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An Efficient 2D-WTMM and PNN Approach to Remove Spurious Radar Echoes.

Mohamed Khider, Boualem Haddad.

Université des Sciences et de la Technologie Houari Boumediene USTHB, FEI, LTIR, BP 32, Bab Ezzouar, Algeria.

ABSTRACT

The proposed method aims to reduce the spurious echoes in weather radar images collected at Melbourne radar site, using parameters from 2D-WTMM method based on the continuous wavelet transform, and including the PNN probabilistic neural network for the classification of pixels into two types of echoes : precipitation or parasite. Indeed, we propose the introduction of parameters related to wavelet transform skeletons, these parameters are proportional to the image texture roughness, anisotropy and the distance of separation between non-zero radar echoes cells and give good separation between rain and non-rain echoes. Radar image is first segmented with Voronoi’s cells according to the spatial distribution of Holder exponents. By comparing with a direct method of classification which takes into account only one parameter at a time by using a threshold, it was found that the combination of these three parameters with PNN approach improves the final results in terms of preserving precipitation echoes and elimination of weather radar clutter. Initial results show approximately the removal of 98% of clutter and preservation of 97% of precipitation echoes.

Keywords: Voronoi’s Cells, PNN, Holder Exponent, Singularity Analysis, Continuous Wavelet Transform, 2D-WTMM method.

1. INTRODUCTION The echoes from the Earth's surface can significantly reduce the performance of weather radar. It's then necessary to

remove them to obtain a good estimation of precipitation. One of the powerful techniques in this field is the neural approach for the treatment of spurious echoes. So, Grecu (1999) and Krajewski and al (2001) have introduced Backpropagation algorithm [1, 2]. In this paper, we propose the use of probabilistic neural networks PNN, this one is of particular interest compared with other models, particularly for pattern recognition [3,4].

The main objective of this work is to exploit the performance of multifractal analysis based on continuous wavelet transform and propose a procedure for texture classification by using the neural approach. The database used in this work is obtained from Melbourne radar site, our objective is to eliminate echoes from the Earth's surface, namely the ground echoes observed around the radar. To do this, the 2D-WTMM method (Wavelet Transform Maxima Modulus) is implemented [5,6,7,8]. This approach is applied to estimate the three parameters that feeds the neural network, and are as follows : (1) The Hölder exponents which show a behavior similar to those of ramps for precipitation and similar to Dirac for the fixed echoes around the radar. (2) The anisotropy calculated from the variance of gradients directions of WTMM contours. (3) The third one is proportional to ramification skeletons related to the distance between cells of non-zero radar echoes.

2. SINGULARITY ANALYSIS In image processing, we can relate singularity analysis with fractal. Mandelbrot (1974) introduced the concept of

fractal dimension to describe objects of unusual properties in classical geometry [9]. However, several geophysical processes and systems present a great variability in a wide range of time and space scales. These processes are highly intermittent and characterized by different levels of intensity [10]. They can’t be described statistically by a single exponent, and fractal dimension alone can’t characterize completely these phenomena. It is necessary to introduce the local fractal dimension to describe the fluctuations of the roughness of each point [11]. Indeed, when the fractal dimension changes from one point to another, we say that the fractal object is inhomogeneous or multi fractal [12].

The multifractal analysis measures the irregularity distribution, we express them by the term of singularity exponent or Holder exponent. Also, we can interpret this exponent as a parameter related to the fractal dimension measured locally. This idea was first developed to take into account the inhomogeneity and the irregularity observed in the

International Conference on Graphic and Image Processing (ICGIP 2012), edited by Zeng Zhu, Proc. of SPIE Vol. 8768, 876846 · © 2013 SPIE

CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2011192

Proc. of SPIE Vol. 8768 876846-1

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JImage Z = f(x, y) ; Z represents the gray level.

Multiresolution wavelet analysis with a Gaussian derivativeon the grid of inertial scale -range from o, to cr,.as with Deriche

recursive filters or by FFT2.

Removal of 30.,.0. distance of 2D - WTM from theedges of the image (to reduce edge effect).

Calculating of gradients, an edge pixel W7-'MM is detected if it'smaximum in the direction of gradient.

Chaining edges with windows that test the adjacencyof 2 x 2 pixels, we numbered each edge and detected WTMM pixels.

Pursuit of skeletons across scales, by usingan Euclidean distance filter of WTMMM.

Estimation ofHolder exponent

Anisotropy byvariance of gradient.

Ramificationof WT skelton.

turbulence, with the phenomenon of intermittency [13]. So one of the motivations to use the multifractal analysis is to interpret the local fluctuations of signals, and we can perform this by singularity analysis to evaluate Holder exponent [14,15].

2.1 Holder Exponent : The Holder exponent h(x) also called local Hurst exponent, locally satisfies the following relation :

(1) Mathematicians have introduced them to measure the degree of irregularity in a given point. The introduction of the

Holder exponent in turbulence analysis is due to the work of Frisch and Parisi (1985) [16], undertaken to describe the irregularity of turbulent flow velocity, specifically, the speed increments δv(x0,l) around the position x0, in the inertial sub-range (when l 0+ means the analysis step). These increments are behaving according to the equation [17] :

(2) Where h(x0) is the Holder exponent at position x0. In image processing, the measurement of the local roughness of a surface is given by the Holder exponent h(X0). It’s the basic ingredient in multifractal analysis, the value of h(X0) is proportional to the irregularity of the image in the position X0=(x0,y0).

2.2 Image Analysis by 2D-WTMM Method: With the advent of the wavelet transform, and the development of numerical calculation tools, Mallat and Hwang

(1992) have successfully implement a theory that links between the evolution of local wavelet transform modulus maxima across analysis scales and the Holder exponent [18]. according to the theory of Mallat and Hwang, a wavelet who has nφ vanishing moments, generates WTMM modules given by Mσ(X0) evolving according to the analysis scale following the power law :

(3) (4)

An analysis wavelet with nφ vanishing moments, must satisfy the formula [11] :

(5) This type of wavelet is orthogonal with low order polynomials. Which help the detection of singularity even with the

presence of smooth forms.

We consider the image as a rough surface Z=f(x,y). So, the wavelet transform gives an interpolation of the measure, by smoothing gray levels of the image along the Z axis and then the computation of the gradient.

Most authors who have worked with WTMM method have used Gaussian derivatives [5, 6, 7, and 17] and Lorentz wavelets [19]. The non-standard version of the Gaussian derivatives wavelet are obtained with:

(6) m indicates the order of derivation, in this work we have used the first order Gaussian derivative wavelet and equation (3) and (4) to estimate Holder exponent (fig.1).

Figure 1. the block diagram used to extract the classification parameter.



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3. PNN AND 2D-WTMM METHOD TO ELIMINATE SPURIOUS ECHOES

3.1 The Probabilistic Neural Network Several advantages resulting from the use of probabilistic neural network PNN, such as rapid learning. Also, it

guarantees convergence to a Bayesian classification. Moreover, we can improve the learning phase without difficulty. In addition, the PNN is robust against noise [20]. In the training step of the network, first we start by normalizing the entries in such a way to obtain: , where x1 : gives the anisotropy, x2 : the roughness and x3 : the ramification scale. Each connection between an input (i) and a given model (k) represents a weight wi k=xi k so the normalized input of the k training model. Each model is connected with one output class : precipitation or spurious echoes ak c=1, c : indicates the class (1 or 2) for precipitation or spurious echoes. In the classification step, we calculate for each model the scalar product : zk=wk

tx, wkt indicates the transpose of the

model weight vector k and x represents the standard input parameters. If there is connection between the class c and the k model, then : ack=1, the discrimination function is given by :

(7)

g1 and g2 is the probability of belonging to the first or second class respectively. The parameter σ is equal to √2 × the size of the Gaussian window. In our calculations we have used : σ²=2. Some results of filtering spurious echoes are given by fig.2 and fig.3.

Figure 2. Radar image before and after the removal of spurious echoes.

Figure 3. Radar image before and after the removal of spurious echoes.

3.2 The Method The first part of the proposed method, consists in dividing the image into a multitude of disjoint sets (precipitation or

parasites). We assume that the spurious echoes and precipitation echoes do not overlap. In the step of training the neural network, three attributes from the 2D-WTMM are used, to feed the probabilistic neural network (PNN) (see fig.4).

Figure 4. PNN diagram with three inputs parameters used in classifying Voronoi’s cells into rain or non-rain echoes.



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The proposed method is based on the following steps :

3.2.1 Calculation of Holder exponents The radar image is firstly analyzed by the 2D-WTMM method. then each skeleton of the wavelet transform WT

indicates a position of singularity, it is given by the top of the cone of influence, So we get for each radar image the positions of Holder exponents, indeed, the degree of singularity or Holder exponent is estimated by the linear regression of modulus for each skeleton (see equations 3 and 4).

3.2.2 Radar Image Segmentation Image is segmented with Voronoi’s cells from the spatial positions of Holder exponents, to deduct the subsets of

precipitation and spurious echoes (see fig.5, fig.6).

Figure 5. Example of segmented radar image from

Melbourne site given in dBZ. Figure 6. Holder exponent in color-coded according to

degree of singularity and segmentation by Voronoi’s cells.

The boundaries of Voronoi’s cells between two Holder exponents neighbors are formed by pixels having the same distances of separation between them and the two exponents (they form an axis of symmetry). We define the cells of the radar echoes Sh(x) that depend on the Holder exponent h(x) as the set of pixels of non-zero radar cell belonging to the Voronoi’s cell with the core h(x).

3.2.3 Training of the PNN We must choose a certain number of radar images for training the PNN, with the help of an expert, we indicate the

positions of the radar spurious echoes and the echoes of precipitation, this will allow us to calculate the weight of our network, for this purpose, we must first calculate the three input parameters for each training image, therefore for all Voronoi’s cells of image, the expert's opinion will allow us to classify the sets Sh(x) as rainfall or spurious.

3.2.4 Calculation of Input Parameters For each cell of the radar echoes Sh(x) with h(x) core, we calculate: (a) Holder exponent: it is directly given by h(x)

(see equations 3 and 4). (b) The anisotropy: obtained from the variance of the gradient directions of WTMM contours [5] (at a fine-scale of analysis σ 0+), we take into consideration only the WTMM contours belonging to the Sh(x) cell. (c) The ramification scale of the wavelet transform WT skeleton: it has been found that the ramification of WT skeleton is proportional to the average distance between the non-zero radar cells. Indeed, the clutter rather represent a texture of aggregate which the separation distance between non-zero echoes is greater than those of precipitation echoes which have a more compact texture, in practice to perform this, we have introduced average phase difference between the

direction of gradient for each WT skeleton ( ) ( )∑ −= + −

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3.2.4 Classification We segment firstly radar image with Voronoi’s cells following the positions of singularity exponents, then we

calculate for each cell the three input parameters as described previously (fig.1), and feeds the neural network by the three parameters to estimate the probability of belonging to precipitation echoes or spurious echoes.



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REFERENCES

[1] GrecuM.,“Detection of anomalous propagation echoes in weather radar data using neural networks,”Geos-cience and Remote Sensing, vol.37, no.1, pp.287–296, 1999.

[2] Krajewski Witold F. and Bertrand Vignal, “Evaluation of anomalous propagation echo detection in wsr-88d data : A large sample case study,”J. Atmos,,no.18,pp.807–814, 2001.

[3] Bankert RL, “Cloud classification of avhrr imagery in maritime regions using a probabilistic neural network,” Journal of Applied Meteorology, vol.33, no.8, pp.909–918, 1994.

[4] E-Liang Chen, Pau-Choo Chung, Ching-Liang Chen, Hong-Ming Tsai, and Chein-I Chang, “Anautomatic diagnostic system for ctliver image classification,” Bio-medical Engineering, IEEE Transactionson, vol.46, no.6, pp.783–794, 1998.

[5] J.F. Muzy, E. Bacry, and A. Arneodo, “The multifractal formalism revisited with wavelets,” International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, vol.4, no.2, pp.245–302, 1994.

[6] A.Arneodo, E. Bacry, and J.F. Muzy, “Thethermody-namics of fractals revisited with wavelets,” Physica A-Statistical Mechanics and its Applications, vol.213, pp.232–275, 1995.

[7] A.Arneodo, Y. d’Aubenton Carafa, E. Bacry, P.V. Graves, J.F. Muzy, and C. Thermes, “Wavelet based fractal analysis of dna sequences,” Physica D : Non li-near Phenomena, vol.96, pp.291–320, 1996.

[8] M. Khider, B. Haddad and A. Taleb-Ahmed, “Analyse multi fractale des échos radar par la méthode des Maximums des Modules de la Transformée en ondelettes (MMTO) 2D pour les sites de Bordeaux (France), Sétif (Algérie) : Application à l’élimination des échos parasites”. Revue de Télédétection. vol 8. n 4. P. 271-283, 2009.

[9] B. B. Mandelbrot, “Intermittent turbulence in self-similar cascade : Divergence of high moment sanddi-mension of carrier,” J. Fluid Mech., vol. 62, pp. 331–358, 1974.

[10] Schertzer D. and S. Lovejoy, “Generalized scale in va-riance en turbulent phenomena,” Physico Chemical Hy-drodynamics, vol.6 (5-6), pp. 623–635, 1985.

[11] Stoyan D. and H. Stoyan, Fractals, Random Shapes and Point Fields, John Wiley and Sons, 1994. [12] Peitgen H-O, H. Jurgens, and D.Saupe, Chaos and Fractals New Frontiers of Science, Second Edition, Springer,

2004. [13] Marshak A., A. Davis, R. Cahalan, and W. Wiscombe, “Bounded cascade models as nonstationary multifractals,”

Physical Review E, vol. 49, no.1, pp. 55–69, 1993. [14] Stephane Mallat, AWavelet Tour of Signal Processing The Sparce Way, AP Professional,Third Edition, London,

2009. [15] Pesquet-Popescu B. and J.Levy-Vehel, “Stochastic fractal models for image processing,” IEEE signal processing

magazine, pp. 48–62, 2002. [16] Frisch U. and G. Parisi, “Turbulence and predictability in geophysical fluid and climate dynamics,” IEEE signal

processing magazine, pp.84–88, 1985. [17] J.F. Muzy, E. Bacry, and A. Arneodo, “Multifractal for-malism for fractal signals : The structure-function ap-proach

versus the wavelet-transform modulus-maxima method,” Phys. Rev. E, vol. 47,no. 2,pp. 875–884,Feb 1993. [18] Stephane Mallat and Wen Liang Hwang, “Singularity detection and processing with wavelets,” IEEE Transac-

tionson Information Theory, vol.38, no.2, pp. 617–643, 1992. [19] A.Turiel, “Tracking oceanic currents by singularity ana-lysis of microwave sea surface temperature images,” Re-

mote Sensing of Environment, vol.112, no.5, pp.2246–2260, Earth Observations for Terrestrial Biodiversity and Ecosystems Special Issue, 2008.

[20] Duda R.O. and P.E. Hart, Pattern Classification, Edition Wiley InterScience, 2001. [21] Wolff D.B., D.A. Marks, E. Amitai, D.S. Silber-stein B.,L. Fisher, A. Tokay, J. Wang, and J.L. Pippitt, “Ground

validation for the tropical rainfall measurement mission (TRMM),” J. Atmos. Ocean. Tech,, no.31, pp. 51–55, 2005.



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