Browsing by Author "Tofighi, Mohammad"

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Open Access
Deconvolution using projections onto the epigraph set of a convex cost function
(IEEE, 2014) Tofighi, Mohammad; Bozkurt, Alican; Köse, K.; Çetin, A. Enis
A new deconvolution algorithm based on making 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 sets corresponding to the cost function and observations are defined. If the utilized cost function is convex in RN, the corresponding epigraph set is also convex in RN+1. The deconvolution algorithm starts with an arbitrary initial estimate in RN+1. At each iteration cycle of the algorithm, first deconvolution projections are performed onto the hyperplanes representing observations, then an orthogonal projection is performed onto epigraph of the cost function. The method provides globally optimal solutions for total variation, l1, l2, and entropic cost functions.
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
Image restoration and reconstruction using projections onto epigraph set of convex cost fuchtions
(2015) Tofighi, Mohammad
This thesis focuses on image restoration and reconstruction problems. These inverse problems are solved using a convex optimization algorithm based on orthogonal Projections onto the Epigraph Set of a Convex Cost functions (PESC). In order to solve the convex minimization problem, the dimension of the problem is lifted by one and then using the epigraph concept the feasibility sets corresponding to the cost function are defined. Since the cost function is a convex function in R N , the corresponding epigraph set is also a convex set in R N+1. The convex optimization algorithm starts with an arbitrary initial estimate in R N+1 and at each step of the iterative algorithm, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The PESC algorithm provides globally optimal solutions for different functions such as total variation, `1-norm, `2-norm, and entropic cost functions. Denoising, deconvolution and compressive sensing are among the applications of PESC algorithm. The Projection onto Epigraph Set of Total Variation function (PES-TV) is used in 2-D applications and for 1-D applications Projection onto Epigraph Set of `1-norm cost function (PES-`1) is utilized. In PES-`1 algorithm, first the observation signal is decomposed using wavelet or pyramidal decomposition. Both wavelet denoising and denoising methods using the concept of sparsity are based on soft-thresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domain such as Fourier, DCT, and/or wavelet domain and transform domain coefficients of the noisy signal are soft-thresholded to reduce noise. Here, the relationship between the standard soft-thresholding based denoising methods and sparsity-based wavelet denoising methods is described. A deterministic soft-threshold estimation method using the epigraph set of `1-norm cost function is presented. It is demonstrated that the size of the `1-ball can be determined using linear algebra. The size of the `1-ball in turn determines the soft-threshold. The PESC, PES-TV and PES-`1 algorithms, are described in detail in this thesis. Extensive simulation results are presented. PESC based inverse restoration and reconstruction algorithm is compared to the state of the art methods in the literature.
Open Access
Pasif bistatik radarlarda seyreklik temellli ters evrişim kullanılarak hedef tespiti
(IEEE, 2015-05) Arslan, Musa Tunç; Tofighi, Mohammad; Çetin, A. Enis
Bu bildiride pasif radar (PR) sistemlerinin menzil çözünürlüğünü artırmak için seyreklik tabanlı bir ters evrişim yöntemi sunulmaktadır. PR sistemlerinin iki boyutlu uyumlu süzgeç çıktısı bir ters evrişim problemli gibi düşünülerek incelenmektedir. Ters evrişim algoritması, hedeflerin zaman kaymaları ve l1 norm benzeri dışbükey maliyet fonksiyonlarının epigraf kümelerini temsil eden hiperdüzlemler üzerine izdüşümü temellidir. Bütün kısıt kümeleri kapalı ve dışbükey olduklarından dolayı yinelemeli algoritma yakınsamaktadır. FM tabanlı PR sistemleri üzerinde benzetim sonuçları sunulmuştur. Algoritma frekans uzayı tabanlı ters evrişim yöntemlerine göre daha yüksek performansa sahiptir.
Open Access
Projection onto epigraph sets for rapid self-tuning compressed sensing MRI
(IEEE, 2019) Shahdloo, Mohammad; Ilıcak, Efe; Tofighi, Mohammad; Sarıtaş, Emine Ülkü; Çetin, A. Enis; Çukur, Tolga
The compressed sensing (CS) framework leverages the sparsity of MR images to reconstruct from undersampled acquisitions. CS reconstructions involve one or more regularization parameters that weigh sparsity in transform domains against fidelity to acquired data. While parameter selection is critical for reconstruction quality, the optimal parameters are subject and dataset specific. Thus, commonly practiced heuristic parameter selection generalizes poorly to independent datasets. Recent studies have proposed to tune parameters by estimating the risk of removing significant image coefficients. Line searches are performed across the parameter space to identify the parameter value that minimizes this risk. Although effective, these line searches yield prolonged reconstruction times. Here, we propose a new self-tuning CS method that uses computationally efficient projections onto epigraph sets of the ℓ1 and total-variation norms to simultaneously achieve parameter selection and regularization. In vivo demonstrations are provided for balanced steady-state free precession, time-of-flight, and T1-weighted imaging. The proposed method achieves an order of magnitude improvement in computational efficiency over line-search methods while maintaining near-optimal parameter selection.
Open Access
Projections onto convex sets (POCS) based optimization by lifting
(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim Akın
A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.
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
Sıkıştırılmış algılama kullanarak Uzaklık-Doppler radar hedef tespiti
(IEEE, 2014-04) Sevimli, R. Akın; Tofighi, Mohammad; Çetin, A. Enis
Sıkıştırılmış algılama(SA) fikri, az sayıda ölçümlerden seyrek bir sinyalin geri çatımını mümkün kılar. SA yaklaşımı bir çok farklı alanda uygulamalara sahiptir. Bu alanlardan birisi de radar sistemleridir. Bu makalede, radar belirsizlik fonksiyonu (Ambiguity Function) SA çatısı altında gürültüden arındırılmıştır. Bu amaç için dışbükey fonksiyonun epigraf kümesine izdüşüm tabanlı yeni bir gürültüden arındırma metodu geliştirilmiştir. Bu yaklaşım, diğer SA geri çatım algoritmalarıyla karşılaştırılmıştır. Deneysel sonuçlar sunulmuştur.