Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Atmospheric turbulence mitigation for sequences with moving objects using recursive image fusion

This paper describes a new method for mitigating the effects of atmospheric distortion on observed sequences that include large moving objects. In order to provide accurate detail from objects behind the distorting layer, we solve the space-variant distortion problem using recursive image fusion based on the Dual Tree Complex Wavelet Transform (DT-CWT). The moving objects are detected and tracked using the improved Gaussian mixture models (GMM) and Kalman filtering. New fusion rules are introduced which work on the magnitudes and angles of the DT-CWT coefficients independently to achieve a sharp image and to reduce atmospheric distortion, respectively. The subjective results show that the proposed method achieves better video quality than other existing methods with competitive speed.Comment: IEEE International Conference on Image Processing 201

First-order Convex Optimization Methods for Signal and Image Processing

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration com-plexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient meth-ods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple-description problem. We finally present the contributions of the thesis. The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third papers concern discrete linear inverse problems and reliable numerical reconstruction software. The last two papers present a convex opti-mization formulation of the multiple-description problem and a method to solve it in the case of large-scale instances. i i

Nonlinear and distributed sensory estimation

Methods to improve performance of sensors with regard to sensor nonlinearity, sensor noise and sensor bandwidths are investigated and new algorithms are developed. The necessity of the proposed research has evolved from the ever-increasing need for greater precision and improved reliability in sensor measurements. After describing the current state of the art of sensor related issues like nonlinearity and bandwidth, research goals are set to create a new trend on the usage of sensors. We begin the investigation with a detailed distortion analysis of nonlinear sensors. A need for efficient distortion compensation procedures is further justified by showing how a slight deviation from the linearity assumption leads to a very severe distortion in time and in frequency domains. It is argued that with a suitable distortion compensation technique the danger of having an infinite bandwidth nonlinear sensory operation, which is dictated by nonlinear distortion, can be avoided. Several distortion compensation techniques are developed and their performance is validated by simulation and experimental results. Like any other model-based technique, modeling errors or model uncertainty affects performance of the proposed scheme, this leads to the innovation of robust signal reconstruction. A treatment for this problem is given and a novel technique, which uses a nominal model instead of an accurate model and produces the results that are robust to model uncertainty, is developed. The means to attain a high operating bandwidth are developed by utilizing several low bandwidth pass-band sensors. It is pointed out that instead of using a single sensor to measure a high bandwidth signal, there are many advantages of using an array of several pass-band sensors. Having shown that employment of sensor arrays is an economic incentive and practical, several multi-sensor fusion schemes are developed to facilitate their implementation. Another aspect of this dissertation is to develop means to deal with outliers in sensor measurements. As fault sensor data detection is an essential element of multi-sensor network implementation, which is used to improve system reliability and robustness, several sensor scheduling configurations are derived to identify and to remove outliers