Related papers: Rate-Distortion Theory for General Sets and Measur…
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we…
We apply statistical mechanics to an inverse problem of linear mapping to investigate the physics of the irreversible compression. We use the replica symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's result.…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
In lossy compression, Blau and Michaeli [5] introduced the information rate-distortion-perception (RDP) function, extending traditional rate-distortion theory by incorporating perceptual quality. More recently, this framework was expanded…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
End-to-end optimized neural image compression (NIC) has obtained superior lossy compression performance recently. In this paper, we consider the problem of rate-distortion (R-D) characteristic analysis and modeling for NIC. We make efforts…
We consider the spectral radius of a large random matrix $X$ with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the…
Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we…
Rate distortion theory is concerned with optimally encoding a given signal class $\mathcal{S}$ using a budget of $R$ bits, as $R\to\infty$. We say that $\mathcal{S}$ can be compressed at rate $s$ if we can achieve an error of…
Even though rate-distortion optimization is a crucial part of traditional image and video compression, not many approaches exist which transfer this concept to end-to-end-trained image compression. Most frameworks contain static compression…