Quality Assessment of Restored Satellite Data Based on Signal to Noise Ratio

A practical concept of assessing the quality of restored data based on signal to noise ratio (SNR) is reported. The data come from remote sensing satellite and has undergone restoration process due to atmospheric haze effects. The restoration involves removing haze mean due to haze scattering and haze randomness due to haze spatial variability. The results shows that the SNR of restored data can be computed if the haze mean and haze randomness components are known.

( ) ( ) ( ) ( ) ( ) ( ) where L i ሺVሻ, Ti, Hi, Lo, β ୧ ሺଵሻ and β ୧ ሺଶሻ are the hazy dataset, the signal component, the pure haze component, the radiance scattered by the atmosphere, the signal attenuation factor and the haze weighting in satellite band i, respectively.Hi can be expressed as: Where is the haze mean, which is assumed to be uniform within the image or sub-region of the image, and is a zero-mean random variable corresponding to haze randomness.Hence: So Equation ( 1) can be written as: In order to remove the haze effects [4], [5], we need to remove both the weighted haze mean ( ) ( ) and deal with the signal attenuation factor ( ) ( ) From [8], the effects of ( ) ( ) to data quality are not significant, so we will not consider their removal throughout the analysis.We normally do not have prior knowledge about ( ) ( ) V H β therefore we need to estimate it from the hazy data itself.If the estimate is ( ) ( ) Equation ( 5) becomes:

H
Quality assessment of restored satellite data 2445 where ( ) ( ) ( ) ( ) is the error associated with the difference between the ideal and estimated weighted haze mean.
A common way to measure the accuracy of restored data is to compare its quality with uncorrupted data [12], [13], [14].Visual analysis offers a fast and simple way to do this, but suffers from possible analyst bias.Hence we propose two quantitative approaches to assess the quality of restored data.

Signal to Noise Ratio
One measure of performance for single band data is the signal-to-noise ratio (SNR), which quantifies how severely data have been degraded by noise [9].SNR is defined as the ratio between the squared ratio of signal amplitude and noise amplitude: where and are signal power and amplitude respectively, and similarly for noise.SNR also can be measured on a decibel scale (dB): (8) The expression for SNR and its estimates vary between: (a) original hazy data (with nonzero-mean noise), (b) hazy data after subtracting the haze mean and (c) restored data (after filtering).From Equation (1), the SNR of hazy data with nonzero-mean haze noise can be expressed as: β V are the same for all pixels in the scene.
Note that here we assume ( ) ( )  from the hazy data to be the signal amplitude because the effects of ( ) ( )  to data quality is negligible; this applies for all cases.Due to the discrete properties of the hazy data, the exact values are replaced by their estimates: where m Q and n Q are the numbers of pixels in the rows and columns of the image respectively.Note that such calculation is only possible if the values of i T , H , ( ) ( ) Q and n Q are known apriori (e.g.simulated dataset).The exact SNR of degraded data after subtraction of the weighted haze mean can be expressed as: and can be estimated by: Subsequently, the degraded data undergo spatial filtering.From Equation (5.9), for linear filtering, the exact SNR of restored data can be expressed as: and can be estimated by: For median filtering, the exact SNR can be expressed as: and its estimate by:

The SNR of Restored Data when the Haze Mean is Known Exactly
When the haze mean is known exactly,  and therefore can be eliminated.Hence the SNR after subtraction of the haze mean is: For linear filtering we have: For median filtering we have:

Conclusion
In this paper, we have proposed a general concept of assessing the quality of restored data based on SNR.The SNR of restored data depends very much on the a priori knowledge of the haze mean and haze randomness components.These components increase as visibility decreases and therefore need to be known in order to remove haze and finally to estimate the SNR of restored data.