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We address the Normalized Signal to Noise Ratio (NSNR) metric defined in the seminal paper by Reed, Mallett and Brennan on adaptive detection. The setting is detection of a target vector in additive correlated noise. NSNR is the ratio between the SNR of a linear detector which uses an estimated noise covariance and the SNR of clairvoyant detector based on the exact unknown covariance. It is not obvious how to evaluate NSNR since it is a function of the target vector. To close this gap, we consider the NSNR associated with the worst target. Using the Kantorovich Inequality, we provide a closed form solution for the worst case NSNR. Then, we prove that the classical Gaussian Kullback Leibler (KL) divergence bounds it. Numerical experiments with different true covariances and various estimates also suggest that the KL metric is more correlated with the NSNR metric than competing norm based metrics.

We consider the use of deep learning for covariance estimation. We propose to globally learn a neural network that will then be applied locally at inference time. Leveraging recent advancements in self-supervised foundational models, we train the network without any labeling by simply masking different samples and learning to predict their covariance given their surrounding neighbors. The architecture is based on the popular attention mechanism. Its main advantage over classical methods is the automatic exploitation of global characteristics without any distributional assumptions or regularization. It can be pre-trained as a foundation model and then be repurposed for various downstream tasks, e.g., adaptive target detection in radar or hyperspectral imagery.

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this challenging problem were based on geometrical approaches or computationally intensive variational methods. In contrast, we propose a conventional expectation maximization (EM) algorithm which embeds importance sampling. For this purpose, the proposal distribution is chosen as a simple surrogate distribution of the target posterior that is guaranteed to lie in the simplex. This distribution is based on the Gaussian linear minimum mean squared error (LMMSE) approximation which is accurate at high signal-to-noise ratio. Numerical experiments in different settings demonstrate the advantages of this adaptive surrogate over state-of-the-art methods.

We consider the problem of target detection with a constant false alarm rate (CFAR). This constraint is crucial in many practical applications and is a standard requirement in classical composite hypothesis testing. In settings where classical approaches are computationally expensive or where only data samples are given, machine learning methodologies are advantageous. CFAR is less understood in these settings. To close this gap, we introduce a framework of CFAR constrained detectors. Theoretically, we prove that a CFAR constrained Bayes optimal detector is asymptotically equivalent to the classical generalized likelihood ratio test (GLRT). Practically, we develop a deep learning framework for fitting neural networks that approximate it. Experiments of target detection in different setting demonstrate that the proposed CFARnet allows a flexible tradeoff between CFAR and accuracy., Comment: arXiv admin note: substantial text overlap with arXiv:2206.05747

We consider the use of machine learning for hypothesis testing with an emphasis on target detection. Classical model-based solutions rely on comparing likelihoods. These are sensitive to imperfect models and are often computationally expensive. In contrast, data-driven machine learning is often more robust and yields classifiers with fixed computational complexity. Learned detectors usually provide high accuracy with low complexity but do not have a constant false alarm rate (CFAR) as required in many applications. To close this gap, we propose to add a term to the loss function that promotes similar distributions of the detector under any null hypothesis scenario. Experiments show that our approach leads to near CFAR detectors with similar accuracy as their competitors.

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non-linear settings via deep learning with bias constraints. The classical approach to designing non-linear MVUEs is through maximum likelihood estimation (MLE) which often involves real-time computationally challenging optimizations. On the other hand, deep learning methods allow for non-linear estimators with fixed computational complexity. Learning based estimators perform optimally on average with respect to their training set but may suffer from significant bias in other parameters. To avoid this, we propose to add a simple bias constraint to the loss function, resulting in an estimator we refer to as Bias Constrained Estimator (BCE). We prove that this yields asymptotic MVUEs that behave similarly to the classical MLEs and asymptotically attain the Cramer Rao bound. We demonstrate the advantages of our approach in the context of signal to noise ratio estimation as well as covariance estimation. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance. Examples include distributed sensor networks and data augmentation in test-time. In such applications, we show that BCE leads to asymptotically consistent estimators.

Detection and classification of objects in overhead images are two important and challenging problems in computer vision. Among various research areas in this domain, the task of fine-grained classification of objects in overhead images has become ubiquitous in diverse real-world applications, due to recent advances in high-resolution satellite and airborne imaging systems. The small inter-class variations and the large intra class variations caused by the fine grained nature make it a challenging task, especially in low-resource cases. In this paper, we introduce COFGA a new open dataset for the advancement of fine-grained classification research. The 2,104 images in the dataset are collected from an airborne imaging system at 5 15 cm ground sampling distance, providing higher spatial resolution than most public overhead imagery datasets. The 14,256 annotated objects in the dataset were classified into 2 classes, 15 subclasses, 14 unique features, and 8 perceived colors a total of 37 distinct labels making it suitable to the task of fine-grained classification more than any other publicly available overhead imagery dataset. We compare COFGA to other overhead imagery datasets and then describe some distinguished fine-grain classification approaches that were explored during an open data-science competition we have conducted for this task.

We consider distance functions between conditional distributions. We focus on the Wasserstein metric and its Gaussian case known as the Frechet Inception Distance (FID). We develop conditional versions of these metrics, analyze their relations and provide a closed form solution to the conditional FID (CFID) metric. We numerically compare the metrics in the context of performance evaluation of modern conditional generative models. Our results show the advantages of CFID compared to the classical FID and mean squared error (MSE) measures. In contrast to FID, CFID is useful in identifying failures where realistic outputs which are not related to their inputs are generated. On the other hand, compared to MSE, CFID is useful in identifying failures where a single realistic output is generated even though there is a diverse set of equally probable outputs.

Classification between thousands of classes in high-resolution images is one of the heavily studied problems in deep learning over the last decade. However, the challenge of fine-grained multi-class classification of objects in aerial images, especially in low resource cases, is still challenging and an active area of research in the literature. Solving this problem can give rise to various applications in the field of scene understanding and classification and re-identification of specific objects from aerial images. In this paper, we provide a description of our dataset - COFGA of multi-class annotated objects in aerial images. We examine the results of existing state-of-the-art models and modified deep neural networks. Finally, we explain in detail the first published competition for solving this task.

In this paper we consider Multiple-Input-Multiple-Output (MIMO) detection using deep neural networks. We introduce two different deep architectures: a standard fully connected multi-layer network, and a Detection Network (DetNet) which is specifically designed for the task. The structure of DetNet is obtained by unfolding the iterations of a projected gradient descent algorithm into a network. We compare the accuracy and runtime complexity of the purposed approaches and achieve state-of-the-art performance while maintaining low computational requirements. Furthermore, we manage to train a single network to detect over an entire distribution of channels. Finally, we consider detection with soft outputs and show that the networks can easily be modified to produce soft decisions.

In this paper, we consider the use of deep neural networks in the context of Multiple-Input-Multiple-Output (MIMO) detection. We give a brief introduction to deep learning and propose a modern neural network architecture suitable for this detection task. First, we consider the case in which the MIMO channel is constant, and we learn a detector for a specific system. Next, we consider the harder case in which the parameters are known yet changing and a single detector must be learned for all multiple varying channels. We demonstrate the performance of our deep MIMO detector using numerical simulations in comparison to competing methods including approximate message passing and semidefinite relaxation. The results show that deep networks can achieve state of the art accuracy with significantly lower complexity while providing robustness against ill conditioned channels and mis-specified noise variance.

High harmonic generation (HHG) is a unique and useful process in which infrared or visible radiation is frequency up converted into the extreme ultraviolet and x ray spectral regions. As a parametric process, high harmonic generation should conserve the radiation energy, momentum and angular momentum. Indeed, conservation of energy and momentum have been demonstrated. Angular momentum of optical beams can be divided into two components: orbital and spin (polarization). Orbital angular momentum is assumed to be conserved and recently observed deviations were attributed to propagation effects. On the other hand, conservation of spin angular momentum has thus far never been studied, neither experimentally nor theoretically. Here, we present the first study on the role of spin angular momentum in extreme nonlinear optics by experimentally generating high harmonics of bi chromatic elliptically polarized pump beams that interact with isotropic media. While observing that the selection rules qualitatively correspond to spin conservation, we unequivocally find that the process of converting pump photons into a single high-energy photon does not conserve angular momentum, i.e. this process is not self contained. In one regime, we numerically find that this major fundamental discrepancy can be explained if the harmonic photons are emitted in pairs. Yet in another regime, the ionizing electron carries the missing angular momentum. The results presented here, apart from exploring the very foundations of HHG, are also important for a variety of applications, as our system exhibits full control over the harmonics polarization, from circular through elliptical to linear polarization, without comprising the efficiency of the process. This work paves the way for a broad range of applications with HHG, from ultrafast circular dichroism to zepto-clocks and to attosecond quantum optics.

We propose a method for generating only even-order high harmonics. We formulate a condition for a shift in the relative-phase between bi-chromatic drivers that leads to a field sign-flip of only even-order harmonics. Induction of this sign-flip periodically during propagation gives rise to quasi phase matching of only even harmonics. We demonstrate this technique numerically and also show that it leads to attosecond pulse trains with constant carrier envelop phase with high repetition rate. This work opens the door for quasi-phase matching of high harmonics with a designed selective enhancement function., Comment: 5 figures