A practical SNR estimation scheme for remotely sensed optical imagery a
Xinhong WANG*a, Lingli TANGa, Chuanrong LIa, Bo YUANa, Bo ZHUa Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing, 100190, China ABSTRACT
Signal-to-Noise Ratio (SNR) is one of the basic and commonly used statistic parameters to evaluate the imaging quality of optical sensors. A lot of SNR estimation algorithms have been developed in various research fields. However, one intrinsic fact is usually ignored that SNR is not a constant value, but a quantity changing with the incident radiance received by the sensor. So SNR values estimated on different images through commonly used method are not comparable due to their distinct intensity levels between the images. Here we proposed a normalized SNR estimation scheme which can be readily applied to remotely sensed optical images. With this scheme SNR values obtained from different images can be of comparability, thus we can easily evaluate the performance degeneration of the sensor with more sufficient reliability. Keywords: SNR, noise estimation, remote sensing, optical image, imaging quality
1. INTRODUCTION In this paper, the signal is considered to be a quantity measured by an spaceborne or airborne optical sensor. The noise is a quantity describing the random variability of the signal. The ratio of the signal to noise is called the signal to noise ratio (SNR). In order to validate the quality of the payload after launch, to evaluate the quality of observation data, to apply digital filtering to the data, and to analyze the data quantitatively, the signal to noise ratio of the data often needs to be estimated. 1.1 Various SNR estimation algorithms The simplest method for estimating SNR is to find a homogeneous area within the image by inspection and then to compute the mean and the standard deviation of the pixel DN values in the homogeneous area. The ratio of the mean to the standard deviation gives an estimation of the SNR of the image (Fujimoto et al., 1989). Another method, called the geostatistical method, has been developed by Curran and Dungan (1989) for estimating SNR of an image. In this method, a few narrow strips of relatively homogeneous areas are manually selected from and image, and the SNR of the image is estimated from these strips. Based on the observation that many high spatial resolution images contain a large number of small homogeneous areas, Lee and Hoppel (1989) have developed a method for automatic estimation of SNRs of imaging data. In this method, an entire image is divided into small 4 x 4 or 8 x 8 blocks. The mean and variance are calculated for each of the blocks. A scatter plot of the variances versus the squares of the means of all blocks is obtained. A straight line that passes through the maximum number of points in the scatter plot is obtained using the Hough transform. This line determines the noise characteristic of the image. Meer et al. (1990) have developed a parallel algorithm for estimating additive noise from an image. During the estimation, an image is divided into small square blocks for a sequence of block sizes. The variance values for the small blocks are computed. A number of thresholds and rules are defined empirically. The noise of the image is estimated from the variance values of the small imaging blocks using both the thresholds and rules. A method suitable for estimating SNRs of hyperspectral imaging data was presented by Roger and Arnold (1996). In this method, between-band (spectral) and within-band (spatial) correlations are used to decorrelate the image data via linear regression. Each band of the image is divided into small blocks, each of which is independently decorrelated. The decor*
[email protected]; phone 86 10 13671217912 International Symposium on Photoelectronic Detection and Imaging 2009: Advances in Imaging Detectors and Applications, edited by Kun Zhang, Xiang-jun Wang, Guang-jun Zhang, Ke-cong Ai, Proc. of SPIE Vol. 7384, 738434 · © 2009 SPIE CCC code: 0277-786X/09/$18 · doi: 10.1117/12.848049 Proc. of SPIE Vol. 7384 738434-1
relation leaves noise-like residuals whose variance estimates the noise. A homogeneous set of these variances is selected to provide the best estimate of that band’s noise. 1.2 The local standard deviation algorithm Gao (1993) developed a method for unsupervised estimation of the average SNR of an image in which the noise is additive. This method uses the concept of local means and local standard deviations of small imaging blocks and uses a box counting procedure to find the best estimate of the noise standard deviation. Gao’s method will be employed in the scheme to be proposed in section 2. His method will be referred to as the local standard deviation algorithm in this paper. This method mainly consists of three steps: (1) An image is divided into small blocks having 4 x 4, or 5 x 5, …, or 8 x 8 pixels. For each block, the local mean (LM) of the signals for pixels within a block is calculated according to
LM =
1 N
i= N
∑S i =1
(1)
i
where Si is the signal value of the ith pixel in the block and N is the total number of pixels in the block. The local standard deviation (LSD) is calculated according to
⎡ 1 i= N ⎤ LSD = ⎢ ( S i − LM ) 2 ⎥ ∑ ⎣ ( N − 1) i =1 ⎦
1/ 2
(2)
Homogeneous blocks have small LSDs, and these blocks provide information on the noise of the image, while inhomogeneous blocks, such as those containing edges and texture features, have large LSDs. The mean signal of the entire image and the average of LSDs of all blocks are computed, and the minimum and maximum of LSDs of all blocks are also located. (2) Within the minimum and maximum of the LSDs, a number of bins with equal width are set up. The setting up of bins is necessary for numerical computational purposes. The LSDs of all blocks are then grouped into these bins. The number of blocks having LSDs within each bin is counted. The bin having the largest number of blocks corresponds to the mean noise of the image. (3) The SNR of the image is obtained by ratioing the mean signal of the entire image against the mean noise determined in step 2. 1.3 Existing problems However, one intrinsic fact is usually ignored that SNR is not a constant value, but a quantity changing with the incident radiance received by the sensor. So SNR values estimated on different images through commonly used method are not comparable due to their distinct intensity levels between the images.
2. METHODOLOGY Here we proposed a normalized SNR estimation scheme which can be readily applied to remotely sensed optical images. With this scheme SNR values obtained from different images can be of comparability, thus we can easily evaluate the performance degeneration of the sensor with more sufficient reliability. The scheme consists of following five main steps. 2.1 Specify an standard radiance Consider certain common imaging condition (dependent on surface solar irradiance, solar altitude angle, land surface reflectivity, and atmospheric transmittance), then compute the incident radiance observed by the sensor, and refer to it as “standard” radiance. The standard radiance should not be specified too large or too small, and a medium value that can usually be reached is a good choice.
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2.2 Choose homogeneous sub-image blocks Then, we should choose several sub-image blocks carefully from the image. Distribution of pixel values within each block should be relatively uniform, and average values of different blocks may be as disperse as possible. Uniformity in block is to improve the accuracy of SNR estimation for current block, while disperse among blocks is to obtain SNR estimations under different signal magnitude levels. These sub-image blocks need not to be the same size. 2.3 Estimate block SNRs Here, we can use some proper algorithm (e.g. Local Standard Deviation method) to calculate the SNR of each block, and record the mean DN value of each block at the same time. As a result, a (mean DN, block SNR) point set can be obtained naturally. For the requirement of uniformity, usually these sub-image blocks would not be large, so some method like variogram algorithm is not suitable for SNR estimation on these blocks. The local standard deviation method is adopt as the SNR estimating algorithm in this paper. 2.4 Calculate incident radiance According to the calibration parameters of the sensor, we can convert each mean DN value to an incident mean radiance value. As a result, a (mean radiance, block SNR) point set will be ready. The conversion is based on the calibration equation, which form is one of the following two expressions (different satellites may have different forms): DN = Radiance * Gain + Bias
(3)
Radiance = DN * Gain + Bias
(4)
For SPOT satellite data, the former expression is employed. 2.5 Work out the final SNR estimation When the (mean radiance, block SNR) point set is obtained, we can employ an experiential relation to fit the point set, then calculate the normalized SNR result corresponding to the “standard” radiance specified in step 1, by virtue of the coefficient determined experiential relation. In order to relatively finely fit the experiential relation, at least four to six (mean radiance, block SNR) points are recommended, so in step 2 we should find four to six homogeneous sub-image blocks.
3. RESULTS To test the effectivity of the proposed SNR estimation scheme, a SPOT-5 image (2700 column by 2500 row, cropped from an entire SPOT-5 scene) of panchromatic band was used, which is shown in Fig.1 (panoramic viewing). The mean value of the total image is 171.7, and the standard deviation of the total image is 23.2, so the ratio of these two values is 7.39, which means that the image is rather heterogeneous. Even though the local standard deviation method is applied to the total image, the estimated SNR is still no more than 90 (calculated value is 89.86), which is obvious less than the true SNR value. Though the image is far from homogeneous in the total view, some small areas can be found to be rather homogeneous. These small areas are used in the SNR estimation scheme proposed in this paper. As is shown in Fig.1, five sub-image blocks were extracted from the image, and they are all close to be homogeneous areas, in the mean time the mean DN value of each block is different in some extent. The local standard deviation algorithm is used to estimate the SNR of each sub-image block. In addition, the mean DN value of each block is also recorded. Through the calibration equation, the mean DN value can be converted to incident mean radiance.
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block 1 block 2
block 3 block 4 block 5
Fig.1. The SPOT-5 image and five sub-image blocks extracted from the image
In Table 1 some important environment and sensor related parameters are listed. According to the first four parameters we can determine the “standard” radiance, which value is 107.7 W/cm2/sr/m in this test. The last two parameters are needed in the calibration equation, by which we can calculate the incident mean radiance of each block. Table 1. Configuration of environment related parameters and sensor related parameters. Parameter
Value
surface solar irradiance
1000 W/cm2/m
solar altitude angle
70
surface reflectance
0.4
atmospheric transmittance
0.9
sensor gain
1.3884
sensor bias
0.0
The calculated mean DN value, incident mean radiance, and estimated SNR of each block are listed in Table 2.
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Table 2. The mean DN value, incident mean radiance, and estimated SNR of each sub-image block. Block number
Mean DN
Mean radiance
Block SNR
1
178.5
128.6
132.3
2
140.6
101.2
112.9
3
157.1
113.1
117.2
4
127.3
91.7
101.4
5
130.4
94.0
104.3
Now the (mean radiance, block SNR) point set is ready, we can employ an experiential relation (linear relation for example) to fit the point set, then calculate the normalized SNR result corresponding to the “standard” radiance. Fig. 2 shows the (mean radiance, block SNR) point set and the resultant normalized SNR. SNR
115.2
107.7
Radiance_mean
Fig.2. The (mean radiance, block SNR) point set and the eventual SNR estimation.
The final estimated SNR value is 115.2 (i.e., 41.2 dB), which is much better than directly dividing mean DN of the total image by standard deviation of the total image (result SNR = 7.39), or directly applying the local standard deviation algorithm to the total image (result SNR = 89.86).
4. CONCLUSIONS Most of commonly used SNR estimation algorithms consider the total image as computing field, and obtain an SNR value specific to the current image. They may encounter two difficulties: (1) If land surface covers are relatively complicated, they will always underestimate the SNR of the image. (2) The calculated SNR value is only significative to the current image. SNRs extracted from different images can not directly compare to each other. Taking these two problems into account, this paper proposed a new practical SNR estimation scheme for remotely sensed optical imagery. It overcomes the first problem through nearly homogeneous sub-image block selection, and deals with the second problem by way of calculating SNRs of a series of sub-image blocks and interpolating the resultant SNR based on user specified “standard” radiance and some experiential relation model between incident radiance and SNR. This SNR estimation scheme effectively reduces the radiance’s influence on SNR. It is suitable for monitoring imaging quality changes of the in-orbit optical sensors. In this paper, tests on satellite observation images also indicate the effectivity of the proposed SNR estimation scheme.
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