Alican Bozkurt

Projections onto convex sets (POCS) based optimization by lifting

Summary form only given. 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 RN+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.

Multiplication-free Neural Networks

In this article, a multiplication-free artificial Neural Network (ANN) structure is proposed. Inner products between the input vectors and the ANN weights are implemented using a multiplication-free vector operator. Training of the new artificial neural network structure is carried out using the sign-LMS algorithm. Proposed ANN system can be used in applications requiring low-power usage or running on microprocessors that have limited processing power.

Deconvolution using projections onto the epigraph set of a convex cost function

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.

Approximate computation of DFT without performing any multiplications: Application to radar signal processing

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.

Delineation of Skin Strata in Reflectance Confocal Microscopy Images with Recurrent Convolutional Networks

Reflectance confocal microscopy (RCM) is an effective, non-invasive pre-screening tool for cancer diagnosis. However, acquiring and reading RCM images requires extensive training and experience, and novice clinicians exhibit high variance in diagnostic accuracy. Consequently, there is a compelling need for quantitative tools to standardize image acquisition and analysis. In this study, we use deep recurrent convolutional neural networks to delineate skin strata in stacks of RCM images collected at consecutive depths. To perform diagnostic analysis, clinicians collect RCM images at 4-5 specific layers in the tissue. Our model automates this process by discriminating between RCM images of different layers. Testing our model on an expert labeled dataset of 504 RCM stacks, we achieve 87.97% classification accuracy, and a 9-fold reduction in the number of anatomically impossible errors compared to the previous state-of-the-art.