L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

L2 and L1Trend Filtering: A Kalman Filter Approach amodification

<pre>$\ell_2$ and $\ell_1$ trend filtering are two of the most popular denoising algorithms that are widely used in science, engineering, and statistical signal and image processing applications. They are typically treated as separate entities, with the former as a linear time invariant (LTI) filter which is commonly used for smoothing the noisy data and detrending the time-series signals while the latter is a nonlinear filtering method suited for the estimation of piecewise-polynomial signals (\eg, piecewise-constant, piecewise-linear, piecewise-quadratic and \etc) observed in additive white Gaussian noise. In this article, we propose a Kalman filtering approach to design and implement $\ell_2$ and $\ell_1$ trend filtering % (QV and TV regularization) with the aim of teaching these two approaches and explaining their differences and similarities. Hopefully the framework presented in this article will provide a straightforward and unifying platform for understanding the basis of these two approaches. In addition, the material may be useful in lecture courses in signal and image processing, or indeed, it could be useful to introduce our colleagues in signal processing to the application of Kalman filtering in the design of $\ell_2$ and $\ell_1$ trend filtering.</pre>

Graph-Based Feature Reduction for Three-Dimensional Gabor Filter in PolSAR Image Classification

Polarimetric Synthetic Aperture Radar (PolSAR) image classification is one of the most important applications in remote sensing. In this paper, the goal is PolSAR image classification and also introduce a method to obtain the best result for PolSAR image classification and recognition. In this article, we present the 3D-Gabor filters as a way in order to feature extraction of PolSAR images and get the best result with high accuracy for PolSAR image classification. Also, we prove that the 3D-Gabor filter approach can get higher accuracy than traditional methods for PolSAR images classification, but one of the most important challenges of 3D-Gabor filters is the number of features that are extracted from them. Therefore, by using 3D-Gabor filter we can't reach the optimal result because of the curse of dimensionality. So, to achieve the best results we propose a method to reduce the features that are extracted from 3D-Gabor filters. By using our proposed method, the features will be mapped to a new space with smaller dimensions. In the end, the experimental results indicate the superiority of the proposed method.

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data

Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

An ensemble reconstruction of global monthly sea surface temperature and sea ice concentration 1000–1849

This paper describes a global monthly gridded Sea Surface Temperature (SST) and Sea Ice Concentration (SIC) dataset for the period 1000–1849, which can be used as boundary conditions for atmospheric model simulations. The reconstruction is based on existing coarse-resolution annual temperature ensemble reconstructions, which are then augmented with intra-annual and sub-grid scale variability. The intra-annual component of HadISST.2.0 and oceanic indices estimated from the reconstructed annual mean are used to develop grid-based linear regressions in a monthly stratified approach. Similarly, we reconstruct SIC using analog resampling of HadISST.2.0 SIC (1941–2000), for both hemispheres. Analogs are pooled in four seasons, comprising of 3-months each. The best analogs are selected based on the correlation between each member of the reconstructed SST and its target. For the period 1780 to 1849, We assimilate historical observations of SST and night-time marine air temperature from the ICOADS dataset into our reconstruction using an offline Ensemble Kalman Filter approach. The resulting dataset is physically consistent with information from models, proxies, and observations.

Unscented Particle Filter Approach for Underwater Target Tracking

This research aims to find an appropriate approach to improve system accuracy in the Doppler-bearing tracking (DBT) problem for target estimation. The topic of DBT problem is to achieve a target trajectory using bearing and frequency measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. The unscented particle filter approach is proposed to estimate the accuracy in the target motion parameters (TMP). This approach requires the observer maneuver so that the target trajectory is observable. Although in recent research papers, DBT has been proven to work efficiently without observer maneuver, TMP is unknown to the observer, and consequently, there is a need for observer maneuver. So, the algorithm is simulated with observer following s-maneuver and without any maneuver executed by the observer, and results are compared. The effectiveness of the solution and results are determined by using MATLAB simulation. It is shown that the truthfulness of the outcome is superior when the observer performs s-maneuver while compared to that without observer maneuver.