In this paper, a multi-feature detector based on isolation forest (iForest) algorithm is developed to detect floating small targets in sea clutter. The conventional multi-feature detector can only process three features or less. The proposed detector aims to break the limitation of feature dimensions' number of the existed feature-based detectors and to improve the detection performance. It transforms the detection of floating small target into an anomaly detection problem in a high-dimensional feature space, breaking the limitation of the number of features. Firstly, a modified isolation forest is constructed from multiple features extracted from sea clutter. Meanwhile, the relative Doppler coefficient of variation (RCV) is proposed and added into the feature library. Then, taking the average path length as detection statistic, the detection threshold is obtained by Monte-Carlo technique at the given false alarm probability (PFA). Finally, the final decision is made by comparing the path length calculated from the cell under test (CUT) of radar returns with the detection threshold. Detection performances are evaluated based on twenty measured IPIX radar data sets. The experiment results show that the multi-feature detector based on isolation forest can obtain a significant performance improvement and has lower computation cost compared with the existed detectors.

In this paper, we consider nonsubsampled graph filter banks (NSGFBs) to process data on a sparse graph. The analysis filter banks of NSGFBs have small bandwidth, pass/block the normalized constant signal, and have stability on $\ell^2$ . Given an analysis filter bank with small bandwidth, we introduce algebraic and optimization methods to construct well-localized synthesis filter banks such that the corresponding NSGFBs provide a perfect signal reconstruction in the noiseless setting. In this paper, we also prove that the proposed NSGFBs can control the resonance effect in the presence of bounded noise and they can limit the influence of shot noise primarily to a small neighborhood near its location on the graph. We later introduce an iterative distributed algorithm to implement the proposed NSGFBs, and we develop an NSGFB-based denoising technique which is demonstrated to have satisfactory performance on noise suppression.

Graph Signal Processing (GSP) leverages pair-wise relationship between nodes of a graph to formulate operators on signals defined over the nodes. Most existing graph signal operators in the literature are linear, and can be described by linear transformation matrices. Recently, works are emerging that consider the time correlation of graph signals, leading to time-vertex signal processing. By exploiting the joint correlations across the graph topology and time, better results can be obtained. In this work, we propose a median operator that will leverage the joint correlation, for denoising time-varying graph signals. The median operator, known for its robustness to outliers in statistics, has been very successful in traditional signal processing, especially for images. The efficient and highly localised graph median filters developed here are applied to denoising real world sensor network data. Real world sensor nodes are usually resource limited in terms of their computational and communication capacity, hence the imperative requirement for efficient localised filters. Comprehensive experimental results will show that in some cases, the performance is significantly better than the equivalent linear operator counterpart.

Graph signal processing (GSP) is a field that deals with data residing on irregular domains, i.e. graph signals. In this field, the graph filter bank is one of the most important developments, owing to its ability to provide multiresolution analysis of graph signals. However, most of the current research on graph filter bank focuses on static graph signals. The research does not exploit the temporal correlations of time-varying signals in real-world applications, such as in wireless sensor networks. In this paper, the theory and design of joint time-vertex nonsubsampled filter bank are developed, using a generalized product graph framework. Several methods are proposed to design the filter bank with perfect reconstruction, while still achieving filters with good spectral characteristics. A notable feature of the designed filter bank is that it can be completely realized in a distributed manner. The subband filters are either of polynomial type or defined implicitly via iterative equations. In either case, implementing the subband filters requires only the exchange of information between neighboring nodes. The filter banks are therefore of low implementation complexity and suitable for processing large time-varying datasets. Numerical examples will demonstrate the effectiveness of the proposed designed methods. Application in time-varying graph signal denoising will show the superiority of joint time-vertex filter bank over other methods.

Graph filter banks play a crucial role in the vertex and spectral representation of graph signals. The notion of two-channel nonsubsampled graph filter banks (NSGFBs) on an undirected graph was introduced recently. The absence of downsampling/upsampling operators allows greater flexibility in the design of NSGFBs that achieve perfect reconstruction. However the design of NSGFBs that take the spectral response into account has not been adequately addressed yet. Based on the polynomial/rational lifting scheme, this letter presents a simple method to design NSGFBs with good spectral response and perfect reconstruction. Experimental results will demonstrate the effectiveness of the proposed method in tailoring the spectral responses of the lifted NSGFBs. Application of the NSGFB to denoising will also be considered.

The recovery of missing samples from available noisy measurements is a fundamental problem in signal processing. In the graph setting, the aim is to recover missing samples on a subset of vertices using samples from other vertices. This process is also sometimes known as graph signal inpainting, reconstruction, forecasting or inference. Many of the existing algorithms do not scale well with the size of the graph and/or they cannot be implemented efficiently in a distributed manner. In this paper, we develop efficient distributed algorithms for the recovery of time-varying graph signals. The a priori assumptions are that the signal is smooth with respect to the graph topology and correlative across time. These assumptions can be incorporated in an optimization formulation of the algorithm via Tikhonov regularization terms. Although this approach is widely used in many graph signal processing problems, our formulation is tailored to yield algorithms that can be efficiently implemented in a distributed manner. Two different distributed algorithms, arising from two different formulations, are proposed to solve the optimization problems. The first involves the $l_2$ norm, and a distributed least squared recovery algorithm (DLSRA) is proposed that leverages the graph topology and sparsity of the corresponding Hessian matrix. The proposed DLSRA is different from other Newton-like methods as there is no need to update the approximate inverse of the Hessian during the iterations. The second involves the $l_1$ norm and the philosophy of the alternating direction method of multipliers (ADMM) is utilized to develop the algorithm. To achieve a totally distributed algorithm, the proposed inexact Newton method is incorporated into the conventional ADMM to give a distributed ADMM recovery algorithm (DAMRA). The two distributed algorithms require only data exchanges between vertices in localized neighbourhood subgraphs. This is in contrast to centralized methods where global data exchanges are required. Experiments on a variety of synthetic and real-world datasets demonstrate that the proposed algorithms are superior to the existing methods