A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some nonconvex 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 R N the corresponding set which is the epigraph of the cost function is also a convex set in R N +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.In many inverse signal and image processing problems and compressing sensing problems an optimization problem is solved to find a solution: minwhere C is a set in R N and f (w) is the cost function. Bregman developed iterative methods based on the so-called Bregman distance to solve convex optimization problems. In Bregman's approach, it is necessary to perform a D-projection (or Bregman projection) onto a convex set at each step of the algorithm [1], [2]. Unfortunately it may not be easy to compute the Bregman projections in general.In this article, Bregman's projections onto convex sets (POCS) framework is used to solve convex and some non-convex optimization problems without using the Bregman distance approach.We increase the dimension by one and define the following sets in R N +1 corresponding to the cost function f (w) as follows:

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a b s t r a c tA system for removing shell pieces from hazelnut kernels using impact vibration analysis was developed in which nuts are dropped onto a steel plate and the vibration signals are captured and analyzed. The mel-cepstral feature parameters, line spectral frequency values, and Fourier-domain Lebesgue features were extracted from the vibration signals. The best experimental results were obtained using the melcepstral feature parameters. The feature parameters were classified using a support vector machine (SVM), which was trained a priori using a manually classified dataset. An average recognition rate of 98.2% was achieved. An important feature of the method is that it is easily trainable, enabling it to be applicable to other nuts, including walnuts and pistachio nuts. In addition, the system can be implemented in real time.

Özetçe -Radar sinyal işlemenin de dahil oldugu bir çok pratik problemde, ayrık Fourier Dönüşümünü (DFT) mükemmel biçimde hesaplamanın geregi yoktur. Bu makalede, DFT'nin yaklaşık hesaplanmasını olanaklı kılan ve bunu çarpma kullanmadan yapan yeni bir algoritma sunulmuştur. Bütün (a × b)şeklindeki çarpma işlemleri, sign(a × b)(|a| + |b|) işlemi ile degiştirilmiştir. Bu yeni dönüşüm özellikle ilinti hesaplanmasının gerektigi sinyal işleme algoritmalarında kullanışlıdır. Radar sinyal işlemedeki belirsizlik fonksiyonu iki sinyal arasındaki ilintiyi hesaplamak için yüksek miktarda çarpma işlemine ihtiyaç duymaktadır. Bu yeni toplama işlemi, belirsizlik fonksiyonunun çarpma işlemi kullanılmadan yaklaşık hesaplanmasını mümkün kılmıştır. Pasif radarlarda uygulanmış birçok örnek simulasyon sunulmustur.Anahtar Kelimeler-İlinti, pasif algılama sistemi, pasif radar, DFT, dogrusal olmayan DFT, saçılımlı DFT Abstract-In many radar problems it is not necessary to compute the ambiguity function in a perfect manner. In this article a new multiplication free algorithm for approximate computation of the ambiguity function is introduced. All multiplications (a × b) in the ambiguity function are replaced by an operator which computes sign(a × b)(|a| + |b|). The new transform is especially useful when the signal processing algorithm requires correlations. Ambiguity function in radar signal processing requires high number of correlations and DFT computations. This new additive operator enables an approximate computation of the ambiguity function without requiring any multiplications. Simulation examples involving passive radars are presented.

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