A novel insight to the SBR2 algorithm for diagonalising Para-Hermitian matrices

The second order sequential best rotation (SBR2) algorithm was originally developed for achieving the strong decorrelation of convolutively mixed sensor array signals. It was observed that the algorithm always seems to produce spectrally majorized output signals, but this property has not previously been proven. In this work, we have taken a fresh look at the SBR2 algorithm in terms of its potential for optimizing the subband coding gain. It is demonstrated how every iteration of the SBR2 algorithm must lead to an increase in the subband coding gain until it comes arbitrarily close to its maximum possible value. Since the algorithm achieves both strong decorrelation and optimal subband coding, it follows that it must also produce spectral majorisation. A new quantity $\gamma$ associated with the coding gain optimization is introduced, and its monotonic behaviour brings a new insight to the convergence of the SBR2 algorithm

Multichannel spectral factorization algorithm using polynomial matrix eigenvalue decomposition

In this paper, we present a new multichannel spectral factorization algorithm which can be utilized to calculate the approximate spectral factor of any para-Hermitian polynomial matrix. The proposed algorithm is based on an iterative method for polynomial matrix eigenvalue decomposition (PEVD). By using the PEVD algorithm, the multichannel spectral factorization problem is simply broken down to a set of single channel problems which can be solved by means of existing one-dimensional spectral factorization algorithms. In effect, it transforms the multichannel spectral factorization problem into one which is much easier to solve

Structure Invariant Transformation for better Adversarial Transferability

Given the severe vulnerability of Deep Neural Networks (DNNs) against adversarial examples, there is an urgent need for an effective adversarial attack to identify the deficiencies of DNNs in security-sensitive applications. As one of the prevalent black-box adversarial attacks, the existing transfer-based attacks still cannot achieve comparable performance with the white-box attacks. Among these, input transformation based attacks have shown remarkable effectiveness in boosting transferability. In this work, we find that the existing input transformation based attacks transform the input image globally, resulting in limited diversity of the transformed images. We postulate that the more diverse transformed images result in better transferability. Thus, we investigate how to locally apply various transformations onto the input image to improve such diversity while preserving the structure of image. To this end, we propose a novel input transformation based attack, called Structure Invariant Attack (SIA), which applies a random image transformation onto each image block to craft a set of diverse images for gradient calculation. Extensive experiments on the standard ImageNet dataset demonstrate that SIA exhibits much better transferability than the existing SOTA input transformation based attacks on CNN-based and transformer-based models, showing its generality and superiority in boosting transferability. Code is available at https://github.com/xiaosen-wang/SIT.Comment: Accepted by ICCV 202

Life in the Fast Lane: Modeling the Fate of Glass Sponge Larvae in the Gulf Stream

Effective conservation management of deep-sea sponges, including design of appropriate marine protected areas, requires an understanding of the connectivity between populations throughout a species’ distribution. We provide the first consideration of larval connectivity among deep-sea sponge populations along the southeastern coast of North America, illustrate the influence of the Gulf Stream on dispersal, and complement published distribution models by evaluating colonization potential. Connectivity among known populations of the hexactinellid sponge Vazella pourtalesii was simulated using a 3-D biophysical dispersal model throughout its distribution from Florida, United States to Nova Scotia, Canada. We found no exchange with an estimated pelagic larval duration of 2 weeks between populations north and south of Cape Hatteras, North Carolina at surface, mid-water and seabed release depths, irrespective of month of release or application of a horizontal diffusion constant specific to cross-Gulf Stream diffusivity. The population north of Cape Hatteras and south of Cape Cod was isolated. There was some evidence that Gulf Stream eddies formed near Cape Hatteras could travel to the northwest, connecting the populations in the two sub-regions, however that would require a much longer pelagic duration than what is currently known. More likely almost all larval settlement will be in the immediate area of the adults. At sub-regional scales, connectivity was found from the Strait of Florida through to the Blake Plateau, southeastern United States, with the latter area showing potential for recruitment from more than one source population. The influence of the Charleston Bump, a shallow feature rising from the Blake Plateau, was substantial. Particles seeded just north of the Bump were transported greater distances than those seeded to the south, some of which were caught in an associated gyre, promoting retention at the seabed. To the north on the Scotian Shelf, despite weaker currents and greater distances between known occurrences, unidirectional transport was detected from Emerald Basin to the Northeast Channel between Georges and Browns Banks. These major conclusions remained consistent through simulations run with different averaging periods for the currents (decades to daily) and using two ocean model products (BNAM and GLORYS12V1)

Multiple shift second order sequential best rotation algorithm for polynomial matrix EVD

In this paper, we present an improved version of the second order sequential best rotation algorithm (SBR2) for polynomial matrix eigenvalue decomposition of para-Hermitian matrices. The improved algorithmis entitledmultiple shift SBR2 (MS-SBR2) which is developed based on the original SBR2 algorithm. It can achieve faster convergence than the original SBR2 algorithm by means of transferring more off-diagonal energy onto the diagonal at each iteration. Its convergence is proved and also demonstrated by means of a numerical example. Furthermore, simulation results are included to compare its convergence characteristics and computational complexity with the original SBR2, sequential matrix diagonalization (SMD) and multiple shift maximum element SMD algorithms

Decomposition of optical MIMO systems using polynomial matrix factorization

Within the last years the multiple-input multiple-output (MIMO) technology has revolutionized the optical fiber community. Theoretically, the concept of MIMO is well understood and shows some similarities to wireless MIMO systems. The interference in broadband MIMO systems can be removed by applying a spatio-temporal vector coding (STVC) channel description and using singular value decomposition (SVD) in combination with signal pre- and post-processing. In this contribution a newly developed SVD algorithm for polynomial matrices (PMSVD) is analyzed and compared to the commonly used SVD-based STVC. The PMSVD is implemented by an iterative polynomial matrix eigenvalue decomposition (PEVD) algorithm, namely the second order sequential best rotation algorithm (SBR2). The bit-error rate (BER) performance is evaluated and optimized by applying bit and power allocation schemes. For our simulations, the specific impulse responses of the (2 × 2) MIMO channel, including a 1.4 km multi-mode fiber and optical couplers at both ends, are measured for the operating wavelength of 1576 nm. The computer simulation results show that the PMSVD could be an alternative signal processing approach compared to conventional SVD-based MIMO approaches in frequency-selective MIMO channels

Polynomial matrix eigenvalue decomposition techniques for multichannel signal processing

Polynomial eigenvalue decomposition (PEVD) is an extension of the eigenvalue decomposition (EVD) for para-Hermitian polynomial matrices, and it has been shown to be a powerful tool for broadband extensions of narrowband signal processing problems. In the context of broadband sensor arrays, the PEVD allows the para-Hermitian matrix that results from the calculation of a space-time covariance matrix of the convolutively mixed signals to be diagonalised. Once the matrix is diagonalised, not only can the correlation between different sensor signals be removed but the signal and noise subspaces can also be identified. This process is referred to as broadband subspace decomposition, and it plays a very important role in many areas that require signal separation techniques for multichannel convolutive mixtures, such as speech recognition, radar clutter suppression, underwater acoustics, etc. The multiple shift second order sequential best rotation (MS-SBR2) algorithm, built on the most established SBR2 algorithm, is proposed to compute the PEVD of para-Hermitian matrices. By annihilating multiple off-diagonal elements per iteration, the MS-SBR2 algorithm shows a potential advantage over its predecessor (SBR2) in terms of the computational speed. Furthermore, the MS-SBR2 algorithm permits us to minimise the order growth of polynomial matrices by shifting rows (or columns) in the same direction across iterations, which can potentially reduce the computational load of the algorithm. The effectiveness of the proposed MS-SBR2 algorithm is demonstrated by various para-Hermitian matrix examples, including randomly generated matrices with different sizes and matrices generated from source models with different dynamic ranges and relations between the sources’ power spectral densities. A worked example is presented to demonstrate how the MS-SBR2 algorithm can be used to strongly decorrelate a set of convolutively mixed signals. Furthermore, the performance metrics and computational complexity of MS-SBR2 are analysed and compared to other existing PEVD algorithms by means of numerical examples. Finally, two potential applications of theMS-SBR2 algorithm, includingmultichannel spectral factorisation and decoupling of broadband multiple-input multiple-output (MIMO) systems, are demonstrated in this dissertation