Related papers: Multiarray Signal Processing: Tensor decomposition…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
Modeling with multidimensional arrays, or tensors, often presents a problem due to high dimensionality. In addition, these structures typically exhibit inherent sparsity, requiring the use of regularization methods to properly characterize…
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…
A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean…
This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…