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

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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

The performance of the recursive least-squares (RLS) algorithm is governed by the forgetting factor. This parameter leads to a compromise between (1) the tracking capabilities and (2) the misadjustment and stability. In this letter, a variable forgetting factor RLS (VFF-RLS) algorithm is proposed for system identification. In general, the output of the unknown system is corrupted by a noise-like signal. This signal should be recovered in the error signal of the adaptive filter after this one converges to the true solution. This condition is used to control the value of the forgetting factor. The simulation results indicate the good performance and the robustness of the proposed algorithm.

/pdf/a-robust-variable-forgetting-factor-recursive-least-squares-3qcc15zrie.pdf

A Robust Variable Forgetting Factor Recursive Least-Squares Algorithm for System Identification

The adaptive algorithms used for acoustic echo cancellation (AEC) have to provide (1) high convergence rates and good tracking capabilities, since the acoustic environments imply very long and time-variant echo paths, and (2) low misadjustment and robustness against background noise variations and double-talk. In this context, the affine projection algorithm (APA) and different versions of it are very attractive choices for AEC. However, an APA with a constant step-size parameter has to compromise between the performance criteria (1) and (2). Therefore, a variable step-size APA (VSS-APA) represents a more reliable solution. In this paper, we propose a VSS-APA derived in the context of AEC. Most of the APAs aim to cancel p (i.e., projection order) previous a posteriori errors at every step of the algorithm. The proposed VSS-APA aims to recover the near-end signal within the error signal of the adaptive filter. Consequently, it is robust against near-end signal variations (including double-talk). This algorithm does not require any a priori information about the acoustic environment, so that it is easy to control in practice. The simulation results indicate the good performance of the proposed algorithm as compared to other members of the APA family.

A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation

Proportionate-type normalized least-mean-square algorithms were developed in the context of echo cancellation. In order to further increase the convergence rate and tracking, the ?proportionate? idea was applied to the affine projection algorithm (APA) in a straightforward manner. The objective of this letter is twofold. First, a general framework for the derivation of proportionate-type APAs is proposed. Second, based on this approach, a new proportionate-type APA is developed, taking into account the ?history? of the proportionate factors. The benefit is also twofold. Simulation results indicate that the proposed algorithm outperforms the classical one (achieving faster tracking and lower misadjustment). Besides, it also has a lower computational complexity due to a recursive implementation of the ?proportionate history?.

An Efficient Proportionate Affine Projection Algorithm for Echo Cancellation

Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellation. Besides a comprehensive review of the basic proportionate-type algorithms, we also present some of the latest developments in the field and propose some new solutions for further performance improvement, e.g., variable step-size versions and novel proportionate-type affine projection algorithms. An experimental study is also provided in order to compare many sparse adaptive filters in different echo canc...

Sparse Adaptive Filters for Echo Cancellation

In acoustic echo cancellation (AEC) applications, where the acoustic echo paths are extremely long, the adaptive filter works most likely in an under-modeling situation. Most of the adaptive algorithms for AEC were derived assuming an exact modeling scenario, so that they do not take into account the under-modeling noise. In this letter, a variable step-size normalized least-mean-square (VSS-NLMS) algorithm suitable for the under-modeling case is proposed. This algorithm does not require any a priori information about the acoustic environment; as a result, it is very robust and easy to control in practice. The simulation results indicate the good performance of the proposed algorithm.

Silviu Ciochina

Papers

A Robust Variable Forgetting Factor Recursive Least-Squares Algorithm for System Identification

A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation

An Efficient Proportionate Affine Projection Algorithm for Echo Cancellation

Sparse Adaptive Filters for Echo Cancellation

Variable Step-Size NLMS Algorithm for Under-Modeling Acoustic Echo Cancellation