Removal of Large-Scale Stripes Via Unidirectional Multiscale Decomposition

Round 1

Reviewer 1 Report

This article proposes a destriping method called DUMD based on unidirectional multiscale decomposition for image pre-processing. It is well written and clearly states the method and experiments results. I suggest it's publication given that the following minor revision can be made.

Figure 2: A clearer figure is preferred.

Figure 6-8: What are the titles of axes?

Line 288: Radiation corrected should be changed to radiometric corrected.

Author Response

Dear Reviewer 1:

Thanks for your review and valuable suggestions. My modify situation and reply are as follows:

 

Question: Figure 2: A clearer figure is preferred.

Answer: The original picture of Figure 2 is replaced by a clearer version.

 

Question: Figure 6-8: What are the titles of axes?

Answer: In Figure 6-8, the x-axis represents the line number, the y-axis represents the mean value. The titles of axes are added to Figure 6-8.

 

Question: Line 288: Radiation corrected should be changed to radiometric corrected.

Answer: This error has been modified.

Reviewer 2 Report

I have found this paper quite clear and well written.
The Authors have provided a well-structured exposition of their material.
The content is described with a certain amount of details to understand the topic, techniques and results.
The analysis provided and corresponding results are appropriate to the text and its content.
The list of references to the literature related to the field is also appropriate.

Overall, the content is quite original.
But the argument and analysis needs improvement as they lack details and developments in some places.

1) Please specify the hypothesis on both k_j and b_j in (1)

2) A specific value of the treshold delta is set for deciding the presence of small-scale strip noise.
Is this value sufficiently universal or should it be adapted according to the level of small-scale strip noise?

3) What is the confidence in the obtained value of the adjustement coefficient? How to characterize it?

4) In practice, how to tune the value of parameter eta (threshold introduced to reduce the algorithm error)?

More generally and following the first four remarks, what is the degree of expertise required to apply the method in order to obtain appropriate results?
Can the proposed processing scheme be run without interaction of a user?

5) In table 1, detail the spectral bands and their bandwidths for each sensor.

6) An experiment on real data with real stripes (I mean not degraded synthetically) is missing.

Comparison with higher level destriping methods could be discussed as well.

Typo(s):
it set to the median of

Author Response

Dear Reviewer 2:

Thanks for your review and valuable suggestions. My modify situation and reply are as follows:

 

Question: Please specify the hypothesis on both k_j and b_j in (1)

Answer: The explanations of k_j and b_j are modified as:

“k_j is the multiple stripe noise of the jth detector, b_j is the additive stripe noise of the jth detector”

 

Question: A specific value of the treshold delta is set for deciding the presence of small-scale strip noise. Is this value sufficiently universal or should it be adapted according to the level of small-scale strip noise?

Answer: In equation (7), the threshold is set as 1 to remove small-scale stripe noise. Digital images are displayed in DN values. If the image is not stretched, the stripe noise less than 1 is substantially unrecognizable by the human eyes, but the stripe noise bigger than 1 can be directly recognized. Based on the consideration, we set the threshold to 1, which is a generic value.

 

Question: What is the confidence in the obtained value of the adjustement coefficient? How to characterize it?

Answer: There is currently no quantifiable confidence of the adjustment coefficient. In future research work, Kalman filter can be considered to quantify it.

 

Question: In practice, how to tune the value of parameter eta (threshold introduced to reduce the algorithm error)?

Answer: Eta of equation (11) is the only parameter that needs to be manually selected in this algorithm. It is currently set to the median (50%). This is an experience-based parameter used to balance the filtering effect and color cast. In the experiment, I found that 50% is applicable to most data, but some data needs to be manually adjusted according to the effect. There is currently no adaptive method to adjust this parameter.

 

Question: More generally and following the first four remarks, what is the degree of expertise required to apply the method in order to obtain appropriate results? Can the proposed processing scheme be run without interaction of a user?

Answer: Only eta is needs to be manually selected, and other parameters can be fixed. Using this algorithm only needs to know how the value of eta affects the result and adjust eta according to the result. After the article is published, I will upload the MATLAB code.

 

Question: In table 1, detail the spectral bands and their bandwidths for each sensor.

Answer: The detail information are added in table 1 as suggested.

 

Question: An experiment on real data with real stripes (I mean not degraded synthetically) is missing. Comparison with higher level destriping methods could be discussed as well.

Answer: There are two reasons for missing of real stripe images:

1) The real stripe images are rare to obtain. At present, I only have one real stripe image. The stripe and destripe images are as follow figure. 2) If real stripe image is used as input data, there will be no reference image for quantitative evaluation.

Variation-based methods are high-level algorithms. Among the three compared methods used in this manuscript, SAUTV belongs to this class.

(a) Real stripe image	(b) Destripe image

Figure. Real stripe image and its destripe effect

Reviewer 3 Report

The paper presents a method for removing large-scale stripes in images acquired by high resolution imager for Earth observation. The proposed method is an improvement of the of column-by-column non-uniformity correction method, for this reason the novelty of the paper is medium.

The introduction is too general, with few references. The proposed method and the obtained results are not clearly presented.  In particular:

 

In the introduction authors often use generic sentences. For example, the authors should better define the causes of the major factors of stripes by linking the causes of stripes and the method of acquisition.

 

The description of the method suffers of the same problem pointed out for the introduction. For example:

In the “Analysis of stripe noise” at page 3 lines 103-105 the authors affirm …”Additive noise is the secondary component of stripes; its main source is dark current whose intensity is relatively small (generally with DN values between 1 and 2). The error term caused by ignoring additive noise is relatively small”…… These sentences generally refer to a relatively small noise. Authors must quantify how small it is. The statement: “DN values between 1 and 2” is not enough and cannot be true. Author must clearly define for which sensor and in which operative condition dark current exhibits DN values equal to 1 or 2. In the “Scale characteristics of stripes” at page 3 lines 111-115 the authors affirm: “For a single channel (tap), the sources of the stripes include photo shot noise, reset noise, dark current, fixed pattern noise, and quantization noise, et al [15]~[16]. The stripes in the channel appear as thin lines in the image and appear as small-scale impulse noise on the corresponding CMV, as shown in Figure 1(a). The optical sensor in satellite is generally formed by multiple CCDs, and each CCD is formed by multiple taps, causing a linear camera to have multiple channels.” The sentences are too general and confuse. The authors should mention some example of optical sensor formed by multiple CCDs. Figure 1: Axis labels and units are missing. Data in the graphs are related to which sensor? the “Overall description of DUMD” must be improved, some equations are not clear (for example equation 6 and 7). At page 5 line 146: Why δ is equal to 1? Authors must explain the reason of the choice. Experimental data: The authors affirm: ” This paper selects 6 multispectral images as experimental data. They are imaged by different satellites and include a variety of features, such as cities, mountains, waters, and clouds. The experimental data are sufficiently highly representative to evaluate the performances and characteristics of the proposed method and the comparison methods. The specific conditions of the experimental data are shown in Table 1.” Authors must introduce a detailed description of data used for the experiment. The sensors used for the reported acquisitions must be described (i.e name of the sensor, instrument type, spectral band, resolution …). The simulation procedure must be explained and more details must be given.

 

The authors affirm … “The original images have been radiation corrected during the data production and used as reference images. The striped images are obtained by adding random stripes with different scales to the original images, and are used as the input data for testing ….”. Acquired images cannot be fully radiometrically corrected, because the radiometric calibration, even if very accurate, is never perfect. For this reason, when the authors add random stripes, they mix the simulated stripe noise to the small one of the acquired image. The method described in the paper for simulating reference image and striped image is not correct.

 

The authors affirm … “ And this evaluation can be done because of the existence of reference images”. Acquired images cannot be fully radiometrically corrected, such images cannot be used as reference image and they cannot be used for comparing the model performance.

 

Figure 6-8. Axis labels and units are missing

Author Response

Dear Reviewer 3:

Thanks for your review and valuable suggestions. My modify situation and reply are as follows:

 

Question: The introduction is too general, with few references. The proposed method and the obtained results are not clearly presented.  In particular。

Answer: The introduction is modified as required. Some additional references and specific experimental results are added in introduction.

 

Question: In the introduction authors often use generic sentences. For example, the authors should better define the causes of the major factors of stripes by linking the causes of stripes and the method of acquisition.

Answer: An example is added in the introduction, as follows:

“For example, GF-1B is equipped with two multispectral cameras, each camera has three CCDs, and each CCD has two taps. That is, a GF-1B multispectral image forms 12 channels. If the nonuniformity is not effectively corrected, the large-scale stripes will be existed between these channels, and the small-scale stripes will be existed in these channels.”

 

Question: In the “Analysis of stripe noise” at page 3 lines 103-105 the authors affirm …”Additive noise is the secondary component of stripes; its main source is dark current whose intensity is relatively small (generally with DN values between 1 and 2). The error term caused by ignoring additive noise is relatively small”…… These sentences generally refer to a relatively small noise. Authors must quantify how small it is. The statement: “DN values between 1 and 2”is not enough and cannot be true. Author must clearly define for which sensor and in which operative condition dark current exhibits DN values equal to 1 or 2.

Answer: The description “generally with DN values between 1 and 2” is not rigorous enough and has been removed. Section 2.1 is mainly to translate the striping problem into a CMV estimation problem. Currently, I cannot give a quantified value of the additive stripe noise. The intensity of multiplicative stripe noise is much greater than additive stripe noise, which is a qualitative conclusion based on experience.

 

Question: In the “Scale characteristics of stripes” at page 3 lines 111-115 the authors affirm: “For a single channel (tap), the sources of the stripes include photo shot noise, reset noise, dark current, fixed pattern noise, and quantization noise, et al [15]~[16]. The stripes in the channel appear as thin lines in the image and appear as small-scale impulse noise on the corresponding CMV, as shown in Figure 1(a). The optical sensor in satellite is generally formed by multiple CCDs, and each CCD is formed by multiple taps, causing a linear camera to have multiple channels.” The sentences are too general and confuse. The authors should mention some example of optical sensor formed by multiple CCDs.

Answer: This part has been modified and two practical examples have been added to illustrate the difference between small-scale stripes and large-scale stripes.

 

Question: The “Overall description of DUMD” must be improved, some equations are not clear (for example equation 6 and 7).

Answer: This section has been modified as suggestion.

 

Question: At page 5 line 146: Why δ is equal to 1?

Answer: In equation (7), the threshold δ is set as 1 to remove small-scale stripe noise. Digital images are displayed in DN values. If the image is not stretched, the stripe noise less than 1 is substantially unrecognizable by the human eyes, but the stripe noise bigger than 1 can be directly recognized. Based on the consideration, we set the threshold to 1, which is a generic value.

 

Question: Authors must explain the reason of the choice. Experimental data: The authors affirm: ” This paper selects 6 multispectral images as experimental data. They are imaged by different satellites and include a variety of features, such as cities, mountains, waters, and clouds. The experimental data are sufficiently highly representative to evaluate the performances and characteristics of the proposed method and the comparison methods. The specific conditions of the experimental data are shown in Table 1.”

Answer: 1) The data from different sensors is used to prove that the algorithm is consistent for different sensors; 2) Since the effects of many algorithms depend on the terrain, the data with different terrains is used to prove that PSD is robust to terrain.

 

Question: Authors must introduce a detailed description of data used for the experiment. The sensors used for the reported acquisitions must be described (i.e name of the sensor, instrument type, spectral band, resolution …). The simulation procedure must be explained and more details must be given.

Answer: The specific information of sensors have been added in Table 1. The simulation procedure are three function:

“

function AddStripeNoise(inPath, outPath)

 

pic = double(imread(inPath));

maxValue = mean(pic(:));

[~,n,band] = size(pic);

for k=1:band;

    detectorNum = n;

    routeNum = 16;

    [kLine, bLine] = genStripeNoise(detectorNum, routeNum);

    for j=1:n;

        pic(:,j,k) = pic(:,j,k)*kLine(j)+bLine(j);

    end;

end;

 

bits = 1;

while (bits<=16)

    if (2^bits>maxValue)

        grayRange = 2^(bits+1)-1;

        break;

    else

        bits = bits+1;

    end;

end;

pic(pic>grayRange) = grayRange;

pic(pic<0) = 0;

imwrite(uint16(pic), outPath);

 

function [kLine, bLine] = genStripeNoise(detectorNum, routeNum)

N = detectorNum;

kLine1 = 0.04*randn(1,routeNum)+1;

kLine1 = resample(kLine1, N);

kLine2 = 0.01*randn(1,N)+1;

tmpKLine3 = 0.4*randn(1,N)+1;

kLine3 = ones(1,N);

for i=100

    loc = unidrnd(N);

    kLine3(loc) = tmpKLine3(loc);

end;

bLine1 = randn(1,routeNum);

bLine1 = resample(bLine1, N);

bLine2 = randn(1,N);

kLine = kLine1.*kLine2.*kLine3;

bLine = bLine1+bLine2;

 

function rsLine = resample(line, tarN)

[~,initN] = size(line);

rsLine = zeros(1, tarN);

coeff = tarN/(initN-1);

for j=1:tarN;

    loc_j = fix(j/coeff)+1;

    rsLine(j) = line(loc_j);

end;

”

 

Question: The authors affirm … “The original images have been radiation corrected during the data production and used as reference images. The striped images are obtained by adding random stripes with different scales to the original images, and are used as the input data for testing ….”. Acquired images cannot be fully radiometrically corrected, because the radiometric calibration, even if very accurate, is never perfect. For this reason, when the authors add random stripes, they mix the simulated stripe noise to the small one of the acquired image. The method described in the paper for simulating reference image and striped image is not correct。The authors affirm … “ And this evaluation can be done because of the existence of reference images”. Acquired images cannot be fully radiometrically corrected, such images cannot be used as reference image and they cannot be used for comparing the model performance.

Answer: Radiometric-corrected data does have the potential for residual stripes. I have seen a lot of this situation, which is why I want to develop this algorithm. But the experimental data have been selected and their quality is good. There is no obvious stripes in original images. Moreover, compared to the added random stripes, the intensities of the residual stripes are very small. Therefore, these radiometric-corrected images can be treated as reference images.

 

Question: Figure 6-8. Axis labels and units are missing

Answer: In Figure 6-8, the x-axis represents the line number, the y-axis represents the mean value. The titles of axes are added to Figure 6-8.

Round 2

Reviewer 3 Report

Authors have answered to all the questions, with the exception of the one related to simulation, the most critical.

This question is the most critical because the proposed method of simulation is, in my opinion, not correct and therefore the discussion on results is weak. The authors reply that: “ …  compared to the added random stripes, the intensities of the residual stripes are very small”. Even if very small, stripes are still present, for this reason such image cannot be considered as reference image.

Author Response

Dear reviewer：

Thanks for your review, the follows are my illustrations about simulation.

 

The multi-CCD push-broom satellite transmits the level-0 data. The level-1 data are obtained by relative radiometric correction, sensor correction and other processions. In the production of standard images, stripe noise is removed in the step of relative radiometric correction.

If the characteristics and intensity of the stripe noise are stable (i.e. the stripe noise is systematic), stripes can be eliminated completely by relative radiometric calibration. I am responsible for the relative radiometric calibration of more than ten satellites. The main problem encountered was that the characteristics and intensity of the stripe noise are inconsistent in a few cases influenced by some unknown factors (i.e. the stripe noise is not systematic). I designed this algorithm to eliminate stripes in these cases.

In general de-noising articles, the noisy images are obtained by adding random noise to original images. And the original images are treated as reference images for evaluation. In these articles, original images actually have noise (no perfect no-noise images), but they can be regarded as reference images in the effect evaluation because the noise level is very low.

The experimental data of this paper are standard productions, and the relative radiometric accuracy is good enough. The following images (please see attachment) show the original image of GF1B, and there is no stripes. Based on above reasons, the original images can be treated as reference images.

 

Original image of GF1B

 

 

 

 

Author Response File: Author Response.pdf