Browsing by Subject "Sparse recovery"

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    Ellipsoid genişletmeyle seyrek sinyal geri oluşturma
    (IEEE, 2011-04) Gürbüz, A. C.; Pilancı, M.; Arıkan, Orhan
    Bu makalede b = Ax + n şeklinde gürültülü A’nın tam rank ve x’in seyrek olduğu doğrusal bir denklem sistemi için seyrek x sinyallerini doğru olarak geri oluşturmaya yönelik yeni bir yöntem sunulmuştur. Önerilen yöntem kullanılan veri sınırını belirleyen ||Ax − b||2 = ellipsoidinin genişletilirken sırayla eksenlerin sıfırlanmasına dayanan yinelemeli bir yöntemdir. Seyrek sinyal oluşturma alanında yinelemeli ve 1 norm minimizasyon tabanlı standard yöntemlere göre benzer problemlerde daha yüksek başarım gösteren metot, eksik belirtilmiş sistemlerde standard metotların oluşturması gereken seyreklik seviyesini de yumuşatmaktadır
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    A new OMP technique for sparse recovery
    (IEEE, 2012) Teke, Oğuzhan; Gürbüz, A.C.; Arıkan, Orhan
    Compressive Sensing (CS) theory details how a sparsely represented signal in a known basis can be reconstructed using less number of measurements. However in reality there is a mismatch between the assumed and the actual bases due to several reasons like discritization of the parameter space or model errors. Due to this mismatch, a sparse signal in the actual basis is definitely not sparse in the assumed basis and current sparse reconstruction algorithms suffer performance degradation. This paper presents a novel orthogonal matching pursuit algorithm that has a controlled perturbation mechanism on the basis vectors, decreasing the residual norm at each iteration. Superior performance of the proposed technique is shown in detailed simulations. © 2012 IEEE.
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    Subset based error recovery
    (Elsevier BV, 2021-10-12) Ekmekcioğlu, Ömer; Akkaya, Deniz; Pınar, Mustafa Çelebi
    We propose a data denoising method using Extreme Learning Machine (ELM) structure which allows us to use Johnson-Lindenstrauß Lemma (JL) for preserving Restricted Isometry Property (RIP) in order to give theoretical guarantees for recovery. Furthermore, we show that the method is equivalent to a robust two-layer ELM that implicitly benefits from the proposed denoising algorithm. Current robust ELM methods in the literature involve well-studied L1, L2 regularization techniques as well as the usage of the robust loss functions such as Huber Loss. We extend the recent analysis on the Robust Regression literature to be effectively used in more general, non-linear settings and to be compatible with any ML algorithm such as Neural Networks (NN). These methods are useful under the scenario where the observations suffer from the effect of heavy noise. We extend the usage of ELM as a general data denoising method independent of the ML algorithm. Tests for denoising and regularized ELM methods are conducted on both synthetic and real data. Our method performs better than its competitors for most of the scenarios, and successfully eliminates most of the noise.