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NOAA data compression using a multi length DPCM code and a variable length code

Byoung Sun Kim, munekazu Sakamoto, Mikio Takagi
Institute of Industrial Science University Of Tokyo


Abstract
In this paper wee purpose a method to compress meteorological satellite NOAA advanced very high resolution Radiometer data and the result of experiments we examined the entropies of each channels and the correlation between channels .The method is based on differential Pulse code Modulations and Multi length code and a variable length code by Wyle code of hasler code and once. The interchange prediction reduces the total entropies to about 10% of the intracranial prediction though the multi length code shows lower efficient than the variable length code if code words fit in byte and word boundaries the handling of the code words on a computer becomes more convenient using a variable code with inter channel prediction the average compression is slightly under a half of the original data.

Introduction
The remotely sensed data from NOAA can provide very useful and important information in Meteorology Ocean graphy and many other scientific fields because of its simultaneous and repeated broad area observation of the earth. We receive 4~8 scenes a day from two NOAA which are restored on the recorder tapes CLS and the optical disc. However the image data is enormously large AVHRR data account for about 51:2 ~ 57.5 MB channel X10bit for 2048X4000~4500pixels) on the one pass data of 63 MB so we must devise an information preserving compression technique to keep our archival system compact. Data compression has important application in the areas of the data transmission and data storage. Compression data to be stored or transmitted means increasing the capacity of the communication channel. Similarly compression a file for scene to the half of its original size is equivalent to doubling the capacity of the storage we are obliged to store the data at a higher thus faster and reduce the load on the input and out put channels of the our archival system.

In this paper we purpose a method to compress NOAA -AVHRR data with the result of the experiment. We examined the entropies of each channels and the correlation between channels to know the co0mpression limits we employ DPCM and a code based on multi length code word of bit and a variable length code by wyle code B2 code of hasler code and once Iwastia code.

Outline of NOAA AVHRR
The meteorological satellite NOAA-10 NOAA-11 goes around the earth at the average altitude of 810km in about 101.2 minutes and we can get the observation data about 13

Table: 1 Spectral characteristics of AVHRR
Channel wave length Primary use
1 0.55.~0.68 Day time cloud and surface mapping
2 0.73~1.10 Surface water delineation
3 3.55~3.93 Sea surface temperature night time cloud mapping
4 10.5~11.5 SST. day/ night cloud mapping
5 11.5~12.5 SST



figure1: The Entropies of each channel

minutes when it passes the highest orbit. We convert the received raw. Data stream into 16-bit word so that the handling of the data on a computer becomes more convenient. Advanced very high resolution Radiometer data account for about 51.2~57.5 MB on the one pass data of 63 MB one pass data of 63MB is changed the 100MB and we receive 4~8 scenes a day from two CLS the optical disc AVHRR of NOAA is four or five channel scanning radio meter instrument the fifth channel data is the same as the fourth on e so that the same for both the four or five channel version table show the spectral characteristics of each channel.

AVHRR data
  1. Entropy

    First of all we have examined the entropies of each channels fig.1 shows the entropies of the original channel data and their fluctuation in a day. The entropies of the visible channels change from 0-90 to 8.971 reaching the maximum in the afternoon and almost zero in midnight .In in contrast with the visible channels IR channels show a satellite change this is because the visible channels are subjected to the solar reflectance's. The seasonal change of the entropies of the visible near and IR channel is rather moderate in the comparison with their daily change.

  2. Correlation of channel

    Fig 2 Shows the correlation coefficients between adjacent pixels of the original channel .the correlation of the horizontal direction in larger than the vertical one because the earth


    Figure 2 the correlation coefficients between adjacent pixels

    CH-1,CH-2 Ch-2, CH-3 CH-3, CH4 CH-4,Ch-5 CH-6,CH-7
    0.983 0.392 0.731 0.998 0.797

    Any direction table 2 shows the inter channel correlation coefficient of the corresponding pixels. The inter channel between CH-1 and CH-2 and that of CH-4 and CH5 mark very high value. This feature is useful to the inter channel prediction.
Predication
Generally speaking the data system has redundancy from one sample to the next and this fact enables prediction error coding. The prediction error is between adjacent pixels Ek.

Ek=Xj --- X'j

Where the variable Xj denotes the jth sample in data stream and X'j denotes a predicted value of Xj shows four prediction methods we have examined four prediction methods. (1) (2) (3) (4) and (5) for the example only Xj-1 contributed to the prediction process. Formula (1) (2) and (3) are used to the prediction in a channel. Formula (4) and (5) are used to the prediction between channels.

(1) X'j = C   :Previous prediction
(2) X'j = (C+B)%2   :Average prediction
(3) X'j = C - A + B   :Panel prediction
(4) X'j = b   :Inter channel prediction
(5) X'j = c - a + b   :Inter channel prediction


Where A, B, C a, b, c are reference pixels.

Table 3 shows the entropies by the each predictions .the entropies original image is very large. In the intra channel prediction. Prediction (1) is the smallest of the others (Average prediction) (2) and panel prediction (3) and in the inter channel prediction (5) is the smaller entropies the (4) since the variance of the prediction error (5) is smaller than the those of (4) inter channel prediction (5)is the smallest the total entropy of the others selecting CH-1 CH3 Ch-4 of the previous prediction and CH1,2 and Ch-4,5 of the inter channel prediction (5).


Figure 3: Prediction method

Table 3: The entropies by the prediction methods
  CH-1 CH-2 CH-3 CH-4 CH-5 Total entropy
Entropy 7.876 7.903 8.937 8.387 8.437 41.540
(1) 5.705 5.721 6.240 4.611 4.759 27.036
(2) 5.839 5.879 6.330 4.744 4.893 27.685
(3) 6.456 6.474 6.977 5.354 5.513 30.774


  CH-1,2 CH-2,3 CH-3,4 Ch-4,5 CH-5,1 Total entropy
(4) 5.967 9.422 4.747 8.278 37.408 8.993
(5) 3.288 6.779 6.305 3.172 5.544 25.088

Coding
  1. Multi length code

    Though a multi length code usually gives lower coding efficiency than variable length code if a code word fits in byte and word boundaries the handling of the data on a computer becomes more convenient .We encode the prediction error of DPCM using a code based on multi length code word of 2n bit. Shows the assignment of the code word for the multi length code.

  2. Variable length code

    An optimal code could be constructed using Huffman's method [6] the distinguishing feature of a Huffman code is the length is related to the frequencies of the source character the shutter code word. Is assigned to the frequent character. Huffman code has been known as an optimum code but rarely used in communication because of the complexity of implementation. We have examined variables code called Wyle code [7] Hasler code[8] and once Iwastia code [9] the code word for the hasler code are multi pile of fixed Length blocks characterized by the block length. In this case we used 3 it clock one code is based on Huffman code. The code for the difference value of ore than 5 consists of a special code followed by the original data. Here a special code is provided for the difference value of more than 10 this modification hardly impair the efficiency of Huffman code because the portability of the special code is less than a few per cent table 5 shows the assignment of code word for Wyle code hasler code and onoeiwastia code.

    Table 4: The multi-length code



    Table 5: Wyle code, Hasler code and Onoe-Iwasita code

    Entropy

    Multi

    Wyle

    B2O

    noe-

    Iwastia    		 CH-1

    5.705

    6.776

    6.134

    6.137

    7.782    		 CH-1

    23.288

    4.466

    3.599

    3.932

    3.379    		 CH-3

    6.240

    7.497

    6.992

    6.934

    9.401    		 Ch-4

    4.611

    5.489

    4.789

    5.055

    5.552    		 CH-4 ,5

    3.172

    4.417

    3.530

    3.851

    3.233    		 Total Length

    23.016

    28.645

    25.044

    25.909

    29.347

    Table 6 The average code word length by multi length code and variable code.
Coding experiments
The experimental data is obtained from the NOAA -II from 14.06 to 14:17 on 16th Dec 1989 of entropies reaching the maximum in the after noon .In the inter channel predictions previous prediction has usually a smaller entropy than the others average panel prediction with the inter channel prediction the total entropies is reduced to about 10% of those of the intra channel prediction So we used CH-1 Ch3 and Ch-4 of the previous prediction and CH,1,2 and CH-4,5 of the inter channel prediction (5) table 6 shows the average code word length by using multi length code and variable results if we use the multi length code efficient the total code length is 28,.50 bit .From the experimental result Wyle code is more efficient than the Hasler code and onoe code but hasler code often is efficiently in the high entropy of CH-3 onoe Iwastia code is more efficient in the inter channel predictions and if wyle code of CH1 CH3 Ch4 of the previous predictions and Onoe Iwastia become from25.04 bit to 24.53 bit using variable code with the inhere channel prediction it reduces to 24.53 bit of the original data operating with a four channel instrument the fifth channel version table 7 shows the average code word length by using multi length code and variable code in NOAA -10 using the Wyle and One Iwstia code the total code word length becomes to 2100bit of the original data.

Summary and conclusion
We have developed an information preserving compression technique to make our archival system compacter .We find the image data characteristics of the passing time schedule .The entropies of the visible channels reach the maximum in the after noon and become almost zero at mid night and the seasonal change of the entropies of the visible and visible /IR channel is at rather moderate in tye compression with their daily change .The experiment yields the following result using the inter channel prediction the total entropies reduce to about 105 of those of the

Table-7 average code word length by multi length code variable code.
Entropy

Multi

Wyle

B2O

noe-

Iwastia		 CH-1

5.635

6.637

6.112

6.168

7.220		 CH-1,2

2.975

4.300

3.413

3.717

2.993 		CH-3

6.396

7.830

7.268

7.142

8.707		 Ch-4

4.418

5.366

4.626

4.837

4.830		 Total Length

19.424

24.133

21.419

21.864

23.750

We have not used the inter channel prediction of the visible and IR channels because inter channel prediction is not so efficient as the inter channel predictions .In variable code Wyle code is the most efficient than the Wyle code in the inter channel prediction (CH1,2 and CH-4-5 ) not efficient in the previous prediction (CH-1 Ch3 and Ch-4) because the different value of less than 10 of those is lower probability than one of the inter channel prediction the combination of Wyle code and Onoe code Iwastia code are used/. The compression efficiency of the multi length code Wyle code the of the original data using a variable code with the inter channel prediction the compression ratio is slightly under and One Iwastia of the original data using the combination of Wyle code and Onoe Iwastia code NOAA 10 the total code word length becomes 2100 bit on 40bit of the original data the Wyle code of more efficient than the Onoe code Iwastia code in the previous prediction. Using Wyle code is the previous prediction and the one Iwastia code in the inter channel prediction we can reduce the redundancy we are still studying the efficient coding for any scene and now how to select more efficient for the different image data.

References
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