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Table Of Integrals Series And Products

Due to object detection’s close relationship with video analysis and image understanding, it has attracted much research attention in recent years. Traditional object detection methods are built on handcrafted features and shallow trainable architectures. Their performance easily stagnates by constructing complex ensembles that combine multiple low-level image features with high-level context from object detectors and scene classifiers. With the rapid development in deep learning, more powerful tools, which are able to learn semantic, high-level, deeper features, are introduced to address the problems existing in traditional architectures. These models behave differently in network architecture, training strategy, and optimization function. In this paper, we provide a review of deep learning-based object detection frameworks. Our review begins with a brief introduction on the history of deep learning and its representative tool, namely, the convolutional neural network. Then, we focus on typical generic object detection architectures along with some modifications and useful tricks to improve detection performance further. As distinct specific detection tasks exhibit different characteristics, we also briefly survey several specific tasks, including salient object detection, face detection, and pedestrian detection. Experimental analyses are also provided to compare various methods and draw some meaningful conclusions. Finally, several promising directions and tasks are provided to serve as guidelines for future work in both object detection and relevant neural network-based learning systems.

Object Detection With Deep Learning: A Review

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Sphere Packings, Lattices and Groups

Frequencies from 100 GHz to 3 THz are promising bands for the next generation of wireless communication systems because of the wide swaths of unused and unexplored spectrum. These frequencies also offer the potential for revolutionary applications that will be made possible by new thinking, and advances in devices, circuits, software, signal processing, and systems. This paper describes many of the technical challenges and opportunities for wireless communication and sensing applications above 100 GHz, and presents a number of promising discoveries, novel approaches, and recent results that will aid in the development and implementation of the sixth generation (6G) of wireless networks, and beyond. This paper shows recent regulatory and standard body rulings that are anticipating wireless products and services above 100 GHz and illustrates the viability of wireless cognition, hyper-accurate position location, sensing, and imaging. This paper also presents approaches and results that show how long distance mobile communications will be supported to above 800 GHz since the antenna gains are able to overcome air-induced attenuation, and present methods that reduce the computational complexity and simplify the signal processing used in adaptive antenna arrays, by exploiting the Special Theory of Relativity to create a cone of silence in over-sampled antenna arrays that improve performance for digital phased array antennas. Also, new results that give insights into power efficient beam steering algorithms, and new propagation and partition loss models above 100 GHz are given, and promising imaging, array processing, and position location results are presented. The implementation of spatial consistency at THz frequencies, an important component of channel modeling that considers minute changes and correlations over space, is also discussed. This paper offers the first in-depth look at the vast applications of THz wireless products and applications and provides approaches for how to reduce power and increase performance across several problem domains, giving early evidence that THz techniques are compelling and available for future wireless communications.

/pdf/wireless-communications-and-applications-above-100-ghz-arnwwogno0.pdf

Wireless Communications and Applications Above 100 GHz: Opportunities and Challenges for 6G and Beyond

Several measures for the density of sets of integers have been proposed, such as the asymptotic density, the Schnirelmann density, and the Dirichlet density. There has been some work in the literature on extending some of these concepts of density to higher dimensional sets of integers. In this work, we propose an extension of the Dirichlet density for sets of Gaussian integers and investigate some of its properties.

An Extension of the Dirichlet Density for Sets of Gaussian Integers

The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and
dimensionality reduction. The KLT is able to optimally retain the signal energy
in only few transform components, being mathematically suitable for image and
video compression. However, in practice, because of its high computational cost
and dependence on the input signal, its application in real-time scenarios is
precluded. This work proposes low-computational cost approximations for the
KLT. We focus on the blocklengths $N \in \{4, 8, 16, 32 \}$ because they are
widely employed in image and video coding standards such as JPEG and high
efficiency video coding (HEVC). Extensive computational experiments demonstrate
the suitability of the proposed low-complexity transforms for image and video
compression.

Data-independent Low-complexity KLT Approximations for Image and Video Coding

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier intensive, and accumulate round-off errors. Recently proposed fast algorithm arithmetic cosine transform (ACT) calculates the DCT exactly using only additions and integer constant multiplications, with very low area complexity, for null mean input sequences. The ACT can also be computed non-exactly for any input sequence, with low area complexity and low power consumption, utilizing the novel architecture described. However, as a trade-off, the ACT algorithm requires 10 non-uniformly sampled data points to calculate the 8-point DCT. This requirement can easily be satisfied for applications dealing with spatial signals such as image sensors and biomedical sensor arrays, by placing sensor elements in a non-uniform grid. In this work, a hardware architecture for the computation of the null mean ACT is proposed, followed by a novel architectures that extend the ACT for non-null mean signals. All circuits are physically implemented and tested using the Xilinx XC6VLX240T FPGA device and synthesized for 45 nm TSMC standard-cell library for performance assessment.

VLSI Computational Architectures for the Arithmetic Cosine Transform

This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an analysis with a filter bank of constant quality factor is revisited on these bases. It is shown that if the wavelet spectral support is limited into the band $[f_m,f_M]$, then an orthogonal analysis is guaranteed provided that $f_M \leq 3f_m$, a quite simple result, but that invokes some parallel with the Nyquist rate. Nevertheless, in cases of orthogonal wavelets whose spectrum does not verify this condition, it is shown how to construct an "equivalent" filter bank with no spectral overlapping.

A Kotel'nikov Representation for Wavelets

The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a robust estimation process is proposed as a more realistic approach to model this type of data. This article aims at obtaining Rayleigh regression model parameter estimators robust to the presence of outliers. The proposed approach considered the weighted maximum likelihood method and was submitted to numerical experiments using simulated and measured SAR images. Monte Carlo simulations were employed for the numerical assessment of the proposed robust estimator performance in finite signal lengths, their sensitivity to outliers, and the breakdown point. For instance, the nonrobust estimators show a relative bias value 65-fold larger than the results provided by the robust approach in corrupted signals. In terms of sensitivity analysis and break down point, the robust scheme resulted in a reduction of about 96% and 10%, respectively, in the mean absolute value of both measures, in compassion to the nonrobust estimators. Moreover, two SAR datasets were used to compare the ground type and anomaly detection results of the proposed robust scheme with competing methods in the literature.

/pdf/robust-rayleigh-regression-method-for-sar-image-processing-3l3h0ehg4w.pdf

Renato J. Cintra

Papers

An Extension of the Dirichlet Density for Sets of Gaussian Integers

Data-independent Low-complexity KLT Approximations for Image and Video Coding

VLSI Computational Architectures for the Arithmetic Cosine Transform

A Kotel'nikov Representation for Wavelets

Robust Rayleigh Regression Method for SAR Image Processing in Presence of Outliers