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

This paper aims to present an affine projection algorithm (APA) tailored for the identification of system impulse responses with intrinsic symmetric/antisymmetric characteristics. Such an algorithm uses a combination, based on the Kronecker product decomposition, of two (short length) adaptive filters to efficiently estimate a long length system impulse response. As a result of that, the proposed algorithm outperforms the conventional APA in terms of convergence speed and tracking ca-pabilities. Simulation results are shown and discussed, confirming the improved performance achieved by the proposed algorithm in several operating conditions.

An Affine Projection Algorithm for the Identification of Impulse Responses with Symmetric/Antisymmetric Characteristics

Acoustic system identification, which aims at estimating the channel impulse response from a source of interest to the microphone position, plays an important role in many applications, e.g., echo cancellation for full-duplex speech communication. Generally, an acoustic channel impulse response is modeled as a linear finite-impulse-response (FIR) filter, so the objective of system identification is to identify it. While much effort has been devoted to this topic over the last five decades, identifying the room FIR filters accurately with only a small number of observation data snapshots remains a significant challenge. This paper studies this problem and proposes to model the acoustic impulse response, i.e., the FIR filter, with a tensor decomposition, which can be expressed as a multidimensional Kronecker product of a series of shorter filters. Then, a partially time-varying model is applied to acoustic system identification, where the global filter is decomposed into two parts: a time-invariant part, which captures the common properties of acoustic channels, and a time-varying part, which, as its name indicates, represents the components of acoustic channels that change with time. During the identification process, the time-invariant filters can be identified or learned in advance, while the time-varying filters are optimized through an iterative procedure. Simulation results demonstrate that the proposed technique can achieve better acoustic system identification performance with a small number of data snapshots.

Acoustic System Identification with Partially Time-Varying Models Based on Tensor Decompositions

Multi-channel Ground-based Bistatic SAR Receiver for Single-pass Opportunistic Tomography

The recursive least-squares (RLS) algorithm is an appealing choice for system identification problems, mostly due to its fast convergence. However, its high computational complexity limits the implementation of this algorithm in applications like acoustic echo cancellation (AEC), where long length adaptive filters are needed. Nevertheless, the fast RLS (FRLS) algorithm represents a practical alternative for such challenging scenarios, since its computational amount is proportional to the filter length. At the same time, the FRLS algorithm becomes unstable especially for nonstationary inputs, like speech. To overcome this limitation, we present an improved version of the FRLS algorithm based on the data-reuse (DR) method. The resulting algorithm, namely DR-FRLS, is able to work using the maximum value of its forgetting factor (which leads to good stability), at the same time controlling its tracking behavior by tuning the data-reuse parameter. Simulations conducted in the framework of AEC support the good performance of the DR-FRLS algorithm, which could become a reliable candidate in real-world applications.

On the Performance of a Data-Reuse Fast RLS Algorithm for Acoustic Echo Cancellation

Bistatic radar receivers that use an opportunistic transmitter require a reference channel to capture the original transmitted signal, which is then used as a reference signal for constructing the matched-filter during the range compression step. Because the reference signal is received from line-of-sight, it is orders in magnitude larger than the reflections captured by the receive channel. It is generally difficult to construct the system such that the reference signal is not leaked into the received signal, either via coupling in the circuitry or via reflections off objects in the vicinity of the receiver. Due to its much larger amplitude, the reference signal can easily mask smaller targets with its side-lobes. In this paper we propose a novel deconvolution method for bistatic SAR images as a means of eliminating leakage of the reference signal.

Silviu Ciochina

Papers

An Affine Projection Algorithm for the Identification of Impulse Responses with Symmetric/Antisymmetric Characteristics

Acoustic System Identification with Partially Time-Varying Models Based on Tensor Decompositions

Multi-channel Ground-based Bistatic SAR Receiver for Single-pass Opportunistic Tomography

On the Performance of a Data-Reuse Fast RLS Algorithm for Acoustic Echo Cancellation

Deconvolution Method for Eliminating Reference Signal Coupling/Reflections in Bistatic SAR