Related papers: A new probabilistic model for optimal frames in er…

Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction error when erasure occurs,is a deep-rooted problem in frame…

Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this…

This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and…

The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs)…

Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…

The perceived quality of real-time media delivered over IP networks depends on both the rate and burstiness of packet loss. In this paper, we develop a new mathematical model for the residual burstiness of loss under erasure coding. We…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

We propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…

In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate…

An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…

In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…

Data erasure can often occur in communication. Guarding against erasures involves redundancy in data representation. Mathematically this may be achieved by redundancy through the use of frames. One way to measure the robustness of a frame…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for…

We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category…

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…

Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…