A Recursive Method for Enumeration of Costas Arrays

In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically reduce the computational burden (when compared to the exhaustive search), and at the same time, still can find all possible Costas arrays of given size. Similar to exhaustive search, the proposed method can be conveniently implemented in parallel computing. The efficiency of the method is discussed based on theoretical and numerical results

Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.Comment: This is a pre-print version of the original conference paper that has been accepted at the 2018 IEEE Asilomar Conference on Signals, Systems, and Computer

Deep Signal Recovery with One-Bit Quantization

Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal reconstruction from its one-bit noisy measurements. Namely, we propose a model-based machine learning method and unfold the iterations of an inference optimization algorithm into the layers of a deep neural network for one-bit signal recovery. The resulting network, which we refer to as DeepRec, can efficiently handle the recovery of high-dimensional signals from acquired one-bit noisy measurements. The proposed method results in an improvement in accuracy and computational efficiency with respect to the original framework as shown through numerical analysis.Comment: This paper has been submitted to the 44th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019

HDR Imaging With One-Bit Quantization

Modulo sampling and dithered one-bit quantization frameworks have emerged as promising solutions to overcome the limitations of traditional analog-to-digital converters (ADCs) and sensors. Modulo sampling, with its high-resolution approach utilizing modulo ADCs, offers an unlimited dynamic range, while dithered one-bit quantization offers cost-efficiency and reduced power consumption while operating at elevated sampling rates. Our goal is to explore the synergies between these two techniques, leveraging their unique advantages, and to apply them to non-bandlimited signals within spline spaces. One noteworthy application of these signals lies in High Dynamic Range (HDR) imaging. In this paper, we expand upon the Unlimited One-Bit (UNO) sampling framework, initially conceived for bandlimited signals, to encompass non-bandlimited signals found in the context of HDR imaging. We present a novel algorithm rigorously examined for its ability to recover images from one-bit modulo samples. Additionally, we introduce a sufficient condition specifically designed for UNO sampling to perfectly recover non-bandlimited signals within spline spaces. Our numerical results vividly demonstrate the effectiveness of UNO sampling in the realm of HDR imaging.Comment: arXiv admin note: text overlap with arXiv:2308.0069