Browsing by Subject "Denoising"

Now showing 1 - 6 of 6

Open Access
Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)
(Springer U K, 2015) Tofighi M.; Kose, K.; Çetin, A. Enis
In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.
Open Access
Denoising using projections onto the epigraph set of convex cost functions
(IEEE, 2014) Tofighi, Mohammad; Köse, K.; Çetin, A. Enis
A new denoising algorithm based on orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and feasibility sets corresponding to the cost function using the epigraph concept are defined. As the utilized cost function is a convex function in RN, the corresponding epigraph set is also a convex set in RN+1. The denoising algorithm starts with an arbitrary initial estimate in RN+1. At each step of the iterative denoising, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The method provides globally optimal solutions for total-variation, ℓ1, ℓ2, and entropic cost functions.1
Open Access
Phase-correcting non-local means filtering for diffusion-weighted imaging of the spinal cord
(John Wiley, 2018) Kafalı, Sevgi Gökçe; Çukur, Tolga; Sarıtaş, Emine Ülkü
Purpose: DWI suffers from low SNR when compared to anatomical MRI. To maintain reasonable SNR at relatively high spatial resolution, multiple acquisitions must be averaged. However, subject motion or involuntary physiological motion during diffusion-sensitizing gradients cause phase offsets among acquisitions. When the motion is localized to a small region, these phase offsets become particularly problematic. Complex averaging of acquisitions lead to cancellations from these phase offsets, whereas magnitude averaging results in noise amplification. Here, we propose an improved reconstruction for multi-acquisition DWI that effectively corrects for phase offsets while reducing noise. Theory and Methods: Each acquisition is processed with a refocusing reconstruction for global phase correction and a partial k-space reconstruction via projection-onto-convex-sets (POCS). The proposed reconstruction then embodies a new phase-correcting non-local means (PC-NLM) filter. PC-NLM is performed on the complex-valued outputs of the POCS algorithm aggregated across acquisitions. The PC-NLM filter leverages the shared structure among multiple acquisitions to simultaneously alleviate nuisance factors including phase offsets and noise. Results: Extensive simulations and in vivo DWI experiments of the cervical spinal cord are presented. The results demonstrate that the proposed reconstruction improves image quality by mitigating signal loss because of phase offsets and reducing noise. Importantly, these improvements are achieved while preserving the accuracy of apparent diffusion coefficient maps. Conclusion: An improved reconstruction incorporating a PC-NLM filter for multi-acquisition DWI is presented. This reconstruction can be particularly beneficial for high-resolution or high-b-value DWI acquisitions that suffer from low SNR and phase offsets from local motion.
Open Access
Polynomial fitting and total variation based techniques on 1-D and 2-D signal denoising
(2010) Yıldız, Aykut
New techniques are developed for signal denoising and texture recovery. Geometrical theory of total variation (TV) is explored, and an algorithm that uses quadratic programming is introduced for total variation reduction. To minimize the staircase effect associated with commonly used total variation based techniques, robust algorithms are proposed for accurate localization of transition boundaries. For this boundary detection problem, three techniques are proposed. In the first method, the 1−D total variation is applied in first derivative domain. This technique is based on the fact that total variation forms piecewise constant parts and the constant parts in the derivative domain corresponds to lines in time domain. The boundaries of these constant parts are used as the transition boundaries for the line fitting. In the second technique proposed for boundary detection, a wavelet based technique is proposed. Since the mother wavelet can be used to detect local abrupt changes, the Haar wavelet function is used for the purpose of boundary detection. Convolution of a signal or its derivative family with this Haar mother wavelet gives responses at the edge locations, attaining local maxima. A basic local maximization technique is used to find the boundary locations. The last technique proposed for boundary detection is the well known Particle Swarm Optimization (PSO). The locations of the boundaries are randomly perturbed yielding an error for each set of boundaries. Pursuing the personal and global best positions, the boundary locations converge to a set of boundaries. In all of the techniques, polynomial fitting is applied to the part of the signal between the edges. A more complicated scenario for 1−D signal denoising is texture recovery. In the technique proposed in this thesis, the periodicity of the texture is exploited. Periodic and non-periodic parts are distinguished by examining total variation of the autocorrelation of the signal. In the periodic parts, the period size was found by PSO evolution. All the periods were averaged to remove the noise, and the final signal was synthesized. For the purpose of image denoising, optimum one dimensional total variation minimization is carried to two dimensions by Radon transform and slicing method. In the proposed techniques, the stopping criterion for the procedures is chosen as the error norm. The processes are stopped when the residual norm is comparable to noise standard deviation. 1−D and 2−D noise statistics estimation methods based on Maximum Likelihood Estimation (MLE) are presented. The proposed denoising techniques are compared with principal curve projection technique, total variation by Rudin et al, total variation by Willsky et al, and curvelets. The simulations show that our techniques outperform these widely used techniques in the literature.
Open Access
Range-doppler radar target detection using denoising within the compressive sensing framework
(IEEE, 2014-09) Sevimli, R. Akın; Tofighi, Mohammad; Çetin, A. Enis
Compressive sensing (CS) idea enables the reconstruction of a sparse signal from a small set of measurements. CS approach has applications in many practical areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented1. © 2014 EURASIP.
Open Access
Target detection and imaging on passive bistatic radar systems = Pasif bistatik radar sistemleri üzerinde hedef tespiti ve görüntülenmesi
(2014) Sevimli, Rasim Akın
Passive Bistatic Radar (PBR) systems have become more popular in recent years in many research communities and countries. Papers related to PBR systems have increasingly received significant attention in research. There are many target detection methods for PBR system in the literature. This thesis assumes a system scenario based on stereo FM signals as transmitters of opportunity. Ambiguity function (AF) is a function that determines the locations of targets in range-Doppler map turns out to be noisy in practice. This can cause a problem with low SNR-valued targets because they cannot be visible. To solve this problem, compressive sensing (CS) and projection onto the epigraph set of the `1 ball (PES-`1) are used to denoise the range-Doppler map. Some CS methods are applied to the system scenario, which are Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), Compressed Sampling Matching Pursuit (CoSaMP), Iterative Hard Thresholding (IHT). In addition, AF is generally used to determine the similarities between two signals. Therefore, different correlation methods can be also used to compare the surveillance and time delayed frequency shifted replica of the reference signal. Maximal Information Coefficient (MIC), Pearson correlation coefficient, Spearman’s rank correlation coefficient are used for the target detection. This thesis proposes a least squares (LS) based method which outperforms other correlation algorithms in terms of PSNR and SNR. Two LS coefficients are obtained from the real and imaginary parts of predicting the surveillance signal using the modulated reference signal. Norm of LS coefficients exhibit a peak at target locations. The proposed method detects close targets better than the ordinary AF method and decreases the number of sidelobes on multiple FM channels based the PBR system.