相关论文: Polarization of the Renyi Information Dimension wi…

This paper investigates the construction of deterministic matrices preserving the entropy of random vectors with a given probability distribution. In particular, it is shown that for random vectors having i.i.d. discrete components, this is…

R\'enyi Information Dimension (RID) plays a central role in quantifying the compressibility of random variables with singularities in their distribution, encompassing and extending beyond the class of sparse sources. The RID, from a high…

Compressive sensing involves the inversion of a mapping $SD \in \mathbb{R}^{m \times n}$, where $m < n$, $S$ is a sensing matrix, and $D$ is a sparisfying dictionary. The restricted isometry property is a powerful sufficient condition for…

In this paper, we study the lossless analog compression for i.i.d. nonsingular signals via the polarization-based framework. We prove that for nonsingular source, the error probability of maximum a posteriori (MAP) estimation polarizes…

Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…

The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the…

One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…

This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors $\pm X_1,...,\pm X_N\in\R^n$, ($N\ge n$). We introduce a class of random sampling matrices and show that they…

Hadamard matrix-based aperture encoding is a method for producing synthetic aperture datasets with high Signal-to-Noise Ratios. Recently, the pulse inversion capabilities of bias-sensitive Top-Orthogonal to Bottom Electrode (TOBE) arrays…

Consider the problem of detecting one of M i.i.d. Gaussian signals corrupted in white Gaussian noise. Conventionally, matched filters are used for detection. We first show that the outputs of the matched filter form a set of asymptotically…

EXSY, TOCSY and NOESY lie at the foundation of homonuclear NMR experiments in organic and pharmaceutical chemistry, as well as in structural biology. Limited magnetization transfer efficiency is an intrinsic downside of these methods,…

Compressed Sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…

In this paper, we propose a method of structured construction of the optimal measurement matrix for noiseless compressed sensing (CS), which achieves the minimum number of measurements which only needs to be as large as the sparsity of the…

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…

Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of challenging problems in compressed sensing is to construct deterministic matrices having restricted isometry property (RIP). So…

Wireless sensors are everywhere. To address their energy supply, we proposed an end-to-end design for polar-coded integrated data and energy networking (IDEN), where the conventional signal processing modules, such as…