Introduction to linear and nonlinear programming

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

贝叶斯滤波与平滑 (Bayesian filtering and smoothing)

Super-resolution, the process of obtaining one or more high-resolution images from one or more low-resolution observations, has been a very attractive research topic over the last two decades. It has found practical applications in many real-world problems in different fields, from satellite and aerial imaging to medical image processing, to facial image analysis, text image analysis, sign and number plates reading, and biometrics recognition, to name a few. This has resulted in many research papers, each developing a new super-resolution algorithm for a specific purpose. The current comprehensive survey provides an overview of most of these published works by grouping them in a broad taxonomy. For each of the groups in the taxonomy, the basic concepts of the algorithms are first explained and then the paths through which each of these groups have evolved are given in detail, by mentioning the contributions of different authors to the basic concepts of each group. Furthermore, common issues in super-resolution algorithms, such as imaging models and registration algorithms, optimization of the cost functions employed, dealing with color information, improvement factors, assessment of super-resolution algorithms, and the most commonly employed databases are discussed.

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Super-resolution: a comprehensive survey

Recent advances in airborne and spaceborne hyperspectral imaging technology have provided end users with rich spectral, spatial, and temporal information. They have made a plethora of applications feasible for the analysis of large areas of the Earth?s surface. However, a significant number of factors-such as the high dimensions and size of the hyperspectral data, the lack of training samples, mixed pixels, light-scattering mechanisms in the acquisition process, and different atmospheric and geometric distortions-make such data inherently nonlinear and complex, which poses major challenges for existing methodologies to effectively process and analyze the data sets. Hence, rigorous and innovative methodologies are required for hyperspectral image (HSI) and signal processing and have become a center of attention for researchers worldwide.

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Advances in Hyperspectral Image and Signal Processing: A Comprehensive Overview of the State of the Art

LMS adaptive cancellation has been found to be effective in various applications of active noise control of periodic disturbances. A deterministic periodic waveform can be used for the reference when the period of the disturbance is known a priori. However, the algorithm behavior is determined by so-called Non-Wiener solutions. This paper presents a new vector subspace model for simplifying the analysis of the Non-Wiener behavior. The LMS weights are modelled as a deterministic time-varying mean plus a zero-mean fluctuating part. Each weight component is analyzed separately with the subspace model.

Analysis of an LMS adaptive feedforward controller for periodic disturbance rejection: Non-wiener solutions for the LMS algorithm with a noisy reference-revisited

Robust recursive least squares algorithm for automotive suspension identification

Endmember (EM) variability has an important impact on the performance of hyperspectral image (HI) analysis algorithms. Recently, extended linear mixing models have been proposed to account for EM variability in the spectral unmixing (SU) problem. The direct use of these models has led to severely ill-posed optimization problems. Different regularization strategies have been considered to deal with this issue, but none so far has consistently exploited the information provided by the existence of multiple pure pixels often present in HIs. In this work, we propose to break the SU problem into a sequence of two problems. First, we use pure pixel information to estimate an interpolated tensor of scaling factors representing spectral variability. This is done by considering the spectral variability to be a smooth function over the HI and confining the energy of the scaling tensor to a low-rank structure. Afterwards, we solve a matrix-factorization problem to estimate the fractional abundances using the variability scaling factors estimated in the previous step, what leads to a significantly more well-posed problem. Simulation swith synthetic and real data attest the effectiveness of the proposed strategy.

Improved Hyperspectral Unmixing With Endmember Variability Parametrized Using an Interpolated Scaling Tensor

Quantization effects in the NLMS algorithm are investigated for a white Gaussian data model. Nonlinear recursions are derived for the weight mean error and mean-square deviation (MSD) that include the effects of various quantization operations in the implementation of the algorithm. The nonlinear recursion for the MSD is solved numerically and shown in excellent agreement with Monte Carlo simulations, supporting the theoretical model assumptions. The theory is extended to tracking a Markov channel and accurately predicts the tracking behavior as well. For the white data case, the excess mean square-error (EMSE) is simply related to the MSD. The tradeoff between the number of bits in the quantizers, steady-state EMSE, and algorithm convergence rate is studied using these results.

A stochastic analysis of the NLMS algorithm implemented in finite precision

We introduce a new space-time adaptive processing (STAP) algorithm for clutter mitigation in airborne MTI radar systems. The algorithm, named RSMI, is order-recursive and allows data processing in the fast-time, an idle period for most algorithms (data acquisition period). We show that the RSMI optimum output converges in the mean-square sense to the SMI optimum output as the number of pulses increases from 1 to the SMI order, always with smaller computational cost. We also show that the whole CPI may not be required to obtain satisfactory performance. Thus, the new algorithm opens the possibility of real-time adaptation to further reduce complexity

Jose C. M. Bermudez

Papers

Analysis of an LMS adaptive feedforward controller for periodic disturbance rejection: Non-wiener solutions for the LMS algorithm with a noisy reference-revisited

Robust recursive least squares algorithm for automotive suspension identification

Improved Hyperspectral Unmixing With Endmember Variability Parametrized Using an Interpolated Scaling Tensor

A stochastic analysis of the NLMS algorithm implemented in finite precision

The RSMI algorithm for airborne MTI radar