JEEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991 35

THE MEASUREMENT OF SIGNAL TO NOISE RATIO OF A TELEVISION BROADCAST PICTURE

C D JANSE VAN RENSBURG

G DE JAGER. MEMBER, IEEE

Department of Electrical and Electronic Engineering University of Cape Town,Rondebosch,7700

A L CUKE SABC ,Auckland Park, Johannesburg

Abstmct - Instruments exist which measure the signal to noise ratio (SNR) in the picture area of a television broadcast picture. l3ese use the deviations of the signal from some average along one or more scan lines in the horizontal direction only. i%is paper presents a method by which an estimate of the SNR can be made using excursions from the mean signal level in both the horizontal and vertical directions. n e method depends on a determination of the two-dimensional spectral components of the noise and can yield non-intrusive measurements during normal broadcasts. In addition the method can be used on pictures with no areas of constant luminance. 'Ihe results obtained are consistent with those produced by an industry standard instrument.

1. INTRODUCTION

Television broadcasting technology has advand to the point where the picture quality is less a function of the equipment and the channel than the care with which these are operated. There is some evidence that the viewing public are more critical of levels of noise in pictures than they were 20 years ago [l]. Nevertheless, picture noise whether due to camera limitations, multi-generation recording in video editing, film grain or low level of the received signal, remains ubiquitous.

However readily the eye may perceive noise on a television picture, the problem with electronically measuring television noise is that of discriminating between picture signal and the noise it bears. Apart from a television camera performance measurement on a uniformly illuminated white field, the broadcasting industry does not even attempt to measure picture noise directly. Instead noise is measured on signal areas that do not carry picture information such as clear

lines in the vertical blanking interval, in the line blanking interval, or, more usually, by stimulating the channel with a constant luminance signal and measuring the noise on that. Not only do these techniques not measure the picture noise directly, but the blanking intervals are often regenerated in the playback and transmission process so that they bear only a tenuous relation to the picture noise. Furthermore, the widely used stimulus response techniques of measuring noise with a constant luminance signal rest on the questionable assumption that channel noise is representative of the picture noise. In fact, with the channel technology of today this is rarely the case.

Before we propose a new method to measure the signal to noise ratio with none of these limitations, we describe some characteristics of a normal television broadcast picture in Part 2. In Part 3 we give the fundamentals underlying the two-dimensional spectrum method which we propose for measuring the noise level in a television picture in a non- intrusive manner. Part 4 presents the algorithm we used, Part 5 compares the results obtained with this method with those yielded by an industry standard instrument and in Part 6 our conclusions are summarised.

2. THE CHARACTERISTICS OF A NORMAL BROADCAST TELEVISION PICTURE.

Although the different pixels in a moving sequence of pictures can vary rapidly and independently, the shape of the two-dimensional power density spectrum (2D PDS) does not change much with time. The shape of the spectrum is more a function of picture attributes and television system constraints than of picture content. System constraints include frequency response (5.5 MHz in the South African

0018-9316/91/0600-0035$01.~ 0 1991 JEEE

36 IEEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991

625 line PAL I television standard) and signal amplitude limitations.

the region of those frequencies where the signal strength is low, i.e. the higher spatial frequencies.

Schreiber [2] asserts that picture attributes that are important to human observers are:

that movement in the picture should be slow enough to be noticeable,

scenes may not change so rapidly as to be disturbing, and

there should not be too much detail and clutter in the image.

An example of the latter is the high spatial frequency information in areas with fine grid lines in a test pattern such as the Philips Test Pattern that is popular in Europe that skimmers with Moire' effects and is fatiguing and unpleasant to look at for any length of time. These constraints result in a spatial frequency spectrum for normal broadcast television pictures with most of the power concentrated at the lower frequency end and usually dropping off monotonically with increasing frequency. The shape of the spectrum is well known and has been described by Biick [3] as:

where SL(g is the PDS of the luminance signal PL is the luminance power BL is the luminance bandwidth f is frequency.

Schreiber extend this to two dimensions:

where S(f,,fy) is the two-dimensional power density spectrum f, and fy are spatial frequencies in two orthogonal directions.

According to these formulae, very low picture power is expected at the high spatial frequencies. This is indeed the caseascanbeseenfromFigure 1

White noise added to such a picture would, however, add a constant power spectral density at all frequencies. This would result in a bigger relative increase in the noise level at the lower picture power levels which occurs at the higher spatial frequencies. The result would be a greater reduction in signal to noise ratio (SNR) than at the lower spatial frequencies. If one were to look for a sensitive indicator of change in signal to noise ratio, one would therefore look in

Figure 1. A 2D PDS of a television picture. The power is plotted on a logarithmic scale. Note the low power level in the comers (high frequencies).

After the addition of white noise, the shape of the 2D PDS changes especially at the high spatial frequencies. An example of this is shown in Figure 2 where white noise was added to the picture used in Figure 1 and the 2D PDS recalculated. Note how much the power levels in the comers (high spatial frequencies) have increased.

Figure 2. A 2D PDS of a picture to which white noise has been added. Note the high power level in the

comers.

IEEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991 37

3. THE FUNDAMENTALS UNDERLYING THE 2-D SPECTRUM METHOD.

3.1 A statistical measure of the noise level in a picture.

From the discussion in Part 2 it should be clear that white noise should be much more easily detectable at high spatial frequencies than at low frequencies. Now, in general, pictures with significant content would not have the same spatial frequency characteristics uniformly spread over all parts of the picture. For instance, it may have foreground and background, or sky and ground or some area on which the attention of the viewer would be concentrated.

If we were to break up or tesselate the television picture into 64 x 64 = 4096 subimages, each an 8 by 8 pixel subimage, we could calculate the 2D PDS for each of these subimages. Next we extract only those power density spectrum points at the spatial frequencies, n l , where noise should be most noticable and average them for each subimage. This enables us to obtain an averaged estimate, P,(nl) in the Bartlett sense, of the power spectral density in the picture. We are left with 4096 estimates, each an average of the PDS at the same fixed spatial frequencies, for a particular subimage. In a number of these subimages the luminance of the picture would vary only very little across the subimage. For such subimages the PDS estimates would represent only noise power and these estimates will all cluster about a mean level determind by the noise level in the picture. The estimates for all the subimages can be displayed in a histogram as shown in Figure 3.

Figure 3. Histogram of 4096 measurements of SNR calculated from the corresponding power spectral density estimates. The smoothed curve (see section 3.2.2) has

been scaled up to make the display clearer.

3.2 Eliminating picture power

Two methods were mnsidered for determining an estimate of the noise level from such a histogram viz. finding the histogram for a difference picture and fioding some sort of average from the histogram.

3.2.1 Difference pictures

It is well known that the movement between two successive frames cannot be too much withour being disturbing and that the result of taking the difference between two successive frames would therefore mainly be small image differences, due to motion, and noise (which changes constantly). It might therefore be thought that a method of reducing the effect of the picture power in the noise estimation would be to calculate the difference picture between two successive frames.

However, when the power spectral density estimates as in Figure 3 for such a difference picture are plotted on a histogram the result obtained is shown in Figure 4.

75.0

56.3

37.5

18.8

36.9 44.0 51.1 0.0

22.7 SNR

Figure 4. An example of a histogram of 2d spectral estimates similar to that in Figure 3 but for a difference picture. Note that the higher spatial frequencies spreads

the histogram to lower SNR values.

Here the histogram does not show the single characteristic gaussian hump at low power spectral densities. The explanation seems to be that the motion registered in the difference picture accentuates the power at high spatial frequencies.

38 EEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991

3.2.2 The peak in the histogram

We need to devise a method for eliminating those sub- images which have been contaminated with picture energy, in order to obtain an averaged estimate, <P,(n,)> in the Bartlett sense, of the power spectral density of the noise in the picture.

The histogram in Figure 3 shows a long tail towards higher energies where picture power contaminates some of the sub- images. The Gaussian peak at lower energies indicates that at these lower energies a Gaussian noise process is responsible for the variations in power spectral density. We need to determine the noise level by some measure of this histogram. The best value is the peak in the histogram. The peak corresponds to the mode in a gaussian probability density function which can be identified with gaussian noise process which is responsible for the variations in power spectral density. This peak therefore gives the level of the noise power. The square root of this value is calculated to yield (JP,(q)).

The peak is, however, a very noisy estimator and some smoothing needs to be done on the histogram. We have tested a good method of fmding the peak which proved to be robust and is also fast. This method is described in Appendix I

3.3 Deriving the SNR from the spectrum

dPn(n1) can be shown (see Appendix 11) to be equal to Vrms. With these parameters it is straightforward to calculate estimates for the signal to noise ratio (SNR). The standard SNR calculation in television broadcasting is, according to Weaver [4]:

SNR = 20 log (0,7/V,,)

In this expression a black to white level excursion of 0,7 volts is taken to correspond to the number 255 in an 8 bit representation of the intensities of pixels in an image. The value of Vrms is the root mean square deviation from a constant luminance level. Then

SNR = 20 log (255/d P,(nl))

An estimation of the SNR of a picture can thus be made with the use of the 2 dimensional spectrum.This method of blind noise estimation we shall call the "two-dimensional spectral noise measuring technique", the 2DSMT.

3.4 Limitations of the method.

The 2-D spectrum method we propose for measuring the SNR in the picture area of a television broadcast picture relies on a frame grabber to acquire a digitised version of the image.

The CCIR Recommendation 601-1 on ENCODING PARAMETERS OF DIGITAL TELEVISION FOR STUDIOS of September 1986 states that a scale of 0 to 255 is to be used. This allows a noise signal of 1 in 255 to be detected. With the eight bits of quantization which this corresponds to, a maximum SNR of 59dB can be achieved [5]. This should be an adequate range for most broadcasting applications.

A further limitation inherent in this method, is that it is based on the spectra of normal pictures. It would therfore not be expected to work for pictures like those transmitted on Teletext. This was tested and it is indeed the case - only when the pictures contain very little writing does the measurement yield meaningful results.

4. THE NOISE MEASURING ALGORITHM FOR AN 8x8 PICTURE ELEMENT

4.1 Determining the 2D spectrum

The pixels in an 8 x 8 sub-picture f(x,y) is represented by dots in the diagram below.

7 . . . . . . . . 6 . . . . . . . . 5 . . . * . . . . 4 . . . . . . * . 3 . . . . . . . 2 . . . . . . . . I . . . . . . . . o + . . . . . . .

0 1 2 3 4 5 6 7 f ( X , Y )

It has a Discrete Fourier Transform (DFT) F(u,v) which can be estimated through the Fast Fourier Transform. Transforming the subpicture through the 2-D Fast Fourier Transform yields

EEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991 39

7 * * . . . . * * 6 * . . . . . . * 5 . . . . . . . . 4 . . . . . . . . 3 . . . . . . . . 2 * . . . . . . . 1 * * . . . . . . o + * * . . . . .

We expect most of the strong components to be concentrated at low spatial frequencies. These are indicated by stars (*) in the representation of F(u,v). A + indicates the origin. For ease of interpretation the 2-D DFT can be rearranged to give another display with the origin at the centre: (This step would be left out in an implementation of the algorithm.)

4 . . . . . . . . 3 . . . . . 0 0 . 2 . . . * . . 0 . 1 . . * * * . o . 0 . * * + * * . .

-1 o . * * * . . . -2 0 . . * . . . . . -3 o o . . . . . .

- 3 - 2 - 1 0 1 2 3 4 F(u,v)

In this display the strong components at low spatial frequencies are now shown as a cluster of stars around the origin. The data shows a 180 degree rotational symmetry. This symmetry arises from the Hermitian nature of the transform of the real values of the input image pixel intensities. The DFT has even symmetric real values and odd symmetric imaginaiy values. To show this symmetry small circles have been added at the corresponding spatial frequencies.

If the power spectral density is to be calculated at each of the sample points in the (u,v) plane, complex conjugate points would yield the same values. Hence the 180 degree rotational symmetry would reduce to quadrantal symmetry as shown here:

4 . . . . . . . . 3 o o . . . o o . 2 o . . * . . o . 1 o . * * * . o . 0 . * * + * * . .

-1 o . * * * . o . -2 o . . * . . o . -3 o o . . . o o .

- 3 - 2 - 1 0 1 2 3 4 F(u,v)

The data was originally sampled at 10 millions samples per second. In this representation the sample points at the spacing marked 4 in one of the dimensions can therefore be taken to represent SMhz, the ones at sample point 1 to represent 1,25 Mhz, at sample point 2, 2.5 Mhz and at sample point 3, 3,75 Mhz. But in terms of the picture itself it is, of course, spatial frequencies in both dimensions which are represented. Since we expect scanning effects at the Nyquist frequency which occurs at sample points 4, the values at u=4 and v=4 are not used for power spectral density estimation. The values at u=O and v=O will contain too much picture energy for noise estimation. Because of the quadrantal symmetry we need to use only the average of the 9 values at U = 1, 2, 3 and v = 1, 2, 3 as shown here. (The practical implementation of the algorithm would, of course, use the corresponding points.)

4 . . . . . . . . 3 . . . . x x x . 2 . . . . x x x . 1 . . . . x x x . 0 . . . + . . . .

-1 . . . . . . . . -2 . . . . . . . . -3 . . . . . . . .

- 3 - 2 - 1 0 1 2 3 4 F(u,v)

If we do this we may include some picture energy, but we know from image spectrum models that, on average, the picture energy should be well down at these frequencies.

Those sub-images which contain noticeable picture energy are characterised by higher power density spectrum estimates and these appear in the tail of the histogram. They are therefore e l i h t e d through the use of the peak (mode) determination on the histogram.

40 IEEE TRANSACTIONS ON BROADCASTING, VOL. 37. NO. 2, JUNE 1991

5. RESULTS

The accuracy of the 2DSMT was tested in several different ways. The technique was used on pictures degraded with known amounts of noise, compared to a calculated noise level on constant luminance areas and lastly compared with measurements from an industry standard instrument.

5.1 Noise addition

The 2DSMT could be tested by degrading pictures with known amounts of noise. The results of the ZDSMT is then compared with the RMS value of noise added to the picture. This is a similar method to that used by Meer et. al. [a] to test their noise measuring algorithm.

A set of pictures with NxN pixels each was degraded by adding different levels of noise to each. The mean s q u h noise value (Ems) is given by the equation

Ems = lN2 E E g2(iJ) (5.1)

Where g(iJ) is the added noise. The SNR is given by

SNR = 20 log (255/ sqrt(Ems)) (5.2)

The SNR in equation (5.2) is then compared with the values obtained from the 2DSMT.

This however is only true if the original image is totally noise free. If it is already degraded, the inherent noise may be significant if the added noise is very small and the 2DSMT will show this. If the amount of noise 0 present in the original image is known, the total amount of noise in the picture. ut , can be calculated from:

(5.3)

when the original image is degraded by uI2 of added noise.

We therefore find the SNR of the degraded images as

SNRt = 20 log (255/ ut).

In this method, uo2 was estimated with the 2DSMT . The method was therefore only tested for certain increments of degradation u12. Seven different pictures each with different uo2, was degraded with 5 levels of u12 and measured by the 2DSMT. The results are shown in Table 5.1.

Pictures1 2 3 4 5 6 7

u1 1.6 39.0 38.7 38.3 40.0 38.7 38.0 44.0 3.6 35.0 35.0 35.1 36.0 35.0 35.0 37.0 5.6 33.0 32.0 32.4 33.0 32.0 32.0 33.0 7.6 30.0 30.0 30.1 30.0 30.0 30.0 31.0 9.6 28.0 28.0 28.3 28.0 28.0 28.0 28.0

Table 5.1 (a) SNRs.

u1 1 2 3 4 5 6 7 1.6 -0.2 0.2 -0.1 0.1 0.2 -0.5 0.2 3.6 -0.5 -0.2 -0.1 0.2 -0.2 -0.2 0.0 5.6 0.6 -0.2 0.2 0.5 -0.2 -0.2 0.0 7.6 -0.6 -0.5 -0.4 -0.7 -0.5 -0.5 0.0 9.6 0.2 0.3 0.6 0.2 0.3 0.3 0.0

Table 5.1 (b) Errors.

Table 5.1 Seven different pictures degraded with 5 different noise levels, u1 used to test the 2DSMT. Table 5.1 (a) consists of the 2DSMT SNR estimations where the RMS noise levels indicative the level of noise used to degrade the images. Table 5.1 (b) shows the difference between the expected SNR's for every image and those calculated by the 2DSMT.

5.2 Area of interest

If a channel is stimulated with a conse t luminance signal a noise free picture should show no deviations from the mean level of the picture. By measuring the root mean square (rms) value of the fluctuations of the output signal over and area of interest (the A01 method), M estimate of the noise can be determined. It is possible to measure the noise on a constant luminance area of a picture such as those found in cartoons and graphics. Pictures of natural scenes, that are generated by a camera, do not usually have constant luminance areas. Therefore this method cannot be used on pictures of natural scenes.

A comparison of the results of the A01 and 2DSMT on 5 undegraded cartoons, captured off the air, is compared in Table 5.2. As can be seen the errors are all less than 1dB.

The result for the 1UminanaCe bar is 5- and 55.5dB. At this level the influence of the quantization noise, mentioned in 3.4, will start to manifest itself.

The results in Table 5.1 were obtained when 7 different pictures, consisting of some cartoons and a luminance bar generated in the laboratory, were degraded with known amounts of noise, ul. As can be seen the errors are all less than 1dB.

41 IEEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991

A01 2DSMT

Picture 1 39.1 40.3 2 38.4 38.4 3 37.9 38.9 4 39.6 39.7 5 37.9 38.6

Luminance bar 56 55.5

Table 5.2 A comparison of A01 and 2DSMT results of cartoons captured off the air.

The results of the three measuring techniques can be compared if the picture is a midgrey bar. The results are bibled in 5.3. As may be expected, the A01 measurement yields a smaller SNR because the method assumes that the area of interest has a constant luminance; any small gradient or curvature will contribute to the deviation from the mean and therefore increase the calculated mean noise level and decrease the SNR.

Analogue A01 2DSMT 48.2 47.4 48.6 47.0 45.9 47.2 44.0 44.3 45.0 40.0 40.1 41.2 34.7 35.1 35.6 29.1 29.6 29.9

Table 5.3 A comparison of the results of three measuring techniques with the same input data.

5.3 Comparison of the 2DSMT with an instrument.

The 2DSMT was compared with measurements made with a Rhode and Schwartz UPSFZ noise level measuring instrument. The instrument determines the deviations from the average luminance level in a small square of the television picture and calculates the SNR accordingly. It can therefore be used to determine the SNR on television broadcast pictures provided an area of constant luminance is present in the picture. A comparison of the 2DSMT and the UPFS2 measurements are difficult when these are attempted on the same television pictures. due to timing. The results of such a comparison is shown in Table 5.4 In these measurements the broadcast signal was attenuated in steps of 1OdB. This causes the automatic gain control to compensate by amplifying the front end noise in the receiver to yield a constant signal level at the output. The result is a decrease in the SNR for an increase in attenuation. At low SNR levels both the 2DSMT and the UPSFZ show lOdB decreases in SNR for lOdB increases in attenuation. The mean difference between the two is less than 1dB. The

agreement between the 2DSMT and the measurements obtained by the UpSF2 on test signals is very good, within 1dB.

UPSFZ 2DSMT UPSF2-2DSMT LUMINANCE bar ATTENUATION 0 48.6 47.4 1.2 10 46.5 45.6 0.9 20 37.5 38.0 -0.5 30 27.1 24.6 0.5

MIDGREY bar ATTENU ATION 0 48.4 46.8 1.6 10 45.5 45.5 0.0 20 37.5 37.4 0.1 30 26.0 25.9 0.1

Average of 20 broadcast television pictures with a constant luminance area in it.

40.56 41.36 -0.81

Table 5.4. Comparison of the 2DSMT measurements of SNR with measurements made with the UPSF2 instrument. The attenuation reduces the strength of the incoming signal and causes a decrease in the SNR.

The average of measurements on 20 broadcast pictures shows that the 2DSMT measures a higher SNR than the UPSF2. This would be expected since the UPSF2 assumes an area of constant luminance is present in the picture while the 2DSMT makes no such assumption. If this assumption of constant luminance is not strictly correct, the calculated deviations from the mean will be in error.

PART 6. CONCLUSIONS

The basic problem we faced was the detection of noise on a television picture in a non-intrusive way. Typical television pictures can be modelled by a spectrum with power levels that drop to low levels at high frequencies. If the impairment is due to white noise, noise power levels should be nearly constant at all frequencies. We therefore expect to be able to measure the noise in a detectably impedect television picture at high frequencies where the noise to signal ratio is high.

42 IEEE 'IRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991

The measurements reported here confirm that the two- dimensional power spectrum density method we propose yields results which are consistent with an industry standard instrument. At the same time the measurements are much more representative of the noise in an actual television picture because it determines variations across horizontal television lines as well as along a horizontal line.

Since the quantization noise calculated in part 3 only contributes power at the level of -59 dB it is clear that quantization should not affect the accuracy of the measurement for most television broadcast pictures.

PART 7. ACKNOWLEDGEMENTS

We would like to thank the South African Broadcasting Corporation for supporting this research.

APPENDIX I SMOOTHED HISTOGRAM PEAK DETECTOR

1. power spectral density level i. distribution, Ch(i), for the histogram.

Let the histogram be represented by a count h(i) at Calculate the cumulative

for all i do Ch(i) = h(i) + Ch(i - 1)

2. Find the difference of two values of Ch(i) ten i apart.

for all i do D(i) = Ch(i + 10) - Cb(i)

This calculation yields a running sum of 10 values of h(i),

10 C h(i)

i= 1

3. Find the peak in D(i). This corresponds to the peak in a smoothed version of the histogram where the smoothing was taken as the running average of 10 power spectral density levels.

APPENDIX 11 THE RELATIONSHIP BETWEEN THE ROOT MEAN SQUARE (RMS) VALUE, AND THE POWER DENSITY SPECTRUM (PDS) OF A

WHITE NOISE SIGNAL.

It was assumed that the power density (PD) is equal the mean square (MS) noise value of white noise. The proof of this follows here.

It is known from Schwartz [7] that the zero point of the autocomelation function (r#xx(0)) is equal to the variance (uxz) of a zero mean gaussian white noise signal:

Also for a zero mean gaussian signal is the variance equal to the mean square value (MS), because the mean is zero. Therefore we have:

4,n = MS (11.1)

The autocorrelation can also be written as the inverse fourier transform of power density spectrum (*,(n)):

and 4,(0) is then written as:

Also is it known that the spectrum of zero mean white gaussian noise is equally spread over the frequency range. All @,(n) over all n, is then equal to some constant < P, > , the average power density. Thus we have:

which simplifies to:

+,CO> = <P,>. (11.2)

By combining 11.1 and 11.2 we have a relationship between the average power density and the mean square value:

MS = <P,>,

and then the RMS value is

R M S = d<P,>

8. REFERENCES

[l] Oliphant, A., Taylor, K. J. and Misson, N. T. "The visibility of noise in System I PAL colour television. " Electronics & Communication Engineering Journal, MayIJune 1989 pp 139-148.

IEEE TRANSACTIONS ON BROADCASTING, VOL. 37, NO. 2, JUNE 1991 43

[2] Schreiber, W. F. Fundamentals of Electronic Imaging Systems Springer, New York, 1986

[3] B h k , A. M., Gallois, A. P. and Carpenter, D. C. "Method for the computation of interference and distortion levels in satellite FM-TV systems." IEEE Trans on Broadcasting, vol35. pp 314-320. 1989.

[4] Weaver, L. E. Television video transmission measurements. Marconi Instruments. St Albans, 1977.

[5] Oppenheim, A.V. and Schafer, R.W. "Digital Signal Processing" p413-416 Prentice-Hall. Englewood Cliffs, 1975

[6] Meer, P., Jolion. J.-M. and Rosenfeld, A. '

A fast parallel algorithm for blind estimation of noise variance. IEEE Trans. Pattern Anal. Machine Intell., vol PAMI-12,

end references pp.2 16-223, 1990.

[7] Schwartz. M. and Shaw, L. "Signal Processing; discrete spectral analysis,detection, and estimation." McGraw-Hill, 1975