Published on

  • Be the first to comment

  • Be the first to like this

No Downloads
Total views
On SlideShare
From Embeds
Number of Embeds
Embeds 0
No embeds

No notes for slide


  1. 1. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-1500 Amputation of Motion Blur From Photograph Using Iterative Approach in Frequency Domain Ashish Jain [1], Prof. Delkeshwar Pandey [2] [1] Department of Computer Science & Engineering, U.P. Tech. University, Lucknow, INDIA [2] Department of Computer Science & Engineering, U.P. Tech. University, Lucknow, INDIAABSTRACT In current years blur removing techniques in approximately described by this equation:the presence of noise have become a great deal ofattention in the field of image processing under image g = PSF*f + N,restoration [7], [1]. There are several approaches toimage denoising, which include linear filters, Where: g the blurred image, h the distortionnonlinear filters and Fourier / Wavelet transforms. operator called Point Spread Function (PSF), f theImage denoising problem is equivalent to that of original true image and N Additive noise, introducedimage restoration when blurs are not included in the during image acquisition, that corrupts thenoisy image .Image restoration is the process of image[8].Image deblurring is an inverse problemrecovering the original image from the degraded which is used to recover an image which has sufferedimage and also understand the image without any from linear degradation. The blurring degradation canartifacts errors. Image restoration methods can be be space-invariant or space-in variant [6]. Imageconsidered as direct techniques when their results are deblurring methods can be divided into two classes:produced in a simple one step fashion. Equivalently, nonblind, in which the blurring operator is knownindirect techniques can be considered as those in and blind, in which the blurring operator is unknown.which restoration results are obtained after a numberof iterations. Iterative techniques such as iterative 1.2 Iterative Image Deblurring TechniquesWiener Filtering [5], [3] can be considered as simple i). Iterative Wiener Filter Deblurring Technique-Theindirect restoration techniques. The problem with Wiener filter isolates lines in a noisy image bysuch methods is that they require knowledge of the finding an optimal tradeoff between inverse filteringblur function that is point -spread function (PSF) and and noise smoothing. It removes the additive noiseestimation of power spectrum which is, usually not and inverts the blurring simultaneously so as toavailable when dealing with image blurring. In this emphasize any lines which are hidden in the image.paper Iterative approach in frequency domain using This filter operates in the Fourier domain [3], makingBlind deconvolution approach, for image restoration the elimination of noise easier as the high and lowis discussed, which is the recovery of a sharp version frequencies are removed from the noise to leave aof a blurred image. sharp image. The Wiener filter in Fourier domain can be expressed as follows:Keywords: Blind Deconvolution, DegradationModel, Frequency Domain, Iterative Approach,Image Restoration, PSF1. INTRODUCTION Blurring is a form of bandwidth reduction of Where Sxx(f1,f2),Snn(f1,f2) are power spectrathe image due to imperfect image formation process. of original image and additive noise and H(f1,f2) isIt can be caused by relative motion between camera blurring filter.and original images. Normally, an image can be An iterative procedure for wiener filter indegraded using low-pass filters and its noise. This spatial domain is listed below:low-pass filter is used to blur/smooth the image using 0. Initialization: Rf (0) =Rg, where Rg is the thecertain functions. In digital image there are 3 autocorrelation matrix of g1. Wiener filtercommon types of Blur effects: Average Blur, construction: B(i+1) =Rf(i)HH[ HR f(i) HH +Rn]−1Gaussian Blur and Motion Blur. Image deblurring 2. Restoration: ˜f (i+1) =B(i+1)gcan performed for better looking image, improved 3. Update: Rf (i+1) =E{˜f(i+1) ˜f (i+1)}identification, PSF calibration, higher resolution and Steps 1 to 3 are repeated until the result converges.better quantitative Analysis. The iterative Wiener filter in discrete Fourier domain is given as:1.1 Deblurring Model pg p2 f i ph 2 𝑝𝑓 i + 1 = A blurred or degraded image can be [𝑝 𝑓 i ph 2 + pn ]2 1496 | P a g e
  2. 2. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-1500 The problem with this method is that they like edges which have been degraded by noise.require knowledge of the blur function that is point Results are evaluated and compared based onspread function (PSF) and estimation of power Evaluation Metrics Mean Square Error [MSE] andspectrum. Signal-to-Noise Ratio [SNR]. Fig.1 shows a blockii). Additive iterative algorithm-The questions are diagram of our method.whether the estimate of the power spectral densityconverges, and whether it converges to the true value. 2.1 Blind Deconvolution approachIt is easy to prove that pf (i) is sure to converge to Blind Deconvolution is a subset of Iterativesome value ˜pf, because pf (i) as a sequence is both Constrained algorithms which produce an estimate ofmonotonic (The derivative of pf (i+1) with respect to h(x) concurrently with f(x) [2], [4]. It does not needpf(i) is greater than 0 and bounded. ˜p f can be derived the PSF h(x) to be measured. Other iterativeas follows: constrained algorithms require h(x) to be measured by acquiring data from sub resolution fluorescent 1 pn 3p 2 n 2p n p f beads.˜pf = [˜pf − ± p2 f − − 2 ph 2 ph 4 ph 2 g(x) = f(x)*h(x)+n(x) Where g(x): measurement, f(x): unknown object, The problem is that ˜pf does not converge to h(x): unknown or poorly known PSF, n(x):pf unless 𝑝 𝑛 is 0. So a correction item is added in contaminationevery iteration, and an additive iterative method wasput forward. 𝑝∗ 𝑓 is used as the update of original 2.2 Blurring Parameterimage instead of pf. It can be derived that The parameters needed for blurring an image are PSF, Blur length, Blur angle and type of𝑝∗ 𝑓 i + 1 = 𝑝∗ 𝑓 i noise. Point Spread Function is a blurring function. 2 ∗ 2 2 ∗ 2 When the intensity of the observed point image is ph 𝑝 𝑓 i [ ph 𝑝 𝑓 i − pn ] + spread over several pixels, this is known as PSF. Blur [𝑝∗ 𝑓 i ph 2 + p ]2 n length is the number of pixels by which the image is degraded. It is number of pixel position is shifted2. PROPOSED ALGORITHM from original position. Blur angle is an angle at(ERADICATOR) FOR AMPUTATION OF which the image is degraded. Available types ofMOTION BLUR noise are Gaussian noise, salt and pepper noise, The method proposed in this paper reduces Poisson noise, Speckle noise which is used forthe noise in the image restored by Iterative approach blurring. In this paper, we are using Gaussian noiseusing the Blind deconvolution with different blur which is also known as white noise. It requires meanparameters like length and blur angle. Proposed and variance as parameters.algorithm is to reconstruct frequency components2.3 Architecture of image degradation andamputation of motion blurFig.1 illustrate that the original image is degraded orblurred using degradation model to produce theblurred image. The blurred image should be an inputto the deblurring algorithm. Various algorithms areavailable for deblurring. In this paper, we are goingto use blind deconvolution algorithm. The result ofthis algorithm produces the deblurring image whichcan be compared with our original image. 1497 | P a g e
  3. 3. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-1500 Input Image Degrade Image By AddingBlurring (Motion Blur) Noise Identify Motions by Estimation of PSF Noise models (probability density functions) (based on length and theta) Impulse Gaussian Poisson Speckle Amputation of motion blur (Without noise) Inverse filtering Amputation of noise by algorithms(in frequency domain) Iterative Wiener Proposed algorithm filtering (Eradicator) Fig.1 Block diagram of image degradation and amputation of motion blur with and without noise 3. PROPOSED ALGORITHM simultaneously. Instead of computing the desired (ERADICATOR) (deblurred) image directly, our method computes a Proposed Algorithm (Eradicator) can be sequence of images, which converges to the desired used effectively when no information of distortion image. Our algorithm is based on the following is known; it restores image and PSF steps: 𝑔 Step 1: First assume that ˜fo use a positive constant Øn = ˜h ⱷ𝑛 image with a constant value equal to average of the 𝑔 Where “ ” denotes pixel by pixel division. blurred image. ⱷ𝑛 Step 2: This step of the iteration performs a Assume, if some pixel values of ⱷ𝑛 = 0 , then we convolution of the current assumption with the get 𝑔/ⱷ𝑛 = 0. PSF: Step 4: At the final step, a new assumption is the ⱷn = h ˜fn product of the current one and the correction factor Step 3: In this step compute a correction factor : based on the result of the last operation and the ˜fn+1 = ˜fn . Øn , original (degraded) image: Where “ . ” is the pixel by pixel multiplication. 1498 | P a g e
  4. 4. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-15004. SAMPLE RESULTS The below images Fig.2 represents the result of proposed algorithm. The sample image after applyingthe proposed algorithm will be as follows. Blured image with Image after 20th Image after 40th Image after 60th Image after 80th Noise iterations iterations iterations iterations Image after 100th Image after 120th Image after 140th Image after 160th Image after 180th iterations iterations iterations iterations iterations Fig.2 Results of the proposed algorithm (Eradicator) for image deblur 7.00E+03 6.00E+03 5.00E+03 4.00E+03 MSE 3.00E+03 IWF 2.00E+03 PA 1.00E+03 0.00E+00 20 40 60 80 100 120 140 160 180 No. of Iterations Fig.3 Graph of MSE for comparison of Iterative wiener filter (IWF) and proposed algorithm (PA) 1499 | P a g e
  5. 5. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-1500 20 15 PSNR 10 IWF 5 pa 0 20 40 60 80 100 120 140 160 180 No. of Iterations Fig.4 Graph of PSNR for comparison of Iterative wiener filter (IWF) and proposed algorithm (PA) No. of Iterations IWF PA deblurring images proposed algorithm (pa) is used and the deblurred images obtained are shown in 20 1.92E+03 986.6066 fig.2.Performance measure values obtained are 40 2.36E+03 1.42E+03 shown in table 1 and table 2. 60 3.66E+03 1.75E+03 5. CONCLUSION 80 3.89E+03 2.01E+03 We have presented a method for Iterative 100 4.56E+03 2.24E+03 blind image deblurring. The method differs from 120 5.23E+03 2.43E+03 most other existing methods by only imposing weak restrictions on the blurring filter, being able 140 6.21E+03 2.61E+03 to recover images which have suffered a wide 160 6.68E+03 2.78E+03 range of degradations. Good estimates of both the 180 6.98E+03 2.93E+03 image and the blurring operator are reached by initially considering the main image edges. The restoration quality of our method was visually andTable 1: MSE Performance measure values quantitatively better than those of the otherfor values for IWF and proposed algorithm algorithms. The advantage of our proposed algorithm (Eradicator) is used to deblur theNo. of Iterations IWF pa degraded image without prior knowledge of PSF20 15.2927 18.1894 and estimation of power spectrum.40 1.08E+01 16.6177 REFERENCES60 8.28E+00 15.7116 [1] A. Khare and U. S. Tiwary, Symmetric80 6.62E+00 15.0977 Daubechies Complex Wavelet Transform100 5.45E+00 14.6376 and Its Application to Denoising and Deblurring,120 4.60E+00 14.2671 WSEASTrans.SignalProcessing, Issue5,140 3.97E+00 13.958 Vol.2, pp.738-745, May2006. [2] D. Kundur and D. Hatziankos, “Blind160 3.48E+00 13.692 image deconvolution, “IEEE sig. process.180 3.09E+00 13.4607 Mag., pp. 43-64, May 1996. [3] Furuya, Eda, and T. Shimamura “ImageTable 2: PSNR Performance measure valuesfor Restoration via Wiener Filtering in thevalues for IWF and proposed algorithm Frequency Domain” wseas transactions on signal processing Issue 2, Volume 5, pp. From Fig.3 and Fig.4 it can conclude that 63-73 February 2009.the proposed algorithm (pa) gives better results as [4] Jain-feng cai, hui ji, Chaoqiang lie,compare to the iterative wiener filter (IWF). So for Zuowei Shen., “blind Motion deblurring 1500 | P a g e
  6. 6. Ashish Jain, Prof. Delkeshwar Pandey / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue4, July-August 2012, pp.1496-1500 using multiple images”. Journal of on image processing, Vol 17, pp.105-116, Computation Physics. Pp. 5057-5071, No. 2 Febreary 2008. 2009. [7] P. Bojarczak and S. Osowski, Denoising[5] Jing Liu, Yan Wu “Image Restoration of Images - A Comparison of Different using Iterative Wiener Filter”, ECE533 Filtering Approaches, WSEAS Trans. Digital Image Processing Course project, Computers, Issue 3, Vol.3,pp.738- December 13, 2003 743,July2004.[6] Michal Sorel and Jan Flusser, Senior [8] Salem Saleh Al-amri et. al. “A Member, IEEE., Space-Variant Comparative Study for Deblured Average Restoration of Images Degraded by Blurred Images “, journal Vol. 02, No. Camera Motion Blur, IEEE Transaction 03, 2010, 731-733... 1501 | P a g e