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

Identification of sparse impulse responses was addressed mainly in the last two decades with the development of the so-called “proportionate”-type algorithms. These algorithms are meant to exploit the sparseness of the systems that need to be identified, with the purpose of improving the convergence rate and tracking of the conventional adaptive algorithms used in this framework. Nevertheless, the system identification problem becomes more challenging when the parameter space is large. This issue can be addressed with tensor decompositions and modelling. In this paper, we aim to identify sparse bilinear forms, in which the bilinear term is defined with respect to the impulse responses of a spatiotemporal model. In this context, we derive a proportionate affine projection algorithm for the identification of such bilinear forms. Experimental results highlight the good behavior of the proposed solution.

A Proportionate Affine Projection Algorithm for the Identification of Sparse Bilinear Forms

Double-talk detectors (DTDs) are vital to the operation and performance of SAECs. In this chapter, we discuss the most well-known double-talk detection algorithms. It will be shown that, thanks to the WL formulation, DTDs for single-channel acoustic echo cancellation are easily generalized to the stereo case.

Double-Talk Detection

The normalized least-mean-square algorithm (NLMS) is frequently used in the context of acoustic echo cancellation (AEC) However, in order to meet the conflicting requirements of fast convergence and tracking versus low misadjustment, the variable step-size NLMS (VSS-NLMS) algorithms were found to be more suitable in practice In this paper, we analyze the nonparametric VSS-NLMS (NPVSS-NLMS) algorithm that uses the power estimate of the background noise (ie, the noise that corrupts the near-end speech) in order to control its step-size parameter The estimation method of the noise power is based on a time-recursive averaging algorithm Simulation results indicate the good performance of the NPVSS-NLMS algorithm

Estimation of the noise power in the NPVSS-NLMS algorithm

Infrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available SAR products where the image is already focused in a slant range - azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a scattering center monitoring procedure based on refocusing a set of SAR images on a provided high-resolution DEM of the structure. The scattering centers of the refocused image are detected in the 4-D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution obtained using the Capon estimator. The algorithm is validated on real data acquired with the TerraSAR-X satellite over the Puylaurent water dam in France during March-June 2012. The relative displacements between scattering regions show very good agreement with the in situ measurements.

/pdf/scattering-centers-monitoring-in-refocused-sar-images-on-a-2xklfjhg8e.pdf

Scattering centers monitoring in refocused SAR images on a high-resolution DEM

The most common algorithms used for echo cancellation are the normalized least-mean-square (NLMS) and the affine projection (AP). The classical versions of these algorithms use a constant step-size parameter and need to establish a tradeoff between several performance criteria e.g., high convergence rate versus low misadjustment. In this paper, we present a class of variable step-size NLMS and AP algorithms, which are designed to recover the near-end signal from the error of the adaptive filter. The simulation results indicate a robust behavior of these algorithms against the presence of the near-end signal.

Silviu Ciochina

Papers

A Proportionate Affine Projection Algorithm for the Identification of Sparse Bilinear Forms

Double-Talk Detection

Estimation of the noise power in the NPVSS-NLMS algorithm

Scattering centers monitoring in refocused SAR images on a high-resolution DEM

Practical variable step-size adaptive algorithms for echo cancellation