Related papers: Tensor Completion from Regular Sub-Nyquist Samples
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
We propose Tensor-based 4D Sub-Nyquist Radar (TenDSuR) that samples in spectral, spatial, Doppler, and temporal domains at sub-Nyquist rates while simultaneously recovering the target's direction, Doppler velocity, and range without loss of…
We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…
Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be…
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This…
Magnetic resonance imaging (MRI) nowadays serves as an important modality for diagnostic and therapeutic guidance in clinics. However, the {\it slow acquisition} process, the dynamic deformation of organs, as well as the need for {\it…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
The Compressive Sensing (CS) as a novel acquisition approach that finds its usage in image processing. The hypothesis like this one assures signal recovery with high quality from decreased number of samples compared with the number required…
The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…
Radio maps are important enablers for many applications in wireless networks, ranging from network planning and optimization to fingerprint based localization. Sampling the complete map is prohibitively expensive in practice, so methods for…
Conventional approaches of sampling signals follow the celebrated theorem of Nyquist and Shannon. Compressive sampling, introduced by Donoho, Romberg and Tao, is a new paradigm that goes against the conventional methods in data acquisition…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…