# Signal quality metric

I have floating point data signal. I apply lossy control to it and I need some kind of metric to determine its quality.

In image processing, there is PSNR (or MSE). I tried to use the same for it, It gives me some kind of result. But is there anything better (or any standard used for this kind or problem) ?

What kind of result ? Are all the floating point data positive ? Anyway, I will list down some of the Quality Metrics and when to use them for which quality of data.

$1$. SNR - If the difference between the original signal and the reconstructed signal can be interpreted as a zero-mean noise process. SNR measurements relating to signal power or energy are less usual, because the result will be biased by the mean signal value. For audio and speech, zero-mean property applies anyway.

$$SNR[dB] = 10 \log\frac{\mathcal{E}(s(\textbf{n})-m_{s})^{2}}{\mathcal{E}(s(\textbf{n})-\tilde s(\textbf{n}))^{2}}$$

Sensitive against phase shifts ( whereas linear phase shift are uncritical for high visual quality ). For example, an observer would hardly find any disturbance in an image shifted by half a pixel using a high quality interpolator while the SNR criterion might indicate a poor reconstruction quality.

$2$. PSNR - For image and video signals which are strictly positive and bounded within a maximum value $A_{max}$. PSNR is widely used for image and motion distortion comparison.

$$PSNR[dB] = 10 \log\Sigma \frac{A_{max}^{2}}{(s(\textbf{n})-\tilde s(\textbf{n}))^{2}}$$

$3$. Weighted SNR - A more general form of SNR which additionally allows individual position-dependent weighting of errors is the weighted SNR.

$$PSNR[dB] = 10 \log\Sigma \frac{r(\textbf{n})w(\textbf{n})}{w(\textbf{n})(s(\textbf{n})-\tilde s(\textbf{n}))^{2}}$$

The weight $w(\textbf{n})$ could be used dependent on local structure (e.g. different weights for edge pixels or textured areas). It has value of one for relevant and zero for irrelevant positions and allows comparison of two images over an arbitrary-shaped area.

Then there is,

$4$ Segmental SNR -

SNR criteria are average measures, which do not take into account fluctuations of quality. Often, a signal with only one highly distorted segment or region will be judged to be of bad quality, while the SNR computed over the entire signal may be extremely high. As possible workaround solutions, additional criteria such as SNR measurements over smaller segments, computation of minima, maxima or other criteria which express fluctuations have been proposed. The segmental SNR, which is the mean or expected value of SNR results from equal-size segments [Jayant, Noll 1984], penalizes fluctuations in SNR.

And also there is Perceptually Weighted Criteria.

• Thanks... my data can be of different range, but mostly are in <0,1> – Martin Perry Sep 13 '13 at 16:55
• Is the expectation operator on the denominator of the first method correct? – Henry Gomersall Jun 20 '14 at 12:41