The phase retrieval problem, fundamental in applied physics and engineering, asks to determine the phase of a complex-valued function from modulus data and additional a priori information. Recently, we identified two important methods for phase retrieval, namely Fienup’s Basic Input-Output (BIO) and Hybrid Input-Output (HIO) algorithms, with classical convex projection methods and suggested tha...

Driver assistance systems can help drivers to avoid car accidents by providing warning signals or visual cues of surrounding situations. Instead of the fixed bird’s-eye view monitoring proposed in many previous works, we developed a real-time vehicle surrounding monitoring system that can assist drivers to perceive the vehicle surrounding situations in third-person viewpoints. Four fisheye came...

An advantage of fluorescence methods over other imaging modalities is the ability to concurrently resolve multiple moieties using fluorochromes emitting at different spectral regions. Simultaneous imaging of spectrally separated agents is helpful in interrogating multiple functions or establishing internal controls for accurate measurements. Herein, we investigated multimoiety imaging in the co...

and Applied Analysis 3 It is well known that, in an infinite dimensional Hilbert space, the normal Mann iterative algorithm has only weak convergence, in general, even for nonexpansive mappings. Hybrid projection algorithms are popular tool to prove strong convergence of iterative sequences without compactness assumptions. Recently, hybrid projection algorithms have received rapid developments;...

Convolutional neural networks (CNNs) have yielded the excellent performance in a variety of computer vision tasks, where CNNs typically adopt a similar structure consisting of convolution layers, pooling layers and fully connected layers. In this paper, we propose to apply a novel method, namely Hybrid Orthogonal Projection and Estimation (HOPE), to CNNs in order to introduce orthogonality into...

Principal Components Analysis (PCA) being the most optimal linear mapper in Least-Squares (LS) sense has been predominantly used in subspace-based signal processing methods. In system identification problem, optimal subspace projections must span the joint space of the input and output of the unknown system. In this scenario, subspaces determined by the principal components of the input or the ...

Feature set dimensionality reduction via Discriminant Analysis (DA) is one of the most sought after approaches in many applications. In this paper, a novel nonlinear DA technique is presented based on a hybrid of Artificial Neural Networks (ANN) and the Uncorrelated Linear Discriminant Analysis (ULDA). Although dimensionality reduction via ULDA can present a set of statistically uncorrelated fe...

In this paper we suggest a hybrid method for computing the smallest eigenvalue of a symmetric and positive definite Toeplitz matrix which takes advantage of two types of methods, Newton’s method for the characteristic polynomial and projection methods based on rational interpolation of the secular equation.

The purpose of this paper is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The method of the proof is different from the original one. Our results improve and extend the corresponding results announced by Zhou et al. 2010, Kimura and Takahashi 2009, and some others.