C19. An Efficient Multispectral Images Compression Technique

30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt

C19.An Efficient Multispectral Images Compression Technique A. Hagag1, M. Amin1, F. E. Abd El-Samie2 Mathematics Department, Faculty of Science, Menoufia University, Shebin El-Koom, 32511, Egypt. ([email protected]), ([email protected]) 2 Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, 32952, Menouf, Egypt. ([email protected]) 1

ABSTRACT In this paper, a new compression technique aiming at reducing the size of storage of satellite images is presented. We considered one type of multispectral images; Landsat ETM+. It is common to include data compression as a part of the distribution system for satellite imagery. A dual-tree discrete wavelet transform (DDWT) in the spectral domain, a two-dimensional (2-D) discrete wavelet transform (DWT) in the spatial domain, and a simple Huffman coder are used in the proposed technique. The mean square error (MSE), peak signal-to-noise ratio (PSNR), average difference (AD), spectral angle mapper (SAM) and spectral information divergence (SID) are used in the proposed technique.

Keywords: Multispectral compression; DWT; DDWT. I. INTRODUCTION Satellite images are of interest for a large number of applications, such as geology, earth-resource management, pollution monitoring, meteorology, and military surveillance. As a consequence, there is a constant growth both in the number and in the performance of satellite image facilities, which produce larger and larger amounts of data that have to be transmitted, processed, and stored, efficiently. The problem stems from the raw size of the images considered, and is especially urgent when dealing with satellite images, where the amount of data to be managed further increases with the number of bands. The result is a large amount of data organized in three dimensions. Two dimensions are the spatial dimensions, and the third dimension is spectral dimension indexed by λ. A satellite image has both spatial and spectral resolutions. Data with two spectral bands per pixel is called dual band. Data with three to several (perhaps 6–10) bands is termed multispectral data, and data with more bands is termed hyperspectral data [1]. Multispectral data is typically arranged as a 3-D structure as shown in Fig. 1. Each plane is a band and it consists of rows and columns of pixels. We can interpret each plane of Fig. 1 as an image (pixels displayed in a spatial relationship to one another) and each column as a spectrum (variations within pixels as a function of wavelength).

Fig. 1: The 3-D structure of Multispectral data.

Multispectral image compression is one of the important fields that have useful applications in data storage and transmission. It is necessary in any instance where images need to be stored, transmitted, or viewed, quickly and efficiently. In [2], the quality of multispectral images is very important, and the quality of the original images can be affected by the compression. Therefore, we present an efficient multispectral image compression technique and evaluate its performance with radiometric and spectral distortion measurements [3][4]. The remainder of the paper is organized as follows. Four of today compression techniques for multispectral images are described in Section Ⅱ. In section Ⅲ, an ordering of spectral bands is presented. The proposed technique for multispectral image compression is presented in Section IV. After that, testing for the purposed compression technique is presented in section V, and we present our conclusions in the last section.

978-1-4673-6222-1/13/$31.00 ©2013 IEEE

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt

II. COMPRESSION TECHNIQUES OF MULTISPECTRAL IMAGES Multispectral image compression needs the use of 3-D transformations to benefit from the relation between bands. The 3-D compression techniques are generally extended from their 2-D counterparts. Two techniques of particular interest that will be used in our investigation are the JPEG2000 multicomponent, which is an extension of the wavelet-based 2-D JPEG2000 and the 3-D SPIHT [5], which is extended by the 2-D SPIHT developed in [6]. The JPEG2000 is a new still image compression standard that has replaced the commonly used DCT-based JPEG. It is a wavelet-based compression technique that adds/improves features such as coding of regions of interest, progressive coding, scalability, etc. We will show and explain briefly four popular methods of multispectral image compression:

A. JPEG Compression JPEG compression uses the 3-D DCT. There are two classes of encoding and decoding processes; lossy and lossless. Those based on the discrete cosine transform (DCT) [7] are lossy, thereby allowing substantial compression to be achieved, while producing a reconstructed image with high visual fidelity to the encoder source image. It was suggested in [1] that there is a possibility of extending the DCT to three dimensions as the following two equations [1] and applying it to the compression of multispectral data. The extension is straightforward. Simply partition a large set of multispectral data into cubes of 8×8×8 pixels, apply the 3-D DCT to each cube, collect the resulting transform coefficients in a zigzag sequence, quantize them, and encode the results with an entropy coder such as Huffman coder in [8]. Gijk 

for 0  i, j, k  n  1 and

n 1 n 1 n 1 23 Ci C j C k  p xyz 3 n x 0 y 0 z 0

 (2 x  1)i   (2 y  1) j   (2 z  1)k  cos  cos  cos    , 2 n 2 n 2n     

C f  1/

2 for f  0 

C f  1 for f  0 

(1)

 

and the inverse 3-D DCT is

p xyz 

for 0  x, y, z  n  1 .

2 3 n1 n1 n1  Ci C j Ck Gijk n 3 i 0 j 0 k 0

 (2 x  1)i   (2 y  1) j   (2 z  1)k  cos  cos  cos    , 2n 2n 2n     

(2)

B. SPIHT Compression SPIHT [9] is an embedded coding algorithm that performs bit-plane coding of the wavelet coefficients. Two main features are introduced in the SPIHT algorithm. First, it utilizes a partial ordering of coefficients by magnitude and transmits the most significant bits first. Second, the ordered data are not explicitly transmitted. The decoder running the same algorithm can trace the ordering information from the transmitted information. In [5], two techniques are proposed. In the first, a 3-D transform is taken and a simple 3-D SPIHT is used. In the second, after taking a spatial wavelet transform, spectral vectors of pixels are vector quantized and a gain-driven SPIHT is used.

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt In the karhunen–loeve transform (KLT) [10] is used to decorrelate the data in the spectral domain, followed by a 2-D DCT in the spatial domain. After the transform, we have to define a 3-D hierarchical structure to run the SPIHT algorithm. Based on a few preliminary experiments, we selected the structure shown schematically in Fig. 2.

Fig. 2: Tree structure used in the 3-D SPIHT algorithm.

C. JPEG2000 Compression JPEG2000 is the new ISO/IEC still-image compression standard [11][12]. It not only provides better compression performance over DCT-based JPEG, it also has other good features such as progressive transmission, region of interest (ROI) encoding, error resilience, etc. The JPEG2000 encoder consists of four main stages; DWT, scalar quantization, and two tiers of block coding [13], JPEG2000 supports the 9/7 floating-point and the reversible 5/3 integer wavelet transforms. The 5/3 integer wavelet is based on the lifting scheme [14]. The scalar quantization is implemented with the quantization step size possibly varying for each sub-band. For lossless compression, no quantization is performed. The embedded block coding with optimized truncation (EBCOT) has two tiers. The first tier employs a context based adaptive arithmetic coder called the MQ coder on each block of the sub-bands. The second tier is used for rate distortion optimization and quality layer formation. In [15] JPEG2000 is used for multispectral images compressions, we will using it in the comparison methods to show that the proposed technique achieves the compression with better results than JPEG2000.

D. Compression with the 3-D Dual-Tree Wavelet Transform The dual-tree discrete wavelet transform (DDWT) [16] is a relatively recent enhancement to the DWT, with important additional properties. It is nearly shift-invariant and directionally selective in two and higher dimensions. It achieves this with a redundancy factor of only 2d for d-dimensional signals, which is substantially lower than the undecimated DWT. The multidimensional (M-D) dual-tree DDWT is non-separable, but is based on a computationally efficient, separable filter bank (FB). It was discussed in [17] that the compression of spectral images with the 3-D DDWT. Before the 3-D transform we needed to add a new zeros band (band #8) to the image, this band is very important in the 3-D transform to make the image spectral dimension even. The resulting DDWT sub-bands are arranged in four separate transform combinations with each combination having the same sub-band organization as would a 3-D DWT of the original data but with each combination containing sub-bands of different orientations.

III. BAND ORDERING In this Section, we present the band reordering scheme. The proposed ordering heuristic uses a correlation factor to examine inter-band similarity. When a 3-D image has been split into a set of 2-D bands, the inter-band similarity can be measured. The correlation factor has been chosen to characterize the inter-band similarity due to its simplicity [4][18]. The correlation function takes two vectors as inputs, and computes a real number in the range [-1.0,1.0], where 1.0 indicates that the input vectors are totally identical. The correlation coefficient rA, B between image bands A and B is calculated as follows [4]: M D

rA,B 

N D

 ( A j 0 i 0

M D

j . D ,i . D

N D

 ( A j 0 i 0

 A)( B j . D ,i. D  B) M D

j . D ,i . D

 A) 2  ( B j . D ,i. D  B) 2 j 0 i 0

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N D

(3)

30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt where M is the number of rows and N is the number of columns in the image; A and B denote the mean values of the bands A and B computed for every Dth pixel, respectively. Each Dth pixel in the spatial directions is used for the computation of the correlation coefficients. If D equals 1, the exact value of the correlation between the two image bands is computed; otherwise Equation (3) results in a correlation estimate. The larger the D, the faster the reordering phase of the algorithm; however, at the same time, the estimation accuracy is reduced.

IV. PROPOSED TECHNIQUE FOR MULTISPECTRAL IMAGES C OMPRESSION In this section, we present an efficient multispectral image compression technique. A 3-D transform is implemented to achieve the benefits from spectral bands. After that, a simple Huffman coder is used. The wavelet transform comes in several forms. The critically-sampled form of the wavelet transform provides the most compact representation; however, it has several limitations. For example, it severe shift dependence (due to aliasing in down-samplers) and poor directional selectivity in 2-D, 3-D etc. (due to separable real filters), which is important in image processing. For these reasons, we use the dual tree transform in the spectral dimension. In Fig. 3 illustrates the analysis filter bank (FB) for the dual tree, two real wavelet transforms use two different sets of filters let h0 , h1 denote the low-pass/high-pass filter pair for the upper FB, and let g 0 , g1 denote the lowpass/high-pass filter pair for the lower FB. We will denote the two real wavelets associated with each of the two real wavelet transforms as  h (t ) and  g (t ) [16], this transform is 2-times expansive than DWT then we use specially designed sets of filters as shown in [19][20] to given the two sets of filters are jointly designed so that  g (t ) is approximately the Hilbert transform [21] of  h (t ) [denoted  g (t )  { h (t )} ]. Fig. 4 shows the rotation of the multispectral data that shown in the top right part of the figure then we read it’s data as shown in the left of the same figure as an array before we apply the DDWT on it to achieve the benefits from spectral bands, after that we apply the DWT for the spatial dimension of the multispectral images. Note that before the transformation, we order the bands of the multispectral image as shown in section Ⅲ. After that, we use the same quantization options for the JPEG2000 standard in [15], The last stage is Huffman coding as in [22][23]. Fig. 5 illustrates the steps of the compression technique.

Fig. 3: Analysis FB for the dual-tree DDWT.

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt

Fig. 4: Reading multispectral data before DDWT and DWT.

Fig. 5: Block diagram for the proposed compression technique.

V. EXPERIMENTAL RESULTS We have implemented the proposed compression technique on two multispectral images sets available on [24]; Baltimore, Maryland, 5 October 2001, and Los Angeles, California, 20 September 1999, for comparison Fig. 6.

(a)

(b)

Fig. 6: Original multispectral images (bands 2, 3, and 4): (a) Baltimore (b) Los Angeles.

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt We used these multispectral images in our experiments for comparison between several multispectral image compression techniques; JPEG, SPIHT, JPEG2000, JPEG2000 with the 3D dual-tree DDWT, and the proposed technique. Two experiments have been conducted and the results are shown in Figs. 7 and 8; in the first figure we see the band (or channel) 4 in grayscale for the original Baltimore image with others compressions methods, and the next figure represents the band 3 in grayscale for the original Los Angeles image with others compressions methods. We also show the results in thematic colors with (Blue-Green-Red) classes (Fig. 9); by using specific multispectral analysis software [25]; for Baltimore band 4 and Los Angeles band 3 between the original images and the compressed images with three methods of multispectral compressions; JPEG2000, SPIHT, and the proposed technique, in Figs. 10 and 11, respectively.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7: Baltimore image (Grayscale band 4) compression (CR ~ 10) (a) Original image band. (b) Compressed using JPEG. (c) Compressed using SPIHT. (d) Compressed using JPEG2000. (e) Compressed using JPEG2000 with 3-D dual-tree DDWT. (f) Proposed compression.

(a)

(b)

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(c)

30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt

(d)

(e)

(f)

Fig. 8: Los Angeles image (Grayscale band 3) compression (CR ~ 10) (a) Original image band. (b) Compressed using JPEG.(c) Compressed using SPIHT. (d) Compressed using JPEG2000. (e) Compressed using JPEG2000 with 3-D dualtree DDWT. (f) Proposed compression.

Fig. 9: Snapshot from Mulispec software shows the thematic colors (Blue-Green-Red).

(a)

(b)

(c)

(d)

Fig. 10: Baltimore image (Thematic band 4) results (a) Original image band. (b, c, d) The compressed band with JPEG2000, SPIHT, and the proposed technique, respectively.

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt

(a)

(b)

(c)

(d)

Fig. 11: Los Angeles image (Thematic band 3) results (a) Original image band. (b, c, d) The compressed band with JPEG2000, SPIHT, and the proposed technique, respectively.

The performances of these methods have been compared considering the distortion measurements: 1) Radiometric Distortion: Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), and Average Difference (AD). Let 0  g (i, j )  g fs denote an N-pixel digital image, g fs is the largest pixel and let g (i, j ) be its possibly distorted version achieved by compressing g (i, j ) and decompressing the outcome bit stream. Widely used distortion measurements are the following [4]. 1 MSE  (4) [ g (i, j )  g (i, j )]2 N i j PSNR  10  log10 M

N

i

j

g fs

2

MSE 

(5)

1 12

AD   ( g (i, j )  g (i, j )) / MN

(6)

We tabulate the values of using these measures, the best value for MSE, and AD is 0; this means that it’s the lossless compression, and the PSNR will be upper bounded by10  log10 (12  g fs 2 ) ; the largest value is the best. 2)

Spectral Distortion: Spectral Angle Mapper (SAM) and Spectral Information Divergence (SID). ~

Given two spectral vectors V and V both having L components, let V {v1 , v2 ,..., vL } be the original spectral ~

~

~

~

pixel vector vl  gl (i, j ) and V {v1 , v2 ,..., vL } its distorted version obtained after compression and decompression. Analogously to the radiometric distortion measurements, spectral distortion measurement may be defined. SAM denotes the absolute value of the spectral angle between the couple of vectors we calculate by the following equation [4]: ~

~

SAM (V, V )  arccos(

 V, V  ~

V 2 V

2

)

(7)

in which  ,  stands for scalar product. Another measurement especially suitable for multispectral data is the SID [26] derived from informationtheoretic concepts [26]:

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt ~

L

SID(V, V)   ( pl  ql ) log( l 1

pl ) ql

(8)

in which ~

v vl pl  l , and ql  ~ (9) V1 V1 We tabulate the values of using these measures, the best value for SAM, and SID is 0. Table 1 tabulate the values of these metrics, by applying the radiometric and spectral distortion for the two tested images Fig. 6 after using the different compression methods and the proposed technique, we show all results in the table and the best result is bolded.

Table 1: Radiometric and Spectral Distortion Comparison for Baltimore and Los Angeles Images Radiometric Distortion Comparison Image1: Baltimore

Spectral Distortion Comparison

Image2: Los Angeles

Image1: Baltimore

Image2: Los Angeles

Methods

MSE

PSNR

AD

MSE

PSNR

AD

SAM

SID

SAM

SID

JPEG

922.75

18.48

4.73

118.6

17.39

6.71

4.1209

6.632

4.544

8.8875

SPIHT

169.96

17.95

1.63

675.12

19.12

1.85

2.1665

1.0188

1.45

0.294

JPEG2000

1.48

54.78

0.24

1.48

54.82

0.25

0.0737

0.8945

0.0497

0.2369

JPEG2000 with 3-D dual-tree DDWT

732.92

19.48

9.41

104.4

17.94

11.28

2.3557

0.7880

2.3537

0.5052

Proposed

0.38

60.4

0.13

0.14

61.97

0.13

0.0385

0.8723

0.03141

0.2355

From the obtained results in Table 1 it is clear that the proposed multispectral image compression technique achieves the best results from the distortion measurements perspective.

VI. CONCLUSION An efficient multispectral images compression technique has been proposed in this paper. It is based on a 3-D transform that uses the discrete wavelet transform (DWT), dual tree discrete wavelet transform (DDWT) and a simple Huffman coder. We take full advantage of the multispectral bands in the step of the transformation by using DDWT on the spectral dimension and DWT on the spatial dimension. From the subjectivity and objectivity, we can conclude that the proposed compression technique is more effective than other traditional compression techniques.

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30thNATIONAL RADIO SCIENCE CONFERENCE (NRSC 2013) April 16‐18, 2013, National Telecommunication Institute, Egypt [9] P. Pellegri, G. Novati, and R. Schettini, “Multispectral Loss-less Compression Using Approximation Methods”, IEEE, 0-7803-9134-9/05, 2005. [10] J. Saghri, A. Tescher, and J. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Processing Mag., pp. 32–43, Jan.1995. [11] ISO/IEC 15444-1, Information technology, “JPEG2000 image coding system-part 1: Core coding system”, 2005. [12] A. Skodras, C. Christopoulos, and T. Ebrahimi, “The JPEG 2000 still image compression standard,” IEEE Signal Processing Mag., vol. 18, no. 5, 2001. [13] L. Chung-Jr, K. Chen, H. Chen, and L. Chen, “Analysis and architecture design of block-coding engine for EBCOT in JPEG 2000”, IEEE Trans. on CSVT, Vol. 13, No. 3, pp.219-230, 2003. [14] J.M. Shapiro, “Apparatus and method for compressing information”, United States Patent Number 5,412,741, Issued May 2, 1995. [15] D. Acevedo and A. Ruedin, “Reduction of Inter-band Correlation for Landsat Image Compression”, IEEE, SIBGRAPI’05, 1530-1834/05, 2005. [16] I. Selesnick, R. Baraniuk, and N. Kingsbury, “The Dual-Tree Complex Wavelet Transform”, IEEE Signal Processing Magazine, 2005. [17] J. Boettcher, Q. Du, “Hyperspectral image compression with the 3D dual-tree wavelet transform”, IEEE, 10.1109/IGARSS.2007. [18] S. Tate, “Band Ordering in Lossless Compression of Multispectral Images”, IEEE Trans. On Computer, Vol. 46, No. 4, April 1997. [19] I. W. Selesnick, “The Double-Density Dual-Tree DWT,” IEEE Trans. On Signal Processing, vol. 52, No. 5, 2004. [20] N. Kingsbury, “Image Processing with Complex Wavelets,” Phil. Trans. R. Soc. Lond. A, 1999. [21] A. D. Poularikas, “The Handbook of Formulas and Tables for Signal Processing”, 1999. [22] R. Gonzalez and R. Woods, “Digital Image Processing”, 3rdEdition, Pearson Education, 2008. [23] R. Gonzalez, S. Eddins, and R. Woods, “Digital Image Processing using Matlab”, 1stEdition, Pearson Education, 2004. [24] (Online Sources). Available: http://l7downloads.gsfc.nasa.gov/index.htm (Accessed 18 July 2012). [25] (MultiSpec Software). Available: https://engineering.purdue.edu/~biehl/MultiSpec/ (Accessed 04 May 2012). [26] C.I. Chang, “An information-theoretic approach to spectral variability, similarity, and discrimination for hyperspectral image analysis”, IEEE Trans. Inform. Theory, 2000.

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