Simultaneous denoising and compression of ... - Semantic Scholar

Simultaneous denoising and compression of multispectral images Ahmed Hagag Mohamed Amin Fathi E. Abd El-Samie

Simultaneous denoising and compression of multispectral images Ahmed Hagag,a Mohamed Amin,b and Fathi E. Abd El-Samiec a

Egyptian E-Learning University, Department of Information Technology, Faculty of Information Technology, Dokki, Giza, 12611 Egypt b Menoufia University, Department of Mathematics, Faculty of Science, Shebin El-Koom, 32511 Egypt c Menoufia University, Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menouf, 32952 Egypt [email protected]

Abstract. A new technique for denoising and compression of multispectral satellite images to remove the effect of noise on the compression process is presented. One type of multispectral images has been considered: Landsat Enhanced Thematic Mapper Plus. The discrete wavelet transform (DWT), the dual-tree DWT, and a simple Huffman coder are used in the compression process. Simulation results show that the proposed technique is more effective than other traditional compression-only techniques. © 2013 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.JRS.7.073511]

Keywords: multispectral compression; denoising; discrete wavelet transform; dual-tree discrete wavelet transform. Paper 13249 received Jul. 3, 2013; revised manuscript received Jul. 20, 2013; accepted for publication Aug. 6, 2013; published online Sep. 3, 2013.

1 Introduction The land satellite (LANDSAT) program1 is one of the pioneering observational programs, and it was useful as an introduction to similar land observation satellites operated by other organizations. It was designed in the 1960s and aimed at observing broad-scale land areas of the Earth. There have been eight missions launched since July 1972, and one of them still remains operational.2 Enhanced Thematic Mapper plus (ETM+) was on the Landsat 6 mission in 1993, but it was lost at launch. In April 1999, the ETM+ sensor was placed in orbit with the successful Landsat 7 mission. It extended the capabilities of the previous ETM version by the better use of calibration and the efficiency of data transmission while maintaining the spectral definitions and resolutions of the former sensor version. In this paper, Landsat 7 ETM+ images are used for compression. A Landsat satellite image consists of several bands; each band is a two-dimensional (2-D) gray-scale image. So, we have 8 or 16 bits per pixel per band (bpppb) as shown in Fig. 1. There is a large field of applications that require satellite images, such as geology, earth-resource management, pollution monitoring, meteorology, military surveillance, and study of the Earth’s surface. As a consequence, there is a constant growth both in the number and in the performance of satellite image facilities, which produces larger and larger amounts of data that have to be transmitted, processed, and stored efficiently. Thus, it is common to include data compression as a part of the distribution system for satellite imagery. The first 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 the spectral dimension indexed by λ. A satellite image has both spatial and spectral resolutions.3 The second problem is 0091-3286/2013/$25.00 © 2013 SPIE

Journal of Applied Remote Sensing

073511-1

Vol. 7, 2013

Hagag, Amin, and El-Samie: Simultaneous denoising and compression of multispectral images

Fig. 1 Multispectral image pixels representation.

that the original multispectral image quality can be affected with noise, so there is a need to denoise these images via a filtering layer. Therefore, we present an efficient multispectral image compression technique with denoising and evaluate its performance with radiometric and spectral distortion measurements. Mean square error (MSE), peak signal-to-noise ratio (PSNR), spectral angle mapper (SAM), and spectral information divergence (SID) are used in the evaluation process. The rest of the paper is organized as follows. In Sec. 2, a review of the noise types and noise removal is presented. Three traditional compression techniques for multispectral images are described in Sec. 3. The proposed technique for denoising and compression of multispectral images is presented in Sec. 4. Section 5 presents the simulation results and discussion. Finally, the concluding remarks are presented in Sec. 6.

2 Noise Types and Removal 2.1 Noise Types Images are often corrupted with noise due to various factors during their acquisition and transmission phases. There are different types of noise.4 In this paper, we deal with two popular types of noise.

2.1.1 Gaussian noise This kind of noise randomly occurs as white intensity values. The probability density function (PDF) of a Gaussian random variable z representing the noise intensity is given by 1 2 2 PðzÞ ¼ pffiffiffiffiffi e−ðz−μÞ ∕2σ ; 2π σ

(1)

where μ is the mean of average value of z, and σ is its standard deviation.

2.1.2 Impulse noise This is the occurrence of both black and white given by 8 < Pa PðzÞ ¼ Pb : 0


intensity values. The PDF of impulse noise is for z ¼ a for z ¼ b : otherwise

073511-2

Vol. 7, 2013


Fig. 2 Multispectral Hawaii image (bands 2, 3, and 4). (a) Original image. (b) Image corrupted by Gaussian noise with σ ¼ 10. (c) Image corrupted by impulse noise with a probability of occurrence of 0.02. (d) The zoomed portion of (a). (e) The zoomed portion of (b). (f) The zoomed portion of (c).

If b > a, gray-level b will appear as a light dot in the image. Conversely, level a will appear as a dark dot. Figure 2 shows the Hawaii image contaminated by Gaussian noise with σ ¼ 10 and impulse noise with probability of occurrence of 0.02.

2.2 Filtering Techniques Filtering is an important operation to be performed for various signal, image, and video processing applications.5 There are different ways to remove or reduce noise in an image. In this paper, we use two popular types of filters.

2.2.1 Median filtering Median filtering is a nonlinear smoothing method that is used to reduce impulse noise. Its idea is based on replacing each pixel value by the median of the brightness in its neighborhood. The objective of this process is to reduce the effect of any abnormal value in the neighborhood of each pixel.

2.2.2 Adaptive Wiener filtering Adaptive Wiener filter is used to reduce Gaussian noise and perform smoothing. The adaptive Wiener filtering process estimates the local mean and local variance around each pixel. 1 X aðn ; n Þ; NM n ;n ∈η 1 2

(3)

1 X ½aðn1 ; n2 Þ − μðn1 ; n2 Þ2 ; NM n ;n ∈η

(4)

μðn1 ; n2 Þ ¼

1

σ 2 ðn1 ; n2 Þ ¼

1


2

2

073511-3

Vol. 7, 2013


where η is the N × M local neighborhood of each pixel in the image a. Adaptive Wiener filtering is carried out using these estimates as follows: bðn1 ; n2 Þ ¼ μðn1 ; n2 Þ þ

σ 2 ðn1 ; n2 Þ − V 2 ½aðn1 ; n2 Þ − μðn1 ; n2 Þ; σ 2 ðn1 ; n2 Þ

(5)

where V 2 is the noise variance or the average of all the local estimated variances.

3 Traditional Compression Techniques In this section, a brief discussion is presented for some popular multispectral image compression techniques.

3.1 JPEG Compression JPEG is currently a worldwide standard for compression of digital images. The standard is named after the committee that created it and continues to guide its evolution. The JPEG committee has an official title of ISO/IEC JTC1 SC29 Working Group 1, with a web site given in Ref. 6. We can apply the JPEG compression on every band of the multispectral image, separately or as a three-dimensional (3-D) data, but in this case, an all-zero band (band #8) has to be added. The JPEG encoder is conveniently decomposed into units that are shown in Fig. 3. The JPEG baseline coding system is based on the discrete cosine transform (DCT).7 The coefficient with zero frequency in both dimensions is called the dc coefficient, and the remaining 63 coefficients are called the ac coefficients, as shown in Fig. 4. The dc coefficient passes through differential pulse-code modulation. It was suggested in Ref. 3 that there is a possibility of extending the DCT to three dimensions as in Eqs. (6) and (7) (Ref. 3) 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 zig-zag sequence, quantize them, and encode the results with an entropy coder such as the Huffman coder in Ref. 8. Gijk

rffiffiffiffirffiffiffirffiffiffi n−1 X m−1 X λ−1 X 2 2 2 ¼ pxyz Ci Cj Ck m n λ x¼0 y¼0 z¼0 ð2x þ 1Þiπ ð2y þ 1Þjπ ð2z þ 1Þkπ × cos cos cos ; 2n 2m 2λ

(6)

for 0 ≤ i ≤ n − 1, 0 ≤ j ≤ m − 1, 0 ≤ k ≤ λ − 1. Cl ¼

pffiffiffi 1∕ 2 for l ¼ 0 : 1 for l > 0

Fig. 3 Architecture of the JPEG compression encoder. Journal of Applied Remote Sensing

073511-4

Vol. 7, 2013


Fig. 4 Coefficients of an 8 × 8 rectangular block of data.

The inverse 3-D DCT is given by Pxyz

rffiffiffiffirffiffiffirffiffiffi n−1 m−1 λ−1 2 2 2XXX ¼ CCC m n λ x¼0 y¼0 z¼0 i j k ð2x þ 1Þiπ ð2y þ 1Þjπ ð2z þ 1Þkπ × cos cos cos ; 2n 2m 2λ

(7)

for 0 ≤ x ≤ n − 1, 0 ≤ y ≤ m − 1, 0 ≤ z ≤ λ − 1. Cl ¼

pffiffiffi 1∕ 2 for l ¼ 0 : 1 for l > 0

3.2 Set Partitioning in Hierarchical Trees Compression Set partitioning in hierarchical trees (SPIHT) is an embedded coding algorithm that performs bit-plane coding of the wavelet coefficients.9 In Ref. 10, two implementations of SPIHT compression are proposed. In the first one, a 3-D transform is taken and a simple 3-D SPIHT is used. In the second one, after taking a spatial wavelet transform, spectral vectors of pixels are vector quantized and a gain-driven SPIHT is used. In Ref. 11, the Karhunen-Loéve transform is used to decorrelate the data in the spectral domain, followed by a 2-D DCT in the spatial domain. After the transform, a 3-D hierarchical structure is defined to run the SPIHT algorithm. Based on some preliminary experiments, the structure shown schematically in Fig. 5 was selected.

3.3 JPEG 2000 JPEG 2000 is a new image compression system that uses a state-of-the-art compression technique based on wavelet technology.12 The JPEG 2000 compression engine (encoder and decoder) is illustrated in the block diagram in Fig. 6. JPEG 2000 supports the 9/7 and the 5/3 integer wavelet transforms. The 5/3 integer wavelet forward transform is described by Journal of Applied Remote Sensing

073511-5

Vol. 7, 2013


Fig. 5 Tree structure used in the 3-D SPIHT algorithm.

Eq. (8), and the 9/7 wavelet forward transform is described by Eq. (9).13,14 The inverse transformation equations can be trivially deduced from the forward transformation equations and thus are not given here. The input signal, low-pass sub-band signal, and high-pass sub-band signal are denoted as x½n, LP½n, and HP½n, respectively. 5∕3 wavelet

HP½n ¼ x½2n þ 1 − b1∕2ðx½2n þ x½2n þ 2Þc LP½n ¼ x½2n þ b1∕4ðHP½n − 1 þ HP½nÞ þ 1∕2c

;

(8)

8 < HP½n ¼ x½2n þ 1 þ 1∕16 ðx½2n þ 4 þ x½2n − 2Þ þ 1∕2 9∕7 wavelet : −9ðx½2n þ 2 þ x½2nÞ : LP½n ¼ x½2n þ b1∕4ðHP½n − 1 þ HP½nÞ þ 1∕2c

(9)

After transformation, all coefficients are quantized. In the final steps of the encoding process, the coefficients of each transformed tile-component sub-bands are arranged into rectangular blocks called code blocks, which are coded individually, one bit plane at a time. Starting from the most significant bit plane with a nonzero element, each bit plane is processed in

Fig. 6 Block diagram of the JPEG 2000. (a) Encoder. (b) Decoder. Journal of Applied Remote Sensing

073511-6

Vol. 7, 2013


three passes. Each bit in a bit plane is coded in only one of the three passes: significance propagation, magnitude refinement, or clean-up.15 JPEG 2000 is used for multispectral image compression as shown in Ref. 16.

4 Proposed Technique In this section, we present an efficient multispectral image denoising and compression technique. A filtering layer, multispectral band ordering, and a 3-D transform are implemented to achieve the benefits from spectral bands. After that, a simple Huffman coder is used. Figure 7 shows the block diagram for the proposed compression technique.

4.1 Filtering Layer The effect of noise on lossy image compression has been extensively studied in Refs. 17 and 18. In the proposed technique, the filtering layer based on the type of noise is used for noise reduction in multispectral images. This process plays an important role in achieving a good compression in the rest of the steps.

4.2 Multispectral Band Ordering In this section, we propose an algorithm for multi-/hyperspectral band ordering. This algorithm will be applied on Landsat ETM+ images with seven bands. The data of the bands are reshaped to vectors, and Eq. (10) is applied for the image bands. The correlation coefficient between band #1 and band #2 is estimated as r1;2 , the correlation between band #1 and band #3 is estimated as r1;3 , and so on to obtain a vector of 21 values as [r1;2 , r1;3 ; : : : ; r1;7 , r2;3 , r2;4 ; : : : r2;7 ; : : : r6;7 ]. The absolute values of the correlation vector are sorted in a descending order to determine the bands with the highest correlation. Finally, the bands are interchanged according to the correlation results to achieve the optimal band ordering for the multispectral image. The correlation coefficient rA;B between image bands A and B is calculated as follows:19 PMD PND

¯ ¯ j¼0 i¼0 ðAj:D;i:D − AÞðBj:D;i:D − BÞ ffi; rA;B ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M N M N P D PD P PD ¯ 2 D ¯ 2 ðAj:D;i:D − AÞ ðBl:D;k:D − BÞ j¼0

i¼0

l¼0

(10)

k¼0

Fig. 7 Block diagram for the proposed compression technique. Journal of Applied Remote Sensing

073511-7

Vol. 7, 2013


Algorithm 1 Band ordering (B½1: : : λ). 1

// Order a given multispectral image bands, where λ is the number of bands.

2

// Input: An array B½1: : : λ; multispectral image bands without ordering.

3

// Output: An array B in optimal band ordering.

4

define array R½1: : : λðλ−1Þ 2

λðλ−1Þ 2

// An array R for correlations values

5

I½1: : :

6

define structure Sðk; i; jÞ // A structure S contains the value from 1 to ½λðλ − 1Þ∕2 that . . . //. . . using the k value to return i and j (r 1;2 ; r 1;3 ; r 1;4 ; : : : ; r 6;7 corresponding to. . . //. . . k ¼ 1; 2; 3; : : : ; 21)

7

for i←1 to λ − 1 do

8

// An array I for indices corresponding to R

for j←i þ 1 to λ do

9

r i;j ←corrðbandi ; bandj Þ from Eq. (10)

10

R½ðj − iÞ þ λði − 1Þ←r i;j

11

I½ðj − iÞ þ λði − 1Þ←ðj − iÞ þ λði − 1Þ

12 13 14

λðλ−1Þ ðA½1: : : λðλ−1Þ 2 ; H½1: : : 2 Þ←QuicksortWithIndexðjR½1: : : H for values and their indices, respectively.

N½1: : :

λðλ−1Þ λðλ−1Þ 2 ←reverseðH½1: : : 2 Þ

for n←0 to

ðλðλ−1Þ 2 Þ

// An array A and

// An array N contains ordered indices.

− 1 do

15

k ←N½n

16

ði; jÞ←Sðk ; i; jÞ

17

if (i or j conjugated with two bands)

18

Omit ordering for this step

19

λðλ−1Þ λðλ−1Þ 2 j; I½1: : : 2 Þ

else

20

Set B½i and B½j as conjugated

21

Record that bands i and j are conjugated

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 D’th pixel, respectively. If D equals 1, the exact value of the correlation between the two image bands is computed; otherwise Eq. (10) 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. The steps outlined above can be implemented with the following algorithm. We use the quicksort and partition algorithms20 with a new feature that saves the index for the sorted items. For example, if we have the ordered values from the previous three steps as r1;6 , r1;3 , r1;5 , r6;7 , r3;5 , r3;4 , and r2;7 , then bands #1 and #6 are conjugated as shown in Fig. 8(a). After that, bands #1 and #3 are conjugated as in Fig. 8(b). The value r1;5 is omitted because band #1 has the highest two correlations with bands #6 and #3. For r6;7, bands #6 and #7 are conjugated as shown in Fig. 8(c). Similarly, bands #3 and #5 are conjugated as in Fig. 8(d). The value of r3;4 is omitted because band #3 has the highest two correlation values with bands #1 and #5. Finally, Fig. 8(e) shows that bands #2 and #7 are conjugated. After band ordering, a data rotation step is performed to make the spectral dimension on the x axis. In the decompression, we need to reorder the bands of multispectral images. Therefore, we use the band reordering algorithm (Algorithm 4). Journal of Applied Remote Sensing

073511-8

Vol. 7, 2013


Algorithm 2 Quicksort with index ðA½l: : : r ; I½1: : : nÞ. 1

// Sort a subarray by quicksort.

2

// Input: A subarray A½l: : : r of A½0: : : n − 1, defined by its left and right. . . //. . . indices l and r . An index array I½1: : : n for input items in A.

3

// Output: Subarray A½l: : : r sorted in nondecreasing order, and the. . . //. . . corresponding indices in I½1: : : n.

4

if l < r

5

s←Partition With IndexðA½l: : : r Þ // s is a split position.

6

Quicksort With IndexðA½l: : : s − 1Þ

7

Quicksort With IndexðA½s þ 1: : : r Þ

Algorithm 3 Partition with index ðA½l: : : r ; I½1: : : nÞ. 1

// Partitions a subarray by using its first element as a pivot.

2

// Input: A subarray A½l: : : r of A½0: : : n − 1, defined by its left and right. . . //. . . indices l and r ðl < r Þ. An index array I½1: : : n for input. . . //. . . items in A.

3

// Output: A partition of A½l: : : r , with the split position returned as this. . . //. . . function’s value.

4

p←A½l

5

i←l; j←r þ 1

6

repeat

5

repeat i←i þ 1 until A½i ≥ p

6

j←j − 1 until A½j ≤ p

7

swapðA½i; A½jÞ // undo last swap when i ≥ j.

8

swapðI½i þ 1; I½j þ 1Þ // swap indices.

9

swapðA½l; A½jÞ

10

swapðI½l þ 1; I½j þ 1Þ

11

return j

4.3 Wavelet Transformation A wavelet is a waveform of limited duration that has an average value of zero. Unlike the Fourier transform whose basis functions are sinusoids that theoretically extend from minus to plus infinity, wavelet transforms are based on small waves, called wavelets, of varying frequency and limited duration. 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 suffers severe shift dependence due to aliasing in downsamplers and the poor directional selectivity. For these reasons, the dual-tree discrete wavelet transform (DDWT) is used in this paper as an alternative in the spectral dimension. We use filters from Ref. 21. We apply the 2-D DWT for the spatial dimension of the multispectral images, namely with Daubechies 9-7 filters.13 Journal of Applied Remote Sensing

073511-9

Vol. 7, 2013


Fig. 8 The interchanges between bands. (a) band #1 and band #6. (b) band #1 and band #3. (c) band #6 and band #7. (d) band #3 and band #5. (e) band #2 and band #7. (f) Optimal multispectral band ordering.

Algorithm 4 Band reordering (B½1: : : λ, I½1: : : λ). 1

// Reorder a given multispectral image bands, where λ is the number of bands.

2

// Input: An array B½1: : : λ; multispectral image bands with optimal ordering,. . . //. . . and array I½1: : : λ; indices for ordering. (i.e., 1,3,2,5,4,3,7,6 corresponding. . . //. . . to band #1, band #3, band #2, . . . , band #6).

3

// Output: An array B in original band ordering.

4

definearray NB½1: : : λ←B½1: : : λ // an array NB is a copy from array B.

5

for i←1 to λ do

6

k ←I½i

7

NB½k←B½i

8

B←NB

4.4 Quantization and Coding After applying the 3-D wavelet transform, a quantization process similar to that of the JPEG 2000 standard is performed using Eq. (11)15 and followed by Huffman coding.

jab ðu; vÞj qb ðu; vÞ ¼ sign½ab ðu; vÞ · : Δb

(11)

Coefficient ab ðu; vÞ of sub-band b is quantized to value qb ðu; vÞ, where Δb is the quantization step size in the sub-band b. The step size Δb is represented with two bytes, and it consists of an 11-bit mantissa μb and a 5-bit exponent εb . Journal of Applied Remote Sensing

073511-10

Vol. 7, 2013


Algorithm 5 Denoise and compression with band ordering and wavelets (NB½1: : : λ). 1

// Compress with denoising for multispectral image.

2

// Input: An array NB½1: : : λ; noisy multispectral image bands without ordering.

3

// Output: An array RDB½1: : : λ; reconstructed denoised multispectral image.

4

Noise Type←Get Noise TypeðNB½1: : : λÞ // determine the noise type.

5

Filter Type←Set Filter TypeðNoise TypeÞ // determine the suitable filter type for . . . //. . . the given noise.

6

DNB½1: : : λ←FilteringðNB½1: : : λ; Filter TypeÞ // denoise the noisy multispectral image.

7

RDB½1: : : λ←Compression With Band Ordering And Wavelet TransformsðDNB½1: : : λÞ

8

return RDB½1: : : λ.

Δb ¼ 2

Rb −εb

μb 1 þ 11 ; 2

(12)

where Rb is the number of bits corresponding to the nominal dynamic range of the coefficients in sub-band b. In the reversible path, the step size Δb is set to 1 by choosing μb ¼ 0 and εb ¼ Rb . The steps outlined above in Fig. 7 can be implemented with the following algorithms: Algorithm 6 Compression with band ordering and wavelet transforms (B½1: : : λ). 1

// Compress with denoise for multispectral image.

2

// Input: An array B½1: : : λ; multispectral image bands without ordering.

3

// Output: An array RB½1: : : λ; reconstructed multispectral image.

4

OR½1: : : λ←Band OrderingðB½1: : : λÞ // An array OR for image with band ordering.

5

NOR½1: : : λ þ 1←Add Zero BandðOR½1: : : λÞ // Add zero band#λ+1 for OR in NOR.

6

MIðN; M; λ þ 1Þ←Form MultispectralðNOR½1: : : λ þ 1Þ // form multispectral image. . . // . . . in 3D data in MI with N columns, M rows, and λ þ 1 spectral bands.

7

RMIðN; λ þ 1; MÞ←Data Rotation½MIðN; M; λ þ 1Þ // 3D data rotation.

8

WMI←DWT½RMIðN; λ þ 1; MÞ // 3D discrete wavelet transforms (DDWT and DWT).

9

CMI←Quantization And CodingðWMIÞ // quantization and coding (Huffman).

10

// store or transmit.

11

RWMI←Dequantization And DecodingðCMIÞ // dequantization and decoding.

12

RRMIðN; λ þ 1; MÞ←IDWTðRWMIÞ // inverse 3D discrete wavelet transforms. . . //. . . (IDDWT and IDWT).

13

NRMIðN; M; λ þ 1Þ←Data Rotation½RRMIðN; λ þ 1; MÞ // 3D data rotation.

14

RNOR½1: : : λ þ 1←Get Bands½NRMIðN; M; λ þ 1Þ // get multispectral image. . . // . . . bands from the 3D data in NRMI in RNOR.

15

ROR½1: : : λ←Remove Zero Band½RNOR½1: : : λ þ 1 // remove zero band#λ+1 for RNOR. . . //. . . in ROR.

16

RB½1: : : λ←Band ReorderingðROR½1: : : λÞ // An array RB for reconstructed. . . //. . . multispectral image bands with the original order.

17

return RB½1: : : λ.


073511-11

Vol. 7, 2013


5 Simulation Results We have implemented the proposed technique on two multispectral image sets available in Ref. 22: Kilauea Volcano, Hawaii, 23 May 2001, and Los Angeles, California, 20 September 1999, see Fig. 9. We used these multispectral images in our experiments for comparison between several multispectral image compression techniques: JPEG, SPIHT, JPEG 2000, and the proposed technique. We applied the proposed technique on a noise-free multispectral image and a noisy multispectral image to evaluate it. Two experiments have been conducted and the results are shown in Figs. 10 and 11. Figure 10 shows band #5 in gray scale for the original Hawaii image and its compressed versions. Figure 11 shows band #2 in gray scale for the original Los Angeles image and its compressed versions. The performance of the compression methods has been studied and distortion metrics such as the MSE and the PSNR have been considered. Let 0 ≤ gði; j; kÞ ≤ gfs denote an N-pixel digital image in band k for a multispectral image ðN × M × λÞ, where gfs is the largest pixel value, and let g¯ ði; j; kÞ be its possibly distorted version obtained by compressing gði; j; kÞ and decompressing the output bit stream; the MSE and the PSNR are defined as MSE ¼

λ X N −1 M −1 X 1 X ½gði; j; kÞ − g¯ ði; j; kÞ2 ; NM k¼1 i¼0 j¼0

PSNR ¼

(13)

λ gfs 20 X log10 pffiffiffiffiffiffiffiffiffiffiffiffi ; λ k¼1 MSEk

(14)

where λ is the number of bands, and MSEk is the MSE for band k. Spectral distortion metrics such as the SAM and the SID have also been considered for ˜ both having L components, the comparison purpose.23 Given two spectral vectors V and V, let V ¼ fv1 ; v2 ; : : : ; vL g be the original spectral pixel vector, where vl ¼ gl ði; jÞ, and ˜ ¼ fv˜1 ; v˜2 ; : : : ; v˜L g be its distorted version obtained after compression and decompression. V Analogous to the radiometric distortion metrics, spectral distortion metrics may be defined. SAM denotes the absolute value of the spectral angle between the couple of vectors calculated as24 ! ˜ hV; Vi ˜ SAMðV; VÞ ¼ arccos ; (15) ˜ kVk2 · kVk 2 in which stands for scalar product.

Fig. 9 Original multispectral images (bands 2, 3, and 4). (a) Hawaii. (b) Los Angeles. Journal of Applied Remote Sensing

073511-12

Vol. 7, 2013


Fig. 10 Hawaii image (gray scale band #5) compression (CR ∼7.2). (a) Original image band. (b) Image band corrupted by impulse noise with a probability of occurrence of 0.02. (c) Compressed band using JPEG with filtering. (d) Compressed band using SPIHT with filtering. (e) Compressed band using JPEG 2000 with filtering. (f) Compressed band with the proposed technique.

Fig. 11 Los Angeles image (gray scale band #2) compression (CR ∼3.2) (a) Original image band. (b) Compressed band using JPEG. (c) Compressed band using SPIHT. (d) Compressed band using JPEG 2000. (e) Compressed band with the proposed technique. Journal of Applied Remote Sensing

073511-13

Vol. 7, 2013


Fig. 12 Los Angeles image with and without band ordering and 3-D rotation. (a) MSE versus CR. (b) PSNR versus CR.

The SID is derived from information-theoretic concepts as23 L X p ˜ SIDðV; VÞ ¼ ðpl − ql Þ log l ; ql l¼1 where pl ¼

vl ; and kVk1

ql ¼

v˜ l : ˜ kVk

(16)

(17)

1

Figure 12 shows the MSE and PSNR values for the proposed compression technique with and without band ordering and 3-D rotation. The results in this figure are in favor of band ordering and 3-D rotation. Table 1 shows the results for compressing the noisy (impulse noise with probability ¼ 0.02) Hawaii image. The results in the table are in favor of the proposed technique. Table 2 shows the results for compressing the noise-free Los Angeles image. These results also are in favor of the proposed compression technique. Journal of Applied Remote Sensing

073511-14

Vol. 7, 2013


Table 1 Experimental results for the noisy Hawaii image compressed with different compression techniques. Noisy-Hawaii image (Impulse noise with occurrence probability ¼ 0.02) Technique

MSE

PSNR (dB)

SAM

SID

JPEG þ denoising

60.78

39.77

1.691

0.0023

SPIHT þ denoising

153.70

35.29

2.849

0.0042

JPEG 2000 þ denoising

54.26

40.12

1.523

0.0021

Proposed

46.72

41.03

1.451

0.0011

Table 2 Experimental results for the noise-free Los Angeles image compressed with different compression techniques. Noise-free Los Angeles Technique

MSE

PSNR (dB)

SAM

SID

JPEG

98.37

37.86

1.832

0.17E-2

SPIHT

303.36

32.58

2.978

0.30E-2

JPEG 2000

33.01

41.47

1.163

0.52E-3

Proposed

16.65

44.55

0.775

0.25E-3

6 Conclusion An efficient multispectral image denoising and compression technique has been proposed in this paper. It is based on filtering the noisy multispectral image, optimal multispectral band ordering, a 3-D transform that uses DWT and DDWT, and a simple Huffman coder. We have taken full advantage of the filtering layer on the noisy images and the transformation by using a DDWT on the spectral dimension and a DWT on the spatial dimension. From the subjectivity and objectivity tests, we can conclude that the proposed technique is more effective than other traditional techniques.

References 1. NASA, “The Landsat program,” 19 March 2013, http://landsat.gsfc.nasa.gov/ (28 January 2012). 2. United States Geological Survey, “Landsat missions,” 8 August 2013, http://landsat.usgs .gov/ (28 January 2012). 3. D. Salomon, Data Compression, the Complete Reference, 4th ed., Springer, Berlin (2007). 4. K. Kanagalakshmi and E. Chandra, “Performance evaluation of filters in noise removal of fingerprint image,” in 3rd Int. Conf. on Electronics Computer Technology, Vol. 1, pp. 117–121 (2011). 5. V. Lukin et al., “Image filtering: potential efficiency and current problems,” in IEEE Int. Conf. on Acoustics, Speech and Signal Processing, pp. 1433–1436 (2011). 6. http://www.jpeg.org/ (10 April 2012). 7. N. Ahmed, N. Natarajan, and K. R. Rao, “Discrete cosine transform,” IEEE Trans. Comput. C, C-23(1), 90–93 (1974), http://dx.doi.org/10.1109/T-C.1974.223784. 8. D. A. Huffman, “A method for the construction of minimum-redundancy codes,” Proc. IRE 40(9), 1098–1101 (1952), http://dx.doi.org/10.1109/JRPROC.1952.273898. Journal of Applied Remote Sensing

073511-15

Vol. 7, 2013


9. P. Pellegri, G. Novati, and R. Schettini, “Multispectral loss-less compression using approximation methods,” in IEEE Int. Conf. on Image Processing, pp. 638–641 (2005). 10. P. L. Dragotti, G. Poggi, and A. Ragozini, “Compression of multispectral images by threedimensional SPIHT algorithm,” IEEE Trans. Geosci. Remote Sens. 38(1), 416–428 (2000), http://dx.doi.org/10.1109/36.823937. 11. J. Saghri, A. Tescher, and J. Reagan, “Practical transform coding of multispectral imagery,” IEEE Signal Process. Mag. 12(1), 32–43 (1995), http://dx.doi.org/10.1109/79.363506. 12. http://www.jpeg.org/jpeg2000/index.html (5 June 2012). 13. M. Antonini et al., “Image coding using wavelet transform,” IEEE Trans. Image Process. 1(2), 205–220 (1992), http://dx.doi.org/10.1109/83.136597. 14. A. R. Calderbank et al., “Wavelet transforms that map integers to integers,” Appl. Comput. Harmon. Anal. 5(3), 332–369 (1998), http://dx.doi.org/10.1006/acha.1997.0238. 15. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Prentice Hall, Pearson Education, Englewood Chiffs, New Jersey (2007). 16. J. Wei et al., “Multispectral images compression based on JPEG 2000,” in 2010 2nd International Conf. on Information Engineering and Computer Science (ICIECS), pp. 1–3 (2010). 17. P. Cosman, R. Gray, and R. Olshen, “Evaluation quality of compressed medical images: SNR, subjective rating, and diagnostic accuracy,” Proc. IEEE 82(6), 919–932 (1994), http://dx.doi.org/10.1109/5.286196. 18. P. Melnychuck, M. Barry, and M. Mathieu, “The effect of noise and MTF on the compressibility of high resolution color images,” Proc. SPIE 1244, 255–262 (1990), http://dx.doi .org/10.1117/12.19515. 19. P. Toivanen, O. Kubasova, and J. Mielikainen, “Correlation-based band-ordering heuristic for lossless compression of hyperspectral sounder data,” IEEE Geosci. Remote Sens. Lett. 2(1), 50–54 (2005), http://dx.doi.org/10.1109/LGRS.2004.838410. 20. A. Levitin, Introduction to the Design and Analysis of Algorithms, 2nd ed., Pearson Addison-Wesley, Boston (2007). 21. I. W. Selesnick, “The double-density dual-tree DWT,” IEEE Trans. Signal Process. 52(5), 1304–1314 (2004), http://dx.doi.org/10.1109/TSP.2004.826174. 22. http://data.nasa.gov/landsat-7-data-sets/ (18 July 2012). 23. C. I. Chang, “An information-theoretic approach to spectral variability, similarity, and discrimination for hyperspectral image analysis,” IEEE Trans. Inf. Theory 46(5), 1927–1932 (2000), http://dx.doi.org/10.1109/18.857802. 24. G. Motta, F. Rizzo, and J. Storer, Hyperspectral Data Compression,” 2006 ed., Springer, Science and Business Media, public, Berlin (2005). Ahmed Hagag was studied in Faculty of Science, Menoufia University and got the bachelor’s degree of mathematics and computer science during the period of September 2004 to September 2008. He was pursuing the master degree of computer science in the same University begin from September 2009. He joined the teaching staff of the Faculty of Computer and Informatin Technology, Egyptian E-Learning University, Cairo, Egypt, in 2009. His current research areas of interest include multispectral image compression, multispectral image de-noising, and enhancement for wavelets transforms. Mohamed Amin graduated with a degree in mathematics from Menoufia University in 1983. He studied computer science from 1986 to 1989 at Ain Shams University in Cairo, Egypt, and he received his MSc and PhD in computer science in 1990 and 1997, respectively, from the University of Gdansk, Poland. He is currently an associate professor of computer science with the faculty of science at Menoufia University, Egypt. His areas of interests are formal languages and their application in complier design, cooperating/distributed systems, Petri nets, cryptography, and image processing. Journal of Applied Remote Sensing

073511-16

Vol. 7, 2013


Fathi E. Abd El-Samie received the BSc (Hons.), MSc, and PhD degrees from Menoufia University, Menouf, Egypt, in 1998, 2001, and 2005, respectively. Since 2005, he has been a teaching staff member with the Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University. He is currently a researcher at KACST-TIC in radio frequency and photonics for the e-Society (RFTONICs). He is a coauthor of about 200 papers in international conference proceedings and journals, and four textbooks. His current research interests include image enhancement, image restoration, image interpolation, super-resolution reconstruction of images, data hiding, multimedia communications, medical image processing, optical signal processing, and digital communications. He was a recipient of the Most Cited Paper Award from the Digital Signal Processing journal in 2008.


073511-17

Vol. 7, 2013