There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.

Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning

Thank you very much for downloading spotlight synthetic aperture radar signal processing algorithms. Maybe you have knowledge that, people have search numerous times for their favorite books like this spotlight synthetic aperture radar signal processing algorithms, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they juggled with some harmful virus inside their laptop.

Spotlight Synthetic Aperture Radar Signal Processing Algorithms

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. However, deriving efficient strategies that jointly bring into play the primal and dual problems is a more recent idea that has generated many important new contributions in recent years. These novel developments are grounded in the recent advances in convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with an emphasis on sparsity issues. In this article, we aim to present the principles of primal?dual approaches while providing an overview of the numerical methods that have been proposed in different contexts. Last but not least, primal?dual methods lead to algorithms that are easily parallelizable. Today, such parallel algorithms are becoming increasingly important for efficiently handling high-dimensional problems.

https://hal.archives-ouvertes.fr/hal-01010437/document

Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems

This paper reviews recent progress of portable short-range noncontact microwave radar systems for motion detection, positioning, and imaging applications. With the continuous advancements of modern semiconductor technologies and embedded computing, many functionalities that could only be achieved by bulky radar systems in the past are now integrated into portable devices with integrated circuit chips and printed circuits boards. These portable solutions are able to provide high motion detection sensitivity, excellent signal-to-noise ratio, and satisfactory range detection capability. Assisted by on-board signal processing algorithms, they can play important roles in various areas, such as health and elderly care, veterinary monitoring, human-computer interaction, structural monitoring, indoor tracking, and wind engineering. This paper reviews some system architectures and practical implementations for typical wireless sensing applications. It also discusses potential future developments for the next-generation portable smart radar systems.

A Review on Recent Progress of Portable Short-Range Noncontact Microwave Radar Systems

SUMMARY Regularization plays a fundamental role in adaptive ﬁlter-ing. There are, very likely, many diﬀerent ways to regularize an adaptiveﬁlter. In this letter, we propose one possible way to do it based on a con-dition that makes intuitively sense. From this condition, we show how toregularize the recursive least-squares (RLS) algorithm. key words: echo cancellation, adaptive ﬁlters, regularization, recursiveleast-squares (RLS) algorithm 1. Introduction It is well known that regularization is a must in all prob-lems when a noisy linear system of equations needs to besolved [1]. Any adaptive ﬁlter has a linear system of equa-tions to solve, explicitly or implicitly, so that regularizationis required in order that the algorithm converges smoothlyand consistently to the optimal Wiener solution, especiallyin the presence of additive noise.In many adaptive ﬁlters [2],[3], the regularization pa-rameter is chosen as δ=βσ 2 x ,whereσ x = Ex 2 ( n )is thevariance of the zero-mean input signal

Regularization of the RLS Algorithm

An efficient Kalman filter for the identification of low-rank systems

The regularization parameter is required in most (if not all) adaptive algorithms, while its role becomes very critical in the presence of additive noise. In this paper, we focus on the regularized recursive least-squares (RLS) algorithm and present a method to find its regularization parameter, which is related to the signal-to-noise ratio (SNR). Also, using a proper estimation of the SNR, we further propose a variable-regularized RLS (VR-RLS) algorithm. In addition, a low-complexity version of the VR-RLS algorithm is developed, based on the dichotomous coordinate descent (DCD) method. Due to their nature, the proposed algorithms have good robustness features against additive noise, which make them behave well in all noisy conditions. Simulations performed in the context of acoustic echo cancellation support these findings.

Robust variable-regularized RLS algorithms

System identification problems are always challenging to address in applications that involve long impulse responses, especially in the framework of multichannel systems. In this context, the main goal of this review paper is to promote some recent developments that exploit decomposition-based approaches to multiple-input/single-output (MISO) system identification problems, which can be efficiently solved as combinations of low-dimension solutions. The basic idea is to reformulate such a high-dimension problem in the framework of bilinear forms, and to then take advantage of the Kronecker product decomposition and low-rank approximation of the spatiotemporal impulse response of the system. The validity of this approach is addressed in terms of the celebrated Wiener filter, by developing an iterative version with improved performance features (related to the accuracy and robustness of the solution). Simulation results support the main theoretical findings and indicate the appealing performance of these developments.

Identification of Linear and Bilinear Systems: A Unified Study

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria.

https://www.mdpi.com/2073-8994/13/3/481/pdf

Silviu Ciochina

Papers

Regularization of the RLS Algorithm

An efficient Kalman filter for the identification of low-rank systems

Robust variable-regularized RLS algorithms

Identification of Linear and Bilinear Systems: A Unified Study

Tensor-Based Adaptive Filtering Algorithms