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Frequency-Domain-Based Switching Median Lter for the Restoration of Images Corrupted with High-Density Periodic Noise

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Frequency-Domain-Based Switching Median Lter for the Restoration of Images Corrupted with High-Density Periodic Noise Scientia Iranica D (2017) 24(3), 1312{1324 Sharif University of Technology Scientia Iranica Transactions D: Computer Science & Engineering and Electrical Engineering www.scientiairanica.com Frequency-domain-based switching median lter for the restoration of images corrupted with high-density periodic noise J. Varghese College of Computer Science, King Khalid University, Abha, P.O. No: 394, Zip: 61411, Kingdom of Saudi Arabia. Received 8 April 2015; received in revised form 1 February 2016; accepted 30 May 2016 KEYWORDS Abstract. The paper proposes an adaptive Frequency-Domain-based Switching Median Filter (FDSMF) for the restoration of images corrupted by periodic noise. The proposed Periodic noise; algorithm incorporates region-growing technique to e ectively identify noisy peak areas of Quasi-periodic noise; the Fourier transformed image in a binary noise map image. The restoration phase of the Median lter; algorithm replaces the corrupted frequencies with the median of uncorrupted frequencies Adaptive lter; by recursive median lter. Experimental results from di erent naturally and arti cially Image restoration; corrupted images at various noise levels/types reveal that the performance of the proposed Non-linear lter. algorithm in restoring images corrupted by periodic noise is better than other competing algorithms in terms of subjective and objective metrics. © 2017 Sharif University of Technology. All rights reserved. 1. Introduction by periodic noise due to the errors in Complemen- tary Metal Oxide Semi-conductor Active Pixel Sensor Noise reduction is an important task in image process- (CMOS APS) and Charged-Coupled-Device (CCD)- ing to restore images for facilitating pattern recognition based sensors [6,7]. Periodic noise also a ects digital and computer vision applications [1]. Among all images when images are received by TV receivers with types of noise reduction algorithms, periodic noise poor signal/transmission strength [8]. Many spatial do- reduction algorithms are of extreme importance since main methods are proposed in the literature to restore these noises are very common in all types of imaging periodic noise corrupted images by directly applying processes [1]. Periodic noise corrupts digital images ltering operations to the input corrupted images, by superimposing repetitive patterns in the true signal including mean, median [1-3], and soft morphological content of the image [2]. These noises occur during lters [9-13]; but, the performance of these lters is the image acquisition phase when images are sensed in limited since it is very dicult to di erentiate between the presence of thermal/electrical/electro-mechanical noise and uncorrupted frequencies in spatial domain. interferences. Moreover, they are very common in Frequency domain techniques carry out lter- aerial images captured by sensors tted in vibrating ing operation in the transformed domain by using environments like helicopters, aircrafts, satellites, and Discrete Fourier Transform (DFT), Discrete Wavelet moving cameras [3-5]. Medical imaging processes Transform (DWT), Discrete Cosine Transform (DCT), such as X-ray, Computer Tomography (CT) scan, and etc., and inverse transforms provide the restored image Magnetic Resonance Imaging (MRI) are also a ected in the spatial domain [1]. The Fourier-Transform- based frequency domain techniques [14-23] show much *. Tel.: 00966172418525; Fax: 00966172418185 improved performance in denoising periodic noise since E-mail address: [email protected] noisy frequencies are clearly di erentiated in Fourier J. Varghese/Scientia Iranica, Transactions D: Computer Science & ... 24 (2017) 1312{1324 1313 transformed domain by being made look like star/spike Konstantinidis et al. [23] proposed an interpolation- shaped peak areas [1-3]. The basic ltering techniques based lter to restore images by using pre xed cross applied in frequency domain to attenuate periodic noise shaped window, but this lter could not perform e ec- include Weiner lter, Ideal and Butterworth low-pass tive restoration since the window size was not adaptive lters, band reject lters, and notch lter [1]. Ideal to the varying noise strength. The peak detection and Butterworth low-pass lters admit only the low procedure employed by Grediac,et al. [24], and Sur frequencies clustered around the centre of low fre- and Grediac[25] algorithms uses static approximation quency in the Fourier transformed image and, thereby, of power law transformation, but it is not adaptive to cannot maintain image delity in the restored image, the corrupting noise and image types. since these algorithms discard all high frequencies The paper presents an adaptive Frequency- irrespective of their corruption status. Speci c circular Domain-based Switching Median Filter (FDSMF) op- region around the centre of low frequency in Fourier erator for the restoration of periodic noise corrupted domain is completely rejected by the band reject lters images by incorporating region-growing-based noise de- to dispose noisy frequencies, while regions centred at tection and median-based noise correction phases. The speci c frequency are rejected by the notch lter [1]. paper is organized in four sections. Section 2 describes The notch lters have advantage over band reject the proposed restoration lter. Section 3 provides the lters since they discard only small portions of the experimental result analysis, and conclusions are nally band. Among all notch lters, the Gaussian notch made in Section 4. lter plays an important role in denoising of periodic noise corrupted images since it not only discards the 2. Proposed FDSMF algorithm corrupted centre frequency peak but also suppresses its neighbouring frequencies corresponding to the noisy The proposed frequency-domain-based Switching Me- peak areas. This advantage of Gaussian notch l- dian Fillter (FDSMF) algorithm restores images cor- ters motivated later algorithms [19-22] to incorporate rupted with periodic noise by incorporating the distinct Gaussian notch-based correction algorithms in their stages of noisy frequency identi cation and correction. ltering operation. Aizenberg and Butako proposed The input corrupted image is Fourier transformed and three lters by incorporating noisy peak identi cation its origin is shifted to the centre for isolating noisy and correction phases to restore images [17-19]. The frequencies. The origin shifted Fourier transformed Gaussian notch-based restoration lter proposed by image F of the input corrupted image A of size M N Aizenberg and Butako [19] identi es a frequency in is determined as: the Fourier domain to be corrupted when the ratio of MX1 NX1 1 x+y j2( ux + vy ) the frequency value to the median frequency value from F (u; v)= (1) A(x; y)e M N : MN the pre xed neighbourhood exceeds a static threshold. x=0 y=0 (1) The lter di uses these corrupted frequencies by ap- Here, u = 0; 1; 2; ;M 1, v = 0; 1; 2; ;N 1, and plying Gaussian notch lter with pre xed window size. (1)x+y represent shifting operation. The algorithm Many variations of this lter have been developed by uses ` t2' and ` tshift' functions of Matlab software attempting at di erent peak detection and Gaussian to perform Eq. (1). The noise identi cation stage of notch ltering schemes [8,20,21], but these algorithms the proposed algorithm detects the corrupted frequency fail to e ectively restore periodic noise due to the positions in a binary ag image by nding the noisy following diculties: peak areas in the origin shifted Fourier transformed 1. Gaussian notch lters reject the noisy peak fre- image F . The noise correction phase of the proposed quency without restoring it by uncorrupted neigh- algorithm replaces the detected noisy frequencies in F bouring frequencies; by a valid restorer to di use the noise. Figure 1(b) shows the Fourier transformed image of Figure 1(a). 2. It is very dicult to make the ltering window size It can be observed that the noisy frequencies adaptive to varying noise levels; spreading throughout the corrupted image in spatial 3. The coecients of Gaussian notch lter are de- domain (Figure 1(a)) are concentrated in the Fourier signed in accordance with the distance without transformed image, causing the star/spike-like appear- making them adaptive to the noisy frequency val- ance outside the low frequency region. The motivation ues; hence, these coecients are not precise enough and goal of the proposed algorithm is to e ectively to di use the noisy peak areas. identify and restore these corrupted peaks in frequency domain. Hudhud and Turner [22] proposed a semi- automated algorithm that manually identi ed the noisy 2.1. The noise detection phase peak positions by replacing the noisy frequencies with The noise detection phase of the proposed algorithm median of the neighbouring uncorrupted frequencies. records the noisy frequency positions in a binary noise 1314 J. Varghese/Scientia Iranica, Transactions D: Computer Science & ... 24 (2017) 1312{1324 Figure 1. Di erent stages of FDSMF: (a) Corrupted Image, (b) Fourier transformed image, (c) di erence image, (d) seed points identi ed, (e) initial noise map image, (f) nal noise map image, (g) restored frequency domain image, and (h) nal restored image. map image f of the same size M N as the input the frequency domain image to make the iterative corrupted image A. The aim of the noise detection peak detection process easy, the algorithm nds the algorithm is to set `1' at the positions of the binary average di erence image D as: noise map image f, corresponding to the position of 1 XK1 XK1 corrupted frequencies in the Fourier transformed image D(u; v)= jF (u; v)F (u+k; v+l)j: 2 F . As an initial step, the algorithm resets all positions (W1) k=K1 l=K1 (3) of binary noise map image f to `0', assuming that all the frequencies in F are uncorrupted; hence: Here, W1 is the window size for nding the average di erence and is equal to (2K1 + 1), where K1 is a f =ff(i1; i2)=0 : 0 i1 M 1; 0 i2 N 1g : positive integer not less than 1.
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