NASA Technical Paper 2458 C 2 4 August 1985

NASA

An Image Compression Survey and Algorithm Switching Based on Scene Activity

Michael M. Hart Property of U. S. Air Fora

AEM: LIBRARY F40600-81-C-0004

https://ntrs.nasa.gov/search.jsp?R=19850024793 2018-07-12T18:09:50+00:00Z

~ A S A 1 Tech nica I Paper 2458

I

1985

National Aeronautlcs and Space Administration

Scientific and Technical Information Branch

An Image Compression -

Survey and Algorithm Switching Based on Scene Activity

Michael M. Hart Langley Research Center Hampton, Virginia

~ABSTRAC~ Entropy The entropy is defined as the amount of informa-

tion that is emitted by a data source. The theoreti- cal basis of data compression depends on Shannon's first theorem on the noiseless coding of information. Given a zero memory source S emitting the sym- bols si (i = 1, 2, . . . , n) with the corresponding (independent) probabilities Pi, we can calculate the entropy of the source under the above conditions as

A comprehensive study of data compression tech- lniques is presented in this paper. A description of these techniques is provided along with a per-

1 formance evaluation. The complexity of the hard- ware resulting from their implementation is also ad- dressed. The compression effect on channel distor- tion and the applicability of these algorithms to real- time processing are presented. Also included is a

l proposed new direction for an adaptive compression I technique for real-time processing.

1 .

INTRODUCTION The increase in resolution and in the number of

spectral bands of modern multispectral imaging sys- 1 tems creates a tremendous burden on the down-link

channel and the bandwidth required to transmit data I to ground stations. In fact, the future imaging sys-

tem will produce data at rates that will exceed the capability of the down-link channel. Data compres- sion is one of the most powerful tools available to reduce the data volume to be transmitted. Even-

I tually, data compression will be an essential part of 1 modern telemetry systems. I Since most users insist on reversible processes,

this paper focuses only on reversible data compres- 1 sion techniques and explores the possibility of their ' real-time implementation. Various reversible data

compression techniques are described, and an eval- uation of these techniques in terms of performance,

' implementation complexity, and immunity to chan- nel noise is presented.

l INFORMATION THEORY AND DATA I COMPRESSION 1 The coding of the numerical data is accomplished 1 by means of pulse code modulation (PCM) requiring, 1 in general, a very large bandwidth. In fact, the ~ number of pulses per second to be transmitted is a

function both of the number of samples and of the , number of bits necessary to represent each sample. To reduce this large number of pulses per second

I (and consequently the bandwidth), it is necessary to introduce data transformation represented by data or

l bandwidth compression. Such a transformation can be considered as one which operates on the data given

i by an information source in such a way as to reduce I the amount of nonuseful or redundant data. Since

compressed data are, in general, more sensitive than noncompressed data to the channel noise, a channel encoding might be necessary for a noisy channel. An error in the compressed data will generally introduce a considerable amount of distortion.

n 1

Each of the symbols sl, s2, . . . , sn can be mapped into a fixed sequence of k symbols taken from a finite alphabet X = 21, 22 , . . . , xk. This proce- dure corresponds to encoding each symbol si into a code word xi belonging to the set X I , x2, . . . , xn and having length li. We can define the average length of this code L as

n

L = Pala (2) i = l

Such a code is said to be compact for that source if its average length is less than or equal to that of any uniquely decodable code.

From equations (1) and (2), the following prop- erty of H ( S ) can be proved:

H ( S ) 5 L (3)

Hence, H ( S ) is a lower bound for code average length. The ratio

is defined as the efficiency of the source code, and 1 - q is the redundancy. The term H ( S ) can be used to evaluate an upper bound for the mean compression ratio - -

(4) L C R = d L

The symbols L, and L represent the source and encoded mean word lengths, respectively.

From equations (3) and (4) we can obtain the maximum compression ratio CR,, as

(5)

Equations (3) through (5) are true if the compression method is perfectly reversible.

A higher value for CR than that given by equa- tion ( 5 ) can only be obtained by introducing a certain amount of distortion in the reconstructed signal. In the latter case, the process is said to be irreversible. In this paper, only reversible compression methods are considered.

Channel Capacity The entropy (eq. (1)) can be considered as the

average information associated with the emission of a soiircc synibol. Lct the output alphabet reproducing t,hc source be L3 with r symbols. Then B = {bj} where j = 1, 2, . . . , r , and P(6j) is the probability of b,. Mutual information can be defined as a function of t!ic sciiircc symbols {Si} E S arid of the received syrrlhols { b j } E B by

and it represents the avcrage information obt,aint:d from the emission of a symbol s; when b j is known. The mutua1 iiiforrriatioii Z(S, B ) is a rioiiriegative coIiv(3x fiinction of the probabilit,iw P ( s;) arid always admits ii rnaxiniiim. This niaxiriiurri, taken ovcr all t,hc possible c1ioicc.s of the. source probability distritmtion Z’(si ) , is c a l l d t,hc chanric.1 capacit,y C , wlicw

( 7 )

In fact, if H ( S ) < C , it is always possible to find a channel coding mrt hod for transmission on a noisy channel, such that the error probability a t the re- ceiver is lowcr than an arbitrary small quantity. How- ever, this could imply the use of a prohibitively long codr, which is riot of practical usefulness.

Rate Distortion Function Let a vector X with n components of the source

alphatwt, { X I , 2.2, . . . , z,}, z; E S, be encoded in a vcct,or Y = {yl, y2, . . . , yn} with yi E B. We drriotc the word dist,ortion measure by D,(X, Y ) , which could br expressed as the cost of sending xi anti rev-civing yl where i # j.

Thcl functiori D,,(X, Y ) is dcfined by the user. An o f t cwiisc .c l IIic:isiir(> of distortion is the single-lrtt,cr fic1olit.y c.rit.c.rioii, whcw Z>,,(X, Y ) is t,hc meaii o f the singlv clist.ort,ioiis iIit,rotluccd by rcyr(w:nt,ing zi with y , ; I . ( > . ,

1 , U,,(X. Y ) = n ~ D ( ~ z r Y i ) (8)

2 - 1

For channels with memory, more complex definitions are needed to measure distortion, and in general, these are very difficult to deal with.

In many cases, equation (8) is used as a first ap- proximation for systems with memory. From eqiia- tion (8), the overall average distortion D will depend on the conditional probability P(y,lz,) and is given by

D = P ( ~ Z ) ~ ( Y Z l ~ 2 ) ~ ( ~ Z ~ Yz) (9) SIB I

when D turns out to bc less than a preset quantity D , P ( ~ , I x , ) is called D-admissible. Now we can drfine the rate distortion function R ( D ) as the minimum of the average mutual information

,

where the minimum is taken over all the possible P(y,lz,) values that are D-admissible.

I

REVERSIBLE DATA COMPRESSION TECHNIQUES I

Reversible data compression techniques include redundancy reduction, differential pulse code mod- ulat ioli (DPCM), and linear transformation (refs. 1 4). The various algorithms used in these techniques arc summarized in figure 1.

Redundancy Reduction The redundancy reduction method is based on

whether a data point could be successfiilly deter- mined within a preset tolerance of the actual point. Predictions arid interpolations are carried out accord- ing to the following differcncc polynomial:

Y[ = Yt-1 + AYt-1 + A‘Yt-1 + . . . + Any,-1

whrw

yt! yt-1

predicted data sample a t time t

sample one period prior to t

AYt-1 =Yt 1 -Yt-2

A‘Yyt-1 = AYt-1 - AYt-2

A”Yt- 1 = A7’-’Yt 1 - A’’ ‘1 ; 2

The basic differc.ncc1 b,ctwc.c’ri prcdict orh ;ind i r i t crpo- lators is that prcdictors usc orily past siiIIil)l(’s to prc- dict the present O I ~ C , whcwas irit c’rpolat ors iisc bot 11

past and future samplrs. Comparisori of various de- grees of difference polynomials has shown that abovc

2

I I a third-degree polynomial, there is little or no im-

provement in performance (ref. 5). It is the author's opinion that the improvement from first degree to

1 second or third degree does not justify the added complexity. (See fig. 2 . ) Hence, the evaluation in this paper is done on zero- and first-order polynomials.

' Prediction Algorithms

1 present sample by using a difference polynomial. If The following compression algorithms predict the

I

lyt - Ptl I K (11)

where

Yt actual sample value

fi predicted value

I K tolerance band

, then the sample is not transmitted. The process 1 continues until the condition in equation (11) fails, '

then the actual sample is transmitted with a code appended to inform the ground station of the num-

~ ber of samples that were not transmitted. At the ' ground station, the decompressor fills in the samples that were not transmitted by using the same poly- nomial that was used a t the compressor. The com- pressor and decompressor can use one of the follow- ing polynomials: (1) zero-order predictor, (2) zero- order predictor with an offset, (3) first-order predic- tor, (4) first-order predictor with a slope correction, or (5) optimum linear predictor. These polynomials are discussed in the sections which follow.

I 1

' 1

I ' Zero-order predictor. In the zero-order predictor (ZOP) algorithm, it is always assumed that

( 1 2 ) I Yt = Yt-1

I 1 where

~ ?t sample to be predicted a t time t

I successfully predicted sample

I

Y;-l actual transmitted sample or previous

A graph illustrating this algorithm is shown in fig- ure 3. At time t , we can see that there will be no transmission, since the tolerance band (the two dashed lines) contains the previous sample point. Whereas, at t + 2 the actual data point is transmit- ted, since it falls outside the tolerance band placed on the predicted sample.

Zero-order predictor with ofisset. The zero-order predictor with an offset is basically the same as the

ZOP. The prediction polynomial is fi = Y;-l as long as a sample is not transmitted (redundant). Once a sample is transmitted, the first point in the next interval is offset as follows:

where

Yt-1

Ytl-2

sample at t - I

sample at t - 2 (If the sample is transmitted, the actual sample is used. If not, the predicted value is used.)

161 magnitude of offset

These two algorithms are relatively simple to imple- ment; however, they perform best when the actual data vary very slowly.

First-order predictor. The first-order predic- tor (FOP) algorithm is similar to the above algo- rithms except that the predictor uses a first-order polynomial

A graph illustrating the FOP is shown in figure 4. The implementation complexity for this algorithm is still low, and it performs well with data that vary at a medium rate.

First-order predictor with slope correction. The difference between the first-order predictor with a slope correction and the algorithms previously de- scribed is in the prediction polynomial. In this al- gorithm, as long as l < K (the tolerance band), then

fi = Yt-1 + AY, (15)

where

AY, increment in Y , computed r sample periods prior to t - 1

number of sample periods between t - 1 and time of prior transmission

r

If IC I 2 K , then

where

3

and c = 2 if T > 1; c = 1 if T = 1. The implemen- tation complexity of this algorithm is medium. This algorithm can handle data that are more active, and it follows the data slope faster than the previously discussed predictors.

Optimum linear predictor. The optimum linear predictor algorithm predicts the present sample by using a linear combination of past samples

N

The coefficient,s a k are chosen to minimize the mean sqiiarc wror bctween the predicted and actual values. These cocfficicwts are found by solving N linear equations involving the autocorrelation function

N

wherr

R,[(T - k)T] autocorrc.la for lag of (;

h ) T ] (T = 1 , 2, _ _ . , N )

ion t’urict,iori of signal - k)T

h nu m bcr of sarn plc periods s irice last transtnittcd sample

T timr between sampling

The implementation complexity for this algorithm is quit (> high.

Interpolation Algorithm

The interpolation algorithm approximates the data with a zero- or first-order polynomial curve. The best way to desrribe this method is by an ex- arnplc. First, transmit Yo and Y1, then approximate Yl by using equation (12) or (14). Determine if Y2 is within fK units of Yo and Yl. If true, then ap- proxiniatx~ Y? as above and determine if Y3 is within f K of Yo, Y1, and Yi. Keep repeating this pro- cess iint,il t,he a h v c rondit,ion fails; that, is, Y, is not wit,liiii I f K of all t,he previous samples. When this lii~pp(ws, a start,ing point, arid an ending point of a l i i i v scypicwt, arc t.r;LIisriiit,t,(~d. This linc. segment, rep- rcwnt.s t , l i v I)oiiit.s li), Y1, . . . , UT,- 1 . This process t.licw c.oiit.ii1uc.s wit,li Y,, corisidcrctti as y0 for the new l i i i v sc~gincwt,. S w c d Itic.t,hods cxist for rqxctsent- itig w ( l l i i i ( l i L i i t . siii1ipl(%s by a st,raight.-linc, segment. To acliiwc~ t,hv largcst, coniprctssion, it is necessary t,o svlcct. a lint scyyricmt, within K units of as many

samples as possible (where K is the desired toler- ance). This optimum algorithm requires freedom of both the starting and ending points of the line and results in four degrees of freedom. Since the four- degree-of-freedom algorit,hm is am ext,reme!y mmp!ex process to implement, anchoring the starting point of the line segment to an actual or computed sample greatly simplifies the implementation. One way is to anchor the starting point of a new line to the end of the previous line. (This is called a joined-line seg- ment.) Another way is to anchor the starting point of the line to thc actual out,-of-tolerance sample.

Differential Pulse Code Modulation (DPCM) The general hlork diagram of a DPCM system

is shown in figure 5. In this technique, a predicted sample Y, is evaluated by using any of the predic- tion algorithms. The difference e , between the ac- tual sample and the predicted one is quantized. In basic DPCM, the uniform quantization of the e, val- ues may cause an edge degradation. However, if the correlation of the input signal is high and the pre- diction algorithm is efficicnt, DPCM gcncrally offers a higher efficiency than PCM. In general, wit,h an equal number of bits, the signal-to-noise ratio (SNR) is higher for DPCM than for PCM. With an equal SNR., DPCM requires a lower number of bits than PCM. The gain G in the SNR of DPCM with respect to PCM can be expressed by

where E{Y:} and E { e i } are the variances of Y, and e,, respect,ively.

Minimizing the denominator of equation (18) will improve the gain. Basic DPCM docs offer a bet- t m pcrformancr than PCM. Nevertheless, when non- stationary signals are proc(:sscd, there may be large peak crrors in thc rcconst,ructjed data. To avoid these errors, many adaptivc DPCM techniqucxs were stud- ied (refs. 6 9). In the adaptive DPCM, the step am- plitude of the quantization interval changes to follow the signal evolution. The step value becomes small when the signal is quiescent and large when the signal is more act,ive. However, wit,h adaptive DPCM, the improvement obtained may becornc apparcntf only when large variations of thct sigrial follow quiosc:erit, periods. In t,his case, thc. s t q arnplit,udc~ can assiimr a very low valuc., arid 1 ) c h - c . it has ti1iic- to t ) c m ) r i i c

comparable wit,li t,hc cliffvrcwcx. sigiial, large. orrors can arise.

Linear Transformations The transform coding tcchniqiic iiscs a mathernat,-

4

ical operator to transform the input image data into another domain, where the closely correlated input data are transformed, ideally, into uncorrelated data. The basic block diagram of a transform system is shown in figure 6. To reduce the data throughput, the image is divided into blocks of data for subse- quent processing. Any errors that occur are averaged over a single block, and thus error propagation is re- duced. Until the codpr stage (see fig. 6), the process is completely reversible with no loss of information. The coder provides the data compression by select- ing the various coefficients according to their signif- icance until a preset threshold is met. Beyond this threshold, the remaining coefficients are discarded. This method uses a major property of the transform, by which the input image energy is compacted into a few coefficients. This enables the least important coefficients to be deleted without a large increase in the error of the reconstructed image. Ideally, the thresholding should be adaptive by sending more in- formation when there is higher activity in a block of data (e.g., at an edge of an object). The inverse transformation uses the same information as the for- ward transformation to reconstruct the image. The advantages of this method over other methods are less sensitivity to variations between differing images and superior coding a t the lower bit rates. The main disadvantages are some blurring at the edges and a certain loss of details in the image caused by the loss of high spatial frequencies. In addition, the hardware implementation of these transforms is complex, and the computations are time consuming.

Mat hematically, the transform can be expressed as a summation over the dimensions considered. For an N x M image array f(z, y) , the two-dimensional transformed array P(u , u) is given by

z=1 y=l

where the operator kernel O(z,y : u , v ) represents a weighting constant, which is, in general, a function of both input and output image coordinates.

Similarly, the inverse transformation is given by

N M

Fast algorithms do exist, and the implementation of these algorithms can greatly enhance the throughput of the compression system. Some of the most com- mon operators and their properties are discussed in the following sections.

Karhunen-Loeve Transform In the Karhunen-Loeve transform (K-LT), the

matrix is found by first evaluating the covariance ma- trix of the image, which is of N 2 x N 2 dimensionality for an N x N image. Then the eigenvectors of the covariance matrix are computed and used as the ba- sis for the transformation matrix. These bases are unique for each data block. Because of the tremen- dous amount of computation, the K-LT is only used as a universal reference in the comparison of other transforms.

Discrete Fourier Transform The main advantage of the discrete Fourier trans-

form is the fast Fourier transform (FFT) introduced by Cooley and Tukey in 1965, which reduces the com- putation involved. Typically, the number of complex operations for an N x 1 FFT is N log2 N as compared with N 2 computations required in the conventional approach. The main disadvantage with this trans- form is that complex arithmetic is involved. The per- formance of this method is shown in figure 6 along with that of the other transforms discussed. The discrete Fourier transform is not very efficient at the lower values of block size but does improve as the block size is increased.

Discrete Cosine Transform (DCT) The discrete cosine transform (DCT) provides the

most promising performance of all the techniques be- cause of its near-optimum mean-square-error perfor- mance. (See fig. 7.) The DCT is derived from the Fourier expression by taking the real parts of its ex- ponential form. The two-dimensional forward trans- formation F ( u , v) for an N x N image f(j, I C ) is given by

cos(2j + l ) U T cos(2lc + l ) V T X

2N ( U , U = 0, 1, . . . , N - I) (21)

where G(u ,v) = 1/2 for u = v = 0 and C ( u , v ) = 1 for u,v = 1, 2, . . . , N - 1. The DCT may be implemented by using a double-sized FFT or directly using a fast cosine transform devised recently by Chen et al. (ref. 10). As the block size increases to N 2 16, the basis vectors of the transformation matrix approach the eigenvectors of a first-order Markov process correlation matrix, and hence the performance of the DCT approaches that of the K-LT.

5

Hadamard Transform

The basis vectors of the Hadamard transform are a series of rectangular waveforms taking the values of +1 or -1 only. This simplifies the hardware implementation, since the Hadamard transform dnes not require any multiplication.

The two-dimensional Hadamard transform for an A\r x N f ( ~ , y) array can be written in series form as

where

N - 1

The ternis u,. vZ1 x,, and y, are the binary represen- tation of u, I ) , 2 , and y l respectively, for example

where ui E (0, l}. Thc sunimation in t,he exponcwt, in cqiiat,iori ( 2 2 ) is performed modulo two. The main disadv;tIit,agc of t,his t,rarisforxri is that, it, is not as c.fficicwt. in c w q y cornpact,iori as the previous t.riuisfornis; t,hus, thv coriiprcssiori ratio is dcgradrd.

SOFTWARE EVALUATION OF COM-

Thr performance of each compression algorithm

PRESSION ALGORITHMS I

I

was a s s c x i c d from the following criteria:

1. The scrne activity that gives the best results in trrrris of lowest, mean square error in reconstruction.

2. Cornprcwion cfic%mcy. 3. Irriplcnit.nt,at,iori complexit,y (the suitability for

rml- t irno iInplrnicntat,ion). 4 . Inirnunity t,o channel noise. The comparison

wits t l o ~ i t . according to equation (9), and D(X, Y) was cvaluatcd by iisirig equat,ion (8). The channel was assiinicd to be a binary symmetric channel.

5. Encrgy corripaction property. 6. Additional informat,ion required for linear

t railsformat ion.

Siricv t h c . pc~rforrIiiiricc~ of most of the algorithms is scwitivc t o thc s c ( w ~ corrvlat ion, Gaussian white iioisct ( I t i t ;I w ( w p v i ( w t ( ~ 1 a t i d passcd t,hrough a filter to i t i t r o c l i i w t t i c 1 tlcsirtd corrc.lat,iori t,o thc dat,a. The l i l t c r ('(lllitt i o11 is givcw Ly

where

Y, output of filter

Y,-1 previous output of filter ,

X, input (Gaussian white noise data)

parameter < 1 for stability criterion

Hence

where w is the radian frequcncy arid

where H ( w ) is the Fourier transform of the transfer function of the filter. Then the power spectra of the filter output are given by

I

where S,(w) are the input power spectra. Since the input is white Gaussian, then

2 Sz(w) = 0,

whew o2 is the variance and

Taking the inverse Fourier transform of equation (26) yields

Evaluating equation (27) by contour integration viclds

where R,(n) is the autocovariance of the filter out- put. Notice that Ry(n) is a function of the filter parameter a . In evaluatiIig the compression algo- rit,hms, we increased N from 0.1 to 0.9 in incrrmcrit,s of 0 . 1 , t ,hm from 0.9 to 0.99 in iricrcrricrit,s o f 0.01.

The results of t,hr soft,warc simulation art' siimmit- rizcd in tablc I. The K-LT and t,hr IICT transfornis are h s t in accoIrirnodatirig all t j y p s of sc(~ic1 act,iv- it,y with the best, efficirricy in t,rmns of r r i ( ~ i sqiiarc error and comprwsion ratio. Howwcr, thrir iniplc- rnerltation is complcx. The Hadarnard algorit,lini arid (if bursts are ignorrd, since t,hcy occur infrc:quently)

6

the adaptive DPCM algorithm can handle all types I of scene activity; however, their efficiencies are not I as good as those of the K-LT and the DCT. The pre-

that block. The algorithm-switching aproach offers a considerable improvement over the use of one simple compression algorithm for all types of image data. I

' dictors and interpolators, which are simple to imple- , ment, were best suited for a particular type of scene CONCLUDING REMARKS

activity, as seen in table I. A survey of various compression algorithms and , I an evaluation of their performance and implementa-

SWITCHING DATA tion complexity were presented. It was shown that the more complex algorithms are able to handle all COMPRESSION

Because of the relatively low complexity associ- ated with the implementation of the predictors and interpolators, these algorithms are attractive alterna- tives for implementation in imaging systems. How- ever, the problem associated with them in terms of being able to handle only one type of data activity must be overcome. The author considered combining several predictors and interpolators that could han- dle various types of data activity with an activity- measuring scheme that would select the best algo- rithm to compress the data at hand. In order to implement this system, an analysis of the ZOP, the FOP, and the first-order interpolator (FOI) was per- formed to determine which range of data activity is best handled by each algorithm. The test was per- formed on data that had a wide range of activity. To achieve that activity range, the data were passed through the filter of equation (23), and Q was varied from 0.1 to 0.99. (The symbol Q represents the filter parameter which corresponds to different values of 02, as shown in equation (28), by letting n = 0.) ,4 gain function was defined as a criterion to determine a t which value of Q the switching should occur for each algorithm. This gain function is defined as

CR 62

G = -

where CR is the compression ratio and t2 is the mean square error. Figures 8, 9, and 10 show plots of the gain as a function of the filter parameter Q for values of K = 2, 4, and 6, respectively. It can be seen from these plots that the FOI has the highest gain for values of Q 5 0.91. For Q > 0.91, the ZOP provides the highest gain.

According to the above analysis, the compression system would include two compression algorithms: the ZOP and the FOI. The FOI would be used to compress data for values of 0 5 0.91, then the system would switch to the ZOP for values of Q > 0.91. A general block diagram of that system is shown in figure 11. Notice tha t in such a system, the image is divided into subimages or segments, and a decision is made for every segment. Overhead information is sent at the beginning of each block to inform the ground station of which compressor was used over

- types of data, whereas algorithms which are simple to implement are best suited for a specific type of data activity. An approach has been presented and described which employs a measure of scene activ- ity as a criterion to switch between various simplistic algorithms. This approach offered a considerable im- provement over the use of one simple compression algorithm for all types of image data.

Further evaluation of other algorithms described in the survey (e.g., zero-order predictor with an off- set, first-order predictor with a slope correction, and zero-order interpolator) is necessary to determine their applicability to the system and to optimize per- formance. Furthermore, other scene activity switch- ing mechanisms (e.g., entropy) warrant additional investigation.

NASA Langley Research Center Hampton, VA 23665 April 26, 1985

REFERENCES 1 . Benelli, G.; Cappellini, V.; and Lotti, F.: Data Com-

pression Techniques and Applications. Radio El Electron. Eng., vol. 50, 110. 1-2, Jan. Feb. 1980, pp. 29 5 3 .

2. Kortman, C. M.: Redundancy Reduction-A Practical Method of Data Compression. Proc. IEEE, vol. 55, no. 3, Mar. 1967, pp. 253-263.

3. Andrews, C. A, ; Davies, J . M.; and Schwarz, G. R.: Adaptive Data Compression. Proc. IEEE, vol. 55, no. 3, Mar. 1967, pp. 267-277.

4 . Soame, T. A,: Bandwidth Compression Using Transform Techniques for Image Transmission System. Murconz Rev., vol. 43, no. 219, 1980, pp. 228-240.

5. Habibi, Ali: Comparison of nth-Order DPCM En- coder With Linear Transformations and Block Quan- tization Techniques. IEEE Trans. Commun. Technol., vol. COM-19, no. 6, pt. I , Dec. 1971, pp. 948-956.

6 . Xydeas, C . S.; and Steele, R.: Dynamic Ratio Quantiser. Proc. Inst. Electr. Eng., vol. 125, no. 1 , Jan. 1978,

7. Jayant, Nuggehally S.: Digital Coding of Speech Wave- forms: PCM, DPCM and DM Quantizers. Proc. IEEE, vol. 62, no. 5, May 1974, pp. 611-632.

8. Cummiskey, P.; Jayant, N. S.; and Flangan, J . L.: Adaptive Quantization in Differential PCM Coding of Speech. Bell Syst. Tech. J., vol. 52, no. 7, Sept. 1973,

pp. 25-29.

pp. 1105-1118.

7

~

9. Jayant, N . S.: Adaptive Quantization With a One-Word 10. Chen, Wen-IIsiung; Smith, C . Harrison; and Fral- A Fast Computational Algorithm for the Memory. Bell Syst. Tech. J . , vol. 52, no. 7, Sept. 1973,

pp. 1119 1144. Discrete Cosine Transform. ZEEE Trans. Cornrnun., 1 I

ick, S. C.:

vol. COM-25, no. 9, Sept. 1977, pp. 1004-1009.

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- Optimum l i n e a r p r e d i c t o r

- Z e r o - o r d e r p r e d i c t o r

Z e r o - o r d e r p r e d i c t o r w i t l i o f f s c l t

F i r s t - o r d e r p r e d i c t o r

F i r s t - o r d e r p r e d i c t o r w i t 1 1 s l o p e c o r r e c t i o n

- 1 11 t ii-o r d e r 1) r e d i c tor

I n t e r p o 1 a t i 011

Ze ro-o r d e r i n t e r p o 1 a t o r

F i r s t - o r d e r i n t e r p o 1 ntor

Figure 1. Reversible data compression techniques.

10

.050

.045

.040

u .035 b 0

b aJ ar .030

.025

b KJ 3

VI

.015

.OlO

.005

I- I I I I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 22 24

No. of p o i n t s

Figure 2. Mean square error versus number of points employed in predictor.

0 P r e d i c t e d s a m p l e s

--$ A N o n t r a n s m i t t e d s a m p l e s 0 2 K 0 T r a n s m i t t e d s a m p l e s

Sample p o i n t s

Figure 3. Data sampling and selection: zero-order predictor.

11

0 Predicted samples Transmitted samples

- A Nontransmitted saiiiples

rd

rd LJ

n

Sample points

Figure 4. Data sampling and selrctiori: first-order predictor.

- e e n n Y * Quantizer A v *

Output

Figiirc 5. Block diagram o f diffcrent,ial piilscx codc modulat iori syst.orI1

12

1

M

t

S u b d i v i d e M x M image

' N I-- Image

Forward L i n k f ( x , Y ) s t o r e i n t o N x N * t r a n s f o r m a t i o n * ). + Coder I

b locks t

R e c o n s t r u c t e d I n v e r s e

t r a n s f o r m a t i o n image

Figure 6. Block diagram of transform coding system.

Hadamard

F o u r i e r -\ DCT

I I I I 1 I 8 x 8 16x16 3 2 x 3 2 64x64 1 2 8 x 1 2 ~ 4 x 4

Block size

Figure 7. Mean-square-error performance of different transforms for two-dimensional Markov image source.

13

14

2 1 1 20

19

18

1 7

16

15

14

13

12

11 u C .rl s 10

9

a

7

6

5

4

3

2

1

0

0 Zero-order p r e d i c t o r (ZOP)

0 F i r s t - o r d e r p r e d i c t o r (FOP)

A F i r s t - o r d e r i n t e r p o l a t o r (FOI)

-- . 4 .5 .6 . 7 .8 . 9 . 0 1 . 9 2 . 9 3 .94 . 9 5 . ( I O - 0 7

F i l t e r p a r a m e t e r , \ I

Figure 8. Gain G versus filter parameter a for K = 2.

23

22

21

20

19

18

17

16

15

14

13

12 -

11 -

10 -

9 -

8 -

7 -

6 -

5 -

4 -

3 -

2 -

1 -

0 Zero -o rde r p r e d i c t o r (ZOP) [3 F i r s t - o r d e r p r e d i c t o r (FOP)

A F i r s t - o r d e r i n t e r p o l a t o r (FOI)

. 4 .5 . 6 . 7 . 8 . 9 . 9 1 . 92 . 9 3 . 9 4 . 9 5 . 9 6 . 97

F i l t e r p a r a m e t e r , d

Figure 9. Gain G versus filter parameter a for K = 4.

16

. . .4 .5 . G . 7 .8 . 9 . 9 1 . 9 2 .Y3 .94 . 9 5 .90 . 9 7

F i 1 t c . r par, imcxter, ( Y

Figure 10. Gain G versus filter parameter cr for K = 6.

16

1 I 4

A c t i v i t y d e t e c t o r

* Zero -o rde r * p r e d i c t o r

* I

I

t I

De lay F i r s t - o r d e r * i n t e r p o l a t o r

~

I Figure 11. Block diagram of algorithm-switching system.

17

1. Report No. NASA TP-2458

7. Author(s) Michael M. Hart

2. Government Accession No.

- ___ - ~~ - - ___~__ 3 . Performing Organizntiori Name and Address

NASA Langley Research Center Hamptori, VA 23665

~ _ - 12 Sporisoring Agency Name and Address National Aeronautics and Space Administration Washington, DC 20546

3. Recipient's Catalog No.

5. Report Date

August 1985 6. Performing Organization Code

506-58- 13-02 8. Performing Organization Report No.

L- 15957 ~ -

10. Work Unit No.

~~~

11. ('ontract or Grant No

1.3 Type of Report and Period Covcrcd

Technical Paper ~

14 Sponsoring Agenry Code

15. Supplern(.titary Notes

~~ ~ ~~ . _ ~ ~ ~ _ _ _ _ _ _ _ _ _ _ _ ~ _ _ ~ ~ ~ ~ - ~~

16.. Ahstrnrt

A cornprehensivc study of data cornpression techniques is presented in this paper. A dcscription of these tcchniquc~s is providrd along wit,h a performance evaluation. The complexity of the hardwarc resulting from their irnplcnic,ntat,iori is also addrcsscd. The compression effect on channel distortion and the applicability of thcw algorithms to real-t,inic processing are presented. Also included is a proposed new direction for an adaptive compression tc~chnique for real-time processing.

~~

17 Kt.y Wortih (Sriggrsted by Authors(s)) Reversible compression algorithm Sccm.-act ivity-mrasuring algorithm Switching corriprcission systern

~~ - ~~ ~-

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