DE-STRIPING FOR TDICCD REMOTE SENSING IMAGE BASED ON STATISTICAL FEATURES OF HISTOGRAM

Aim to striping noise brought by non-uniform response of remote sensing TDI CCD, a novel de-striping method based on statistical features of image histogram is put forward. By analysing the distribution of histograms,the centroid of histogram is selected to be an eigenvalue representing uniformity of ground objects,histogrammic centroid of whole image and each pixels are calculated first,the differences between them are regard as rough correction coefficients, then in order to avoid the sensitivity caused by single parameter and considering the strong continuity and pertinence of ground objects between two adjacent pixels,correlation coefficient of the histograms is introduces to reflect the similarities between them,fine correction coefficient is obtained by searching around the rough correction coefficient,additionally,in view of the influence of bright cloud on histogram,an automatic cloud detection based on multi-feature including grey level,texture,fractal dimension and edge is used to pre-process image.Two 0-level panchromatic images of SJ-9A satellite with obvious strip noise are processed by proposed method to evaluate the performance, results show that the visual quality of images are improved because the strip noise is entirely removed,we quantitatively analyse the result by calculating the non-uniformity ,which has reached about 1% and is better than histogram matching method.


INTRODUCTION
Stripe noises of TDI-CCD image is the phenomenon of gray value stochastic change along the array when illuminated by the same uniform light source,the essence of this phenomenon is caused by response non-uniformity of sensors during imaging.Stripe noises influence the quality and quantitative application of image products.Removing stripe noise is accomplished by relative radiometric correction.At present, there are two kinds of de-striping methods: the radiometric calibration method and the scene statistic method (Cao Juliang,2004a).The radiometric calibration method makes use of the calibration equipment onboard such as the solar diffuser board or the calibration lamp to achieve relative radiation calibration.Radiometric calibration has high precision and frequency.The scene statistic method includes histogram matching based on a mass of raw images and moment matching method based on scenery each.Histogram matching establish histogram look up table for each pixel by large numbers of images (Guo Jianning,2005a),the requests for statistical images are: random choice covering dynamic range; percent of cloud coverage is less than 20%,all kinds of ground objects must be involved(Pan Zhiqiang,2005a).The precision of histogram matching method is related to human factors.The moment matching method makes use of the conception that distribution of gray level is similar for each pixel, on the assumption that mean and variance radiation of each pixel is equal approximatively,the correction is realized by adjust static mean and variance through mean value compensation method、 Fourier transformation method or correlation method (Li Haichao,2011a).The moment matching method request the consistency of ground objects severely (Liu Zhengjun,2002a).The proposed method for de-striping is based on character of histogram statistics, by contrast with moment matching method, the precision is improved by increasing amount of statistical character ， furthermore ， in order to avoid cloud influence, a spatial preprocessing with cloud detection is introduced,which improves the precision and applicability.

Histogram statistical principle
The gray level is continuous for symmetrical ground objects(Figure 1(a)),so the shape of each pixel and whole pixels is alike if the amount of row is big enough(Figure 1 The correction coefficient i  of pixel i is calculated by:

Modification based on correlation method
The centroid of histogram is influenced greatly by proportion of one or two grey level as the only criterion,based on correlation definition that correlation coefficient is always used to describe the similarity of two vectors,the correlation coefficient reach maximum while they are exactly the same.Suppose 1 ,  i i h h to be histograms of two adjacent pixels,the correlation coefficient of them is calculated as: The modification process for correction is as follow: correlation reach the maximal,it means that histograms of adjacent pixels are coherent,the responding i c,  is as refine correlation,the basic principle is: To the whole image,histogram of pixel one is regard as a first standard,histogram of pixel two matchs with it,then standard changes to histogram of pixel two, histogram of pixel three matchs with it,the rest pixels are processed in the same manner one by one.

Image filtering based on cloud detection
Cloud noises do not have any information of ground objects,but it changes the grey level distribution of real ground objects with large influence on mean、variance and histogram,which is the common question of scene statistic methods(YAN Yu-song,2010a).The histogram distribution of pixel covered by cloud is altered with right shift of histogram(Figure 3).The gray level includes mean 、 variance 、 difference and entropy.
The texture spatial distribution rule of the inner hue.Gray level cooccurrence matrix is establishd by spatial information of relative position.Each element of gray level co-occurrence matrix p is calculated as: Where S is the set of pixel pairs with given spatial linkage in target area R, numerator is the amount whose gray level is m and n,denominator is the total amount of pixel pairs.Text descriptors based on the gray level co-occurrence matrix include angular second moment、contrast、correlation and entropy.The fractal model is a facility to describe complex image with irregular shape.The cloud of remote sensing image has self-similarity,which is irregular as a whole but regular in different scale, satisfying the fractal geometric feature.The 2D image is regard as a surface of 3D space The fractal dimension is: where ) / 1 log( r and ) log( r N are as abscissa and ordinate separately, the slop of fitting line is fractal dimention after linear least squares fitting.By contrast to ground objects such as mountains、cities an so on,the edge of cloud is blur,the change of gradient is slow,and the edge character of different directions are similar.The edge detection of image H based on Sobel: Two features of the edge are calculated as: where The histogram of  is obtained by sum the G :

L=amount of intervals
The maximum、mean of G and the maximum、deviation of Hs describe edge characters.
To summarize,an eigenvector include thirteen values as the criterion.Support Vector Machine(SVM) is adopt to realize automatic classification.SVM transform the low-dimensional nonlinear question into low-dimensional linear question though kernel function,obtaining global optimal solution by virtue of quadratic form.

Processing flow
The processing flow is broken down into three steps: First is automatic cloud detection comprising multi-features extraction and SVM classification; Next,histogrammic centroid of whole image is regard as standard,the other pixels should approach it by differences; Finally, refine correction based on correlation is used to modify correction precision per-pixel.The detail with even ground object comparision is shown(Figure 8).The visual quality of image processing is improved obviously.We select part of river to quantitatively analyse the non-uniformity,the result by proposed method reachs 1.12% for the 0-level image with non-uniformity of 5.4%.The non-uniformity of this image processed by histogram matching method is 1.28%.By contrast,we can say the proposed method has better result.
Figure 1 (a) one 0-level panchromatic images of SJ-9A satellite,(b) histogram of whole image,(c)histogram of pixel 2000,(d)histogram of pixel 3800 Figure 2 (a)result of correlation search,(b) comparision of histogram before(left) and after refine correction(right) Figure 3 (a) 0-level panchromatic images of SJ-9A satellite(2014-10-14,Laos),(b)histogram of pixel 2000,(c) histogram of pixel 7000 fractal dimention is obtain by by different scale analysis.The image with size of M M  is divided into several image block with size of r r  ,each image block is turn into box with size of the total amount of gray level.The box is numbered from 1 to k, suppose the maximum and minimum of image block amount covering the whole image: Figure 4 processing flow chat

Figure 6
Figure 6 cloud detection Figure 7 (a)image with proposed method applied,(b) image with moment matching method applied