Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation

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GRD Journals- Global Research and Development Journal for Engineering | Volume 2 | Issue 7 | June 2017 ISSN: 2455-5703

Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation Jasdeep Kaur Department of Electronics and Communication Engineering Punjabi University Patiala Er. Bhawna Utreja Department of Electronics and Communication Engineering Punjabi University Patiala

Dr. Charanjit Singh Department of Electronics and Communication Engineering Punjabi University Patiala

Abstract This paper introduces a hyperspectral denoising algorithm hinged on hybrid spatio-spectral total variation. The denoising issue have been hatched as a mixed noise diminution issue. A prevalent noise model has been pondered which reckon for not only Gaussian noise but also sparse noise. The inborn composition of hyperspectral images has been manipulated by using 2-D total variation along the spatial dimension and 1-D total variations along the spectral dimensions. The image denoising issues has been contrived as optimization hitch whose results has been acquired using the split-Bregman approach. The proposed method can minimize a remarkable amount of noise from real noisy hyperspectral images which is demonstrated by observational results. The proffer technique has been compared with prevailing avant-garde approaches. The outcomes reveal an excellence of the proposed method in the form of peak signal-to-noise ratio, structural similarity index and the visual quality. Keywords- Hyperspectral Denoising, Hybrid Spatio-Spectral Total Variation (HSSTV), Optimization, Split-Bregman

I. INTRODUCTION Image denoising is a challenging domain. It is the main issue that occurs in image acquisition process. If an image contains unwanted or some information is lost it is known as noisy image. This undesired information can be in the form of random signals which cause a change in actual intensity value of all pixels [1]. The different type of noise present in image are gaussian noise, salt and pepper noise, random-valued impulse, line strips and shot noise. Hyperspectral imaging (HIS) examines the study of interaction between matter and radiated energy. Images recorded over hundred of electromagnetic spectra varying from 400nm to 2500nm are prevalently known as hyperspectral images [2].These images are beneficial in different aspects such as space research, military and defence, process manufacturing, agriculture, forensics etc. Image denoising is preprocess in many applications [3]. Images are adulterated by noise due to various reasons such as dark current, variation in power supply and nonuniformity of detector response. Hyperspectral denoising is an assorted noise diminution issue consisting of mixture of Gaussian and sparse noise. The noise which corrupts only few pixels in the images but corrupts them heavily is called sparse noise [2]- [4]. The sparse noise involves random valued impulse noise, salt-and-pepper noise, and horizontal and vertical deadlines. In this paper, we intend to diminish mingled Gaussian and sparse noise from hyperspectral images by clearly seeing them in the planned problematic design [5] - [6]. There are various denoising methods [7]- [8] which ponder mixed noise drop from grayscale imageries. We address a representative situation by considering general noise and effort to resolve this problematic for hyperspectral images. A recent low-rank matrix recovery (LRMR)-based denoising approach [5] can diminish mixed noise from hyperspectral images. The low-rank-based model is a world-wide model which, in context of hyperspectral images, exploits spectral correlation, whereas total variation is a local model which exploits spatial correlation within a band. The proposed hybrid spatio-spectral total variation (SSTV) [9]model which is total variation model and accounts for both the spatial and the spectral correlation. The consequential optimization issue has been resolved using a split-Bregman technique [10]. We have compared our technique with prevailing method namely, LRMR [2], wavelet thresholder principle component analysis(PCAW) [11],general synthesis prior(GSP) [12] and SSTV [9].Peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [13]- [14] are used to quantify the denoising results. Experimental outcomes demonstrate that our proposed method is better than prevailing techniques. Section II represents the problem formulation, followed by Section III where we describe the method to solve the proposed formulation. Section IV demonstrates the experimental results, and Section V concludes this paper with some forthcoming directions.

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Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation (GRDJE/ Volume 2 / Issue 7 / 017)

II. PROBLEM FORMULATION Elucidate y = vec(Y) as the vector depiction of any 2-D matrix acquired by the upright hoarding of columns of matrix Y and X = mat(x) as its overturn performance. We manipulate small letter for vectors and capital for matrices.X = [x1, x2, … , xd] is the representation of hyperspectral data cube of size m × n × d where d is spectral band and xi ∈ ℝmn×1 (mn = m × n) is spectral bands attained by upright nexus. The image acquisition model of gaussian and sparse noise can be represented as: Y= X+S+G where X ∈ ℝmn×d =original image Y = noisy image S = sparse noise G = Gaussian noise. This technique was used in LRMR algorithm [15] for hyperspectral denoising. The joint spatio-spectral interrelationship can be utilized using synthesis prior approach. Let Z = D1XD2 is the sparse characterization of image. where D1 and D2 are the 2-D sparsifying transform applies on spatial and spectral coordinates respectively. Using above values the GPS [12]expression for the mixed noise can be written as: min ∥ Z ∥1 + ∥ S ∥1 + λ ∥ Y − DT1 Z DT1 − S ∥2F z,x

In most natural images the pixels are spatially interconnected to its adjacent pixel values. The adjacent bands also show high spectral correlation. This forgoing skills can be used to depict images as piecewise smooth operations which can be done by total -variation regularization. For grayscale image x total variation can be written as: TV(X) =∥ Dh x ∥1 + ∥ Dv x ∥1 where Dh is horizontal and Dv is vertical 2-D finite differencing manipulator. For color images, total variation model used is color total variation (CTV) [16]. For hyperspectral image X with band d,CTV model can be expressed as: d

HTV (X) = ∑ TV (xi ) i=1

Denoising using HTV method is as follows: min ∥ Y − X − S ∥2F + λ ∥ S ∥1 + μ HTV (X) z,s

HTV model of hyperspectral image denoising accounts only for spatial correlation. For both spatial and spectral correlation SSTV model is used which as: SSTV (X) = ∥ Dh × D ∥1 + Dv × D ∥ 1 Where D ∈ ℝb×b is a 1-D finite differencing operator applied on the spectral signature of each pixel such that the discrete gradient at the ith pixel is a i = (DT z)i = zi+1 − zi , where z demonstrates the spectral signature of a pixels and a ∈ ℝb×1 with a b = 0 at the boundary. This model uses both spatial and spectral dimensions of correlation. Denoising using SSTV method can be as below: min ∥ Y − X − S ∥2F + λ ∥ S ∥1 + μ SSTV (X) z,s

Where λ, μ are regularization Parameters. Here G = Y − X − G is depicting Gaussian noise. To decrease the variance of Gaussian noise we are minimizing Frobenius norm of Y − X − S where S is sparse noise. For both spatial and spectral correlation HSSTV model is used, which is combination of both soft and hard thresholding [17]- [18] and can be expressed as: HSSTV (X) = ∥ Dh × D ∥1 + Dv × D ∥1 Denoising using HSSTV method can be expressed as: min ∥ Y − X − S ∥2F + λ ∥ S ∥1 + μ HSSTV (X) z,s

Various studies in hyperspectral denoising have cast-off the total variation technique. Although our research is non-identical from the work in form of hyperspectral denoising. HSSTV Method gives better results at various SNR and impulse noise percentage than SSTV [9]model. No work has been attempted before for hyperspectral images denoising using hybrid thresholding. We are not enlightened of any productive technique which can give us better result of PSNR at various SNR values.

III. PROPOSED ALGORITHM The problem formulation (4)can be written as: 2 min x,s∥ Y − X − S ∥F + λ ∥ S ∥1 + μ ∥ Dh XD ∥1 + μ ∥ Dv XD ∥1 This is a high-dimensional no differentiable optimization problem in X and S. Since the variable X is not separable, we can rewrite it into a constrained formulation min ∥ Y − X − S ∥ 2F + λ ∥ S ∥1 + μ ∥ P ∥1 + μ ∥ Q ∥1 z,s

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Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation (GRDJE/ Volume 2 / Issue 7 / 017)

P = Dh XD Q =Dv XD The previous constrained optimization problem can be written as a un constrained problem using a quadratic penalty function as below: minimize 2 2 2 P,Q,X,SâˆĽ Y − X − S âˆĽF + Îť âˆĽ S âˆĽ1 + Îź âˆĽ P âˆĽ1 + Îź âˆĽ Q âˆĽ1 + v âˆĽ P − Dh XD âˆĽF + v âˆĽ Q − Dv XD âˆĽF Where v is regularization parameter for horizontal and vertical total variation. B1and B2 can be written by using split Bregman [10] as follows: minimize 2 2 2 P,Q,X,SâˆĽ Y − X − S âˆĽ1 + Îť âˆĽ S âˆĽ1 + Îź âˆĽ P âˆĽ1 + Îź âˆĽ Q âˆĽ1 + v âˆĽ P − Dh XD − B1 âˆĽF + v âˆĽ Q − Dv XD − B2 âˆĽF The above equation can be broken down into following sub equations: min 2 L1: P Îź âˆĽ P âˆĽ1 + v âˆĽ P − Dh XD − B1 âˆĽF min 2 L2: Q Îź âˆĽ Q âˆĽ1 + v âˆĽ P − Dv XD − B2 âˆĽF min 2 L3: S Îť âˆĽ S âˆĽ1 +âˆĽ Y − X − S âˆĽF min 2 2 2 L4: X âˆĽ Y − X − S âˆĽF + v âˆĽ P − Dh XD − B1 âˆĽF + v âˆĽ Q − Dv XD − B2 âˆĽF The L1, L2 and L3 are of the form arg min âˆĽ Y − X âˆĽ2F + Îą âˆĽ X âˆĽ1 X This can be solved by using hybrid thresholding [19]- [17] operation sign(f) (|f| − |f|1−β T β ) if |f| ≼ T đ?•? = θThybrid (f) = { } 0 if |f| < T where f = wavelet coefficient T= threshold value β = parameter that controls the thresholding characteristics. Sub equation L4 is least square problem, but variable X is not decoupled. Let ∇h = DT ⊗ Dh ∇v = DT ⊗ Dv We can write the equation L4 as min 2 2 2 X âˆĽ y − x − s âˆĽ2 + v âˆĽ p − ∇h x − b1 âˆĽ2 + v âˆĽ q − ∇v x − b2 âˆĽ2 . By using Kronecker product property: A = BCD can be written as a = (DT ⨂ B)c,where small letters denote the vector form of matrix. The following equation is obtained after differentiating: (I + v∇)x = Îź(y − s) + v∇Th (p − b1 ) + v∇Tv (q − b2 ) With ∇ =∇Th ∇h + ∇Tv ∇v This problem can be solved using Quasi-minimal residual method (QMR) [20]. The B1 and B2 are variables of Bregman which can be revised in every iteration as below: B1k+1 = B1k + Dh XD − P B2k+1 = B1k + Dv XD − Q Subject to

A. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

HSSTV Algorithm input:Y, Îť, Îź, ν, MaxIter output:đ?•? (denoised image). for k = 1 to MaxIter do Îź P k+1 = HybridTh(Dh X k D + B1k , â „ν) Îź Qk+1 = HybridTh(Dv X k D + B2k , â „ν) S k+1 = HybridTh(Y − X k , Îť ) X k+1 = mat(x) B1K+1 = B1k + Dh X K+1 D − P K+1 B2k+1 = B2k + Dv X K+1 D − QK+1 end for return đ?•? = X k+1

IV. EXPERIMENT AND RESULTS The analysis was done on the hyperspectral image of Washington DC mall. The sensors used for the analysis have 1m spatial resolution and band spacing of 10��.The spectral range of image is 400-2500 nm. To perform the experiment, we have taken the patch of WDC image whose size is 256 × 256 × 190. The proposed technique is equated with various other denoising methods: LRMR [2], PCAW [11], GSP [12], HTV [21]and SSTV [9]. The LRMR [2] method is grounded on an LRMR algorithm [4].It reconnoitres the low-rank nature of a hyperspectral

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Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation (GRDJE/ Volume 2 / Issue 7 / 017)

image for denoising. The PCAW [11] tactic is a principle component analysis (PCA)-based method that preserves original high energy PCA components intact and then accomplishes wavelet thresholding on low energy components along both the spatial and the spectral measurement. The GSP [12] method is a general synthesis prior algorithm which also clearly ponders sparse noise in the problematic design. It reconnoitres the sparsity of the hyperspectral data cube along both spatial and spectral measurement. The HTV algorithm is grounded on the band-by-band total variation model which also contemplates sparse noise. The SSTV [9] technique uses the inherent structure of hyperspectral images has been explored by utilizing 2-D total variation along the spatial dimension and 1-D total variation along the spectral dimension. The denoising problematic has been expressed as an optimization problem whose result has been achieved using the split-Bregman method. The various unknown mutable (X, S, P, Q, B1, B2) need for this algorithm are set from zero. The values of the parameters λ=0.1, μ = 0.2 and ν = 0.2 were found empirically. The proposed method (HSSTV) depends on various parameters (λ , μ , υ and β) the algorithm is not very sensitive to the specific values of these parameters and permits abroad range of values. These parameters can be attuned to get the wanted denoising strength; however, we had kept the parameter values constant for all the synthetic as well as real data experiments. The value of parameter λ regulates the denoising strength corresponding to sparse noise, whereas parameters μ and ν provide the trade-off between retaining the original image and smoothness by total-variation regularization, respectively. Table 1: Comparison of PSNR and SSIM Values Obtained by HSSTV algorithms for different values of mixed noise Peak To Signal Noise Ratio (Db)

Noise Gaussian (Snr = 20) Impulse (90%) Gaussian (Snr = 20) Impulse (95%) Gaussian (Snr = 20) Impulse (100%)

Structural Similarity Index

Noisy

Sstv

Hsstv

Noisy

Sstv

Hsstv

4.76

8.86

9.50

0.007

0.065

0.068

4.53

7.65

8.61

0.004

0.029

0.036

4.31

6.51

7.63

0.002

0.008

0.154

Table 2: Peak To Signal Noise Ratio (Db)

Noise Gaussian (Snr = 30) Impulse (90%) Gaussian (Snr = 30) Impulse (95%) Gaussian (Snr = 30) Impulse (100%)

Structural Similarity Index

Noisy

Sstv

Hsstv

Noisy

Sstv

Hsstv

4.79

9.04

9.68

0.008

0.073

0.081

4.54

7.76

8.69

0.004

0.031

0.035

4.31

6.59

7.69

0.001

0.001

0.005

Fig. 1 (a) Fig. 1 (b) Fig. 1 (c) Fig. 1 (d) Fig. 1: Comparison of visual quality of denoising results with synthetic noise in WDC hyperspectral image. (a) Original. (b) Noisy. (c) Denoised Image (SSTV). (d) Denoised Image (HSSTV).

The experiment was conducted with synthetic noise to check the robustness of the proposed method with respect to different noise levels. The denoising results are quantified using PSNR and SSIM. The PSNR between the original image X and the reconstructed image Y was calculated as d

1 max(xi)2 PSNR = ∑ 10 log10 ( ) d MSE (xi, yi) i=1

where MSE (xi, yi)represents the mean square error between bands xi and yi .SSIM considers the hue, contrast, and shape of the restored image and gives a normalized score between zero and one where the maximum value of one represents a perfect match. Table I and II reviews the evaluation of the PSNR (dB) and SSIM values obtained from different experiments. The maximum value of the PSNR and SSIM values for each experiment is bold faced. It can be observed from Table I and II that the proposed HSSTV algorithm have high PSNR and SSIM values when various Gaussian SNR and impulse noise are present in the hyperspectral image.

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Hyperspectral Image Denoising by using Hybrid Thresholding Spatio Spectral Total Variation (GRDJE/ Volume 2 / Issue 7 / 017)

Fig. 1 visually relates the denoising results on band 110 of the WDC image when various noises are present. Fig. 1(a) displays the original band 110 of the WDC image. All bands were corrupted by synthetically added Gaussian noise of SNR = 20 and 95% impulse noise. Bands 60, 110, 111, and 132 were corrupted by four deadlines and line strips. Horizontal deadlines were located at 30, 100, 112, and 220, and vertical deadlines were located at 70, 118, 128, and 220. This mixed noise-corrupted image is shown in Fig. 1(b). SSTV Methods can reduce Gaussian noise and some impulse noise as detected in Fig. 1(c). Visual quality of denoised HSSTV as observed in Fig.1 (d) is better.

V. CONCLUSION In this Paper, we have proposed a mixed noise reduction algorithm based on HSSTV regularization. A universal noise model has been taken which accounts for both Gaussian noise and sparse noise. The inherent structure of hyperspectral image has been investigated by using 2-D total variation along the spatial dimension and 1-D total variation along the spectral dimension. The denoising issue has been expressed as an optimization problem whose results has been derived using the split-Bregman method. Experimental outcomes indicate that the proposed algorithm can decrease a significant amount of noise from real noisy hyperspectral images compared to prevailing techniques.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

X. Liu, S. Bourennane and C. Fossati, "Denoising of hyperspectral images using the PARAFAC model and statistical performance analysis," IEEE Transactions on Geoscience and Remote Sensing, vol. 50, pp. 3717-3724, 2012. H. Zhang, W. He, L. Zhang, H. Shen and Q. Yuan, "Hyperspectral image restoration using low-rank matrix recovery," IEEE Transactions on Geoscience and Remote Sensing, vol. 52, pp. 4729-4743, 2014. H. K. Aggarwal and A. Majumdar, "Compressive hyper-spectral imaging in the presence of real noise," in Geoscience and Remote Sensing Symposium (IGARSS), 2016 IEEE International, 2016. T. Zhou and D. Tao, "Godec: Randomized low-rank & sparse matrix decomposition in noisy case," in International conference on machine learning, 2011. P. Liu, F. Huang, G. Li and Z. Liu, "Remote-sensing image denoising using partial differential equations and auxiliary images as priors," IEEE Geoscience and Remote Sensing Letters, vol. 9, pp. 358-362, 2012. A. Kaur, C. Singh and A. S. Bhandari, "SAR Image Segmentation Based On Hybrid PSOGSA Optimization Algorithm," Int. Journal of Engineering Research and Applications, vol. 4, pp. 5-11, 2014. M. Yan, "Restoration of images corrupted by impulse noise and mixed Gaussian impulse noise using blind inpainting," SIAM Journal on Imaging Sciences, vol. 6, pp. 1227-1245, 2013. J. Liu, X.-C. Tai, H. Huang and Z. Huan, "A weighted dictionary learning model for denoising images corrupted by mixed noise," IEEE transactions on image processing, vol. 22, pp. 1108-1120, 2013. H. K. Aggarwal and A. Majumdar, "Hyperspectral Image Denoising Using Spatio-Spectral Total Variation," IEEE Geoscience and Remote Sensing Letters, vol. 13, pp. 442-446, 2016. T. Goldstein and S. Osher, "The split Bregman method for L1-regularized problems," SIAM journal on imaging sciences, vol. 2, pp. 323-343, 2009. G. Chen and S.-E. Qian, "Denoising of hyperspectral imagery using principal component analysis and wavelet shrinkage," IEEE Transactions on Geoscience and remote sensing, vol. 49, pp. 973-980, 2011. H. K. Aggarwal and A. Majumdar, "Mixed Gaussian and impulse denoising of hyperspectral images," in Geoscience and Remote Sensing Symposium (IGARSS), 2015 IEEE International, 2015. R. Kour and A. S. Sappal, "A Methodical Approach for the Construction of 64-QAM Golay Complementary Sequences Having Low Peak-To-Average Power Ratio," International Journal of Advanced Research in Computer and Communication Engineering, Vols. Vol. 2, Issue 6,, June 2013. Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE transactions on image processing, vol. 13, pp. 600-612, 2004. Z. Zhou, X. Li, J. Wright, E. Candes and Y. Ma, "Stable principal component pursuit," in Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on, 2010. P. Blomgren and T. F. Chan, "Color TV: Total variation methods for restoration of vector-valued images," IEEE transactions on image processing, vol. 7, pp. 304-309, 1998. S. A. Hussain and S. M. Gorashi, "Image denoising based on spatial/wavelet filter using hybrid thresholding function," International Journal of Computer Applications, vol. 42, 2012. H. K. Aggarwal and A. Majumdar, "Hyperspectral unmixing in the presence of mixed noise using joint-sparsity and total variation," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 9, pp. 4257-4266, 2016. M. A. T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Transactions on Image Processing, vol. 12, pp. 906916, 2003. M. A. Saunders, "Solution of sparse rectangular systems using LSQR and CRAIG," BIT Numerical Mathematics, vol. 35, pp. 588-604, 1995. Q. Yuan, L. Zhang and H. Shen, "Hyperspectral image denoising employing a spectral--spatial adaptive total variation model," IEEE Transactions on Geoscience and Remote Sensing, vol. 50, pp. 3660-3677, 2012. Y. Xiao, T. Zeng, J. Yu and M. K. Ng, "Restoration of images corrupted by mixed Gaussian-impulse noise via l 1--l 0 minimization," Pattern Recognition, vol. 44, pp. 1708-1720, 2011. X. Liu, S. Bourennane and C. Fossati, "Nonwhite noise reduction in hyperspectral images," IEEE Geoscience and Remote Sensing Letters, vol. 9, pp. 368372, 2012. D. Cerra, R. Muller and P. Reinartz, "Noise reduction in hyperspectral images through spectral unmixing," IEEE Geoscience and Remote Sensing Letters, vol. 11, pp. 109-113, 2014. J. Xu, W. Wang, J. Gao and W. Chen, "Monochromatic noise removal via sparsity-enabled signal decomposition method," IEEE Geoscience and Remote Sensing Letters, vol. 10, pp. 533-537, 2013. R. Gupta, D. Bansal and C. Singh, "Image Quality Assessment Using Non-Linear MultiMetric Fusion Approach," International Journal of Emerging Technology and Advanced Engineering, vol. 4, pp. 822-826, 2014.

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