verma 2, Sanawer Alam 3 and Harsh Vikram 4 1 M.Tech Scholar, 2&3 Assistant Professors in A.I.E.T Lucknow 4 Associate Professor, KNIT Sultanpur, India. In this paper hybrid Image Compression Technique is used for compression of medical images. The objective of this paper is to obtain compression ratio and peak signal to noise ratio for different values of quality factor for different levels of DWT decomposition [1]. In this DWT is applied on LL and HH bands while DCT is applied on LH and HL bands with varying quality factor while preserving the quality of reconstructed image.dwt and DCT is applied on individual components of YC B C R [4]. After this the image is quantized to calculate probability index for each quantity so as to find out the unique binary code for each unique symbol for their encoding [5]. Keywords: Image Compression, DWT, DCT, Huffman Algorithm, medical image, DPCM. I. INTRODUCTION Wavelet transform provides numerous desirable properties such as multi-resolution representation; scalability and progressive transmission which are beneficial to image compression applications as there is a need to handle lots of medical images in the hospitals [1]. The amount of data produced by X-ray and CT scan techniques is vast and this might be a problem when sending the data over a network. To overcome this problem, image compression has been introduced in the field of medical [4]. Image compression reduces the amount of data required to represent a digital image. Compression is achieved by the removing the redundancies in an image. There have been numerous compression research studies, examining the use of compression as applied to medical images. To achieve higher degree of compression the hybrid scheme of DWT, DCT and Huffman encoding compression technique is used. This paper proposes an approach to improve the performance of medical image compression. There are several types of image compressions available but in case of biomedical images the loss of diagonasability of the image is not tolerable and hence to achieve higher degree of compression without any significant loss in the diagonasability of the image [4]. An effective DWT algorithm has been performed on the input image. Once the DWT is performed on the image then DCT is applied on LH and HL bands [1]. After this quantization is applied on DCT and DWT coefficients using Q factor which calculates probability index for each coefficients. After applying quantization, Huffman coding technique is used to calculate codeword for each unique symbol so as to compress the image [1]. At the end the Compression ratio and Peak-signal-to-noise ratio is calculated for different values of quality factor. 37

II. METHODOLOGY [1]. RGB to YC B C R color conversion First of all RGB color space is converted into YC B C R color space where Y represents the luma component, whereas C B and C R component represents the blue color difference and red color difference respectively. Luma represents the achromatic image, while the chroma components represent the color information. C B and C R are sampled at a lower rate than Y to compress bandwidth, this type of sampling is called "chroma subsampling."[2][3]. Load image data Color conversion RGB to YC b C r Apply FDWT Divide HL and LH into non overlapped 8x8 blocks for last wavelet pass Apply FDCT on each 8x8 blocks Apply quantization on DCT coefficient bands (LH, HL) Apply quantization on DWT coefficient bands (LL, HH) Apply DPCM on quantized indices Apply variable entropy on quantized indices Fig. 1 Flowchart of proposed methodology. Y C C b r 0.257 0.148 0.439 0.504 0.291 0.368 0.098 0.439 0.071 R G B 16 128 128 This means that some color information in the image is being discarded, but not brightness (luma) information[3]. 38

[2]. Discrete Wavelet Transform The wavelet transform describes a multi-resolution decomposition process in terms of expansion of an image onto a set of wavelet basis functions. In wavelet analysis, a signal is separated into approximations and detail coefficients [1]. Approximations are the high-scale, low frequency components of the signal whereas details are the low scale, high frequency components. The low frequency components (smooth variations) constitute the base of an image, and the high frequency components (the edges which give the detail) add upon them to refine the image, thereby giving a detailed image [4]. In the FDWT, each step calculates a set of wavelet averages (approximation or smooth values) and a set of details. If a data set s 0, s 1,... s N-1 contains N elements, there will be N/2 averages and N/2 detail values. The averages are stored in the upper half and the details are stored in the lower half. A low pass filter and a high pass filter are chosen, such that they exactly half the frequency range between themselves. This filter pair is called the Analysis Filter pair. First, the low pass filter is applied for each row of data, thereby getting the low frequency components of the row. But since the LPF is a half band filter, the output data contains only half the original number of samples Now, the high pass filter is applied for the same row of data. This procedure is done for all rows[6]. In Next step filtering is applied across columns of intermediate data, the resulting two-dimensional array of coefficients contains four bands of data, each labelled as LL (low-low), HL (high-low), LH (low-high) and HH (high-high). The LL band can be decomposed once again in the same manner, thereby producing even more subbands. This can be done upto any level, thereby resulting in a pyramidal decomposition as shown below [7]. LL3 HL3 LH3 HH3 LH2 LH1 HL2 HH2 HL1 HH1 Fig.2 Three phase decomposition using DWT [6]. The LL, HH coefficients must be quantized using adaptive quantization. The luminance component Y requires the small step of quantization while C b and C r need a large step. After this step, a large sequence of zeros is obtained especially in HH part of the image [12]. [3]. Discrete Cosine Transform DCT transforms spatial domain into frequency domain, and frequency domain includes low and high frequencies as shown in Figure 3. The low frequency formed on upper left corner is Direct Current (DC) coefficient and the rest is alternate current coefficient. Human eyes are more sensitive to low frequencies in frequency domain, so low frequency area is considered important. DCT input format is a spatial matrix of 8 by 8, where output is a frequency coefficient matrix of 8 by 8[6]. 39

167 136 121 125 123 140 162 152 153 117 106 131 167 125 152 89 116 105 123 149 197 166 153 95 135 126 123 95 133 182 105 129 120 127 102 68 127 166 70 147 86 120 95 88 155 119 89 176 119 124 81 71 110 102 112 172 127 95 67 80 111 200 143 134 DC Fig. 3.The DCT transforms; (a) The spectrum matrix of example; and (b) the coefficients of the DCT blocks of 8x 8[6]. It is widely used in image compression. The one-dimensional DCT is useful in processing onedimensional signals such as speech waveforms. For analysis of two-dimensional (2D) signals such as images, we need a 2D version of the DCT. For an n x m matrix S, the 2D DCT is computed in a simple way: The 1D DCT is applied to each row of s and then to each column of the result. Thus, the transform of S is given by[7] m 1 n 1 2 (2x 1) u (2y 1) u S( u, v) C( u) C( v) s( x, y)cos cos, u 0,..., n; v 0,..., m um 2n 2m y 0 x 0 1 where C (u) 2 2 for u=0 =1 otherwise Fig. 4: Two dimensional DCT basis functions (N = 8)[7]. 40

The image above shows combination of horizontal and vertical frequencies for an 8 x 8 (N 1 =N 2 =8) two-dimensional DCT. Each step from left to right and top to bottom is an increase in frequency by 1/2 cycle. The DCT transformed coefficients are then quantized with the help of quantization tables separately for Y, Cb and Cr components. Each value of transformed coefficients are divided by the corresponding elements in the Q table and they are rounded off to the nearest integer as shown in eq.i S'(u, v) = round(s (u, v)/q (u, v)) (I) where S (u, v) = DCT coefficient matrix Q (u, v) = Quantization matrix Remaining all values is approximated to zeros so that redundant information can be avoided. 16 11 10 16 24 40 51 61 17 18 24 47 99 99 99 99 12 12 14 19 26 58 60 55 18 21 26 66 99 99 99 99 14 13 16 24 40 57 60 59 24 26 55 99 99 99 99 99 14 17 22 29 51 87 80 62 47 66 99 99 99 99 99 99 18 22 37 56 68 109 103 77 99 99 99 99 99 99 99 99 24 35 55 64 81 104 113 92 99 99 99 99 99 99 99 99 49 64 78 87 103 121 120 101 99 99 99 99 99 99 99 99 72 92 95 98 112 100 103 99 99 99 99 99 99 99 99 99 Fig 4. Standard Quantization Tables for DCT(a) Quantization Table for Y space (b) Quantization Table for Cb, Cr space In the resulting matrix many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers[12]. [4]. DPCM (Differential Pulse Code Modulation) In DPCM, a prediction of the next sample value is formed from past values. This prediction can be thought of as instruction for the quantizer to conduct its search for the next sample value in a particular interval. By using the redundancy in the signal to form a prediction, the region of uncertainty is reduced and the quantization can be performed with a reduced number of decisions (or bits) for a given quantization level or with reduced quantization levels for a given number of decisions(or bits). The reduction in redundancy is realized by subtracting the prediction from the next sample value. This difference is called the prediction error. Differential pulse code modulation (DPCM) is an efficient data compression technique, which is useful for reducing transmission rate of digital picture information. DPCM is most common approach to predictive codings this scheme predict the value of pixel based on the correlation between certain neighboring pixel values using certain prediction coefficients the difference between predicted value and the actual value of a pixel gives differential image which is less correlated to the original one. The differential image is then quantized and encoded[12]. 41

The forward differential pulse code modulation is applied on the quantized (LL band) wavelet coefficients and quantized DC coefficients of DCT transform. And then all the coefficients must be converted into positive values by mapping to positive technique. Quantized indices of LL band Quantized indices of DC part of DCT Forward DPCM Fig4. Block diagram of DPCM and mapping[12] [5]. Variable Entropy Coding Different coding techniques are there which can be broadly classified into fixed length and variable length coding of which variable length is more efficient. The number of bits will be less for variable length coding compared to fixed length coding for representing the same amount of information which supports more compression. The proposed coding scheme is a variable shift coding technique which gives a few bits to the short codeword and many bits to the long codeword. The main idea behind the shift coding algorithm is to find the maximum hybrid transform coefficients in the data set and optimized these coefficients to take a small numbers of bits. The other coefficients within the set are coded with the same number of bits [8].Huffman coding algorithm is used in this paper. The basic steps of algorithm are[7] : 1. Re-order the source symbols in decreasing order of symbol probability 2. Reduce the source by combining the last two symbols and re-ordering the new set in decreasing order 3. Assign a compact code for the final reduced source. For a two symbol source the trivial code is {0, 1} 4. Back track to the original source S assigning a compact code Consider a 5 symbol source with the following probability P(s 1 )=0.2, P(s 2 )=0.4, P(s 3 )=0.1, P(s 4 )=0.1, P(s 5 )=0.2 Mapping to positive Entropy Coding 42

Symbol P(s i ) Huffman code s 1 0.2 01 s 2 0.4 1 s 3 0.1 0010 s 4 0.1 0011 s 5 0.2 000 The average length is 2.2 bits/symbol.the efficiency is 96.5% [6]. Decoding Algorithm H RGB to YC bc r conversion DWT transform (LL, HL, LH and LL) L H DCT transform DCT quantizatio The original LL DWT quantizatio DPCM Encoder Quantized indices of LL Quantized indices of LL Mapping to positive Figure 5(a). Block Diagram for Hybrid DWT-DCT encoder[12] Encoded image data Variable entropy decoding Mapping to negative DPCM decoder The compressed image YC b C r to RGB conversion Inverse DWT transform Inverse DCT transform [III]. Calculation of CR and PSNR Figure 5(b). Block Diagram for Hybrid DWT-DCT decoder[12] After the image is compressed, last step is to calculate the CR and PSNR of medical image for different quality factor. Compression ratio is defined as the ratio of an original image to the compressed image CR=((original size-compressed size)/original size) * 100; Peak Signal to-noise ratio is the ratio between the maximum possible power of a signal to the power of corrupting noise that affects the fidelity of its MSE 1 M N MN i 1 j 1 ( x( i, j) y( i, j)) 2 43

PSNR n (2 1) 10log10 MSE PSNR I 10log10 ( ) db MSE where I is the maximum intensity level[12]. [IV]. TEST RESULTS 2 The tests are performed on medical image of size 168x256 taking by many images of different sizes see figure 6. Table 1, 2 and 3 present the test results for the number of pass 2, 3 and 4 respectively. Fetal (168x256) Table1.Resulting parameters where no. of pass=2 Quality factor Compression ratio PSNR 1 35.05 31.50 2 27.64 25.80 3 30.29 20.46 4 21.86 28.80 5 32.25 27.40 6 27.99 27.24 Table2.Resulting parameters where no. of pass=3 Quality factor Compression ratio PSNR 1 32.94 26.58 2 25.17 23.01 3 29.38 21.53 4 20.54 27.02 5 29.15 24.50 6 24.63 23.97 Table3.Resulting parameters where no. of pass=4 Quality factor Compression ratio PSNR 1 33.20 25.07 2 24.44 20.34 3 26.34 23.38 4 20.27 24.97 5 29.29 22.21 6 23.24 19.17 44

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