Related papers: On the Rate-Distortion-Perception Function for Gau…
In this paper, we develop {finite-time horizon} causal filters using the nonanticipative rate distortion theory. We apply the {developed} theory to {design optimal filters for} time-varying multidimensional Gauss-Markov processes, subject…
Quantum random variable, distortion operator are introduced based on canonical operators. As the lower bound of rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. General Gaussian…
In this paper, the rate-distortion theory of the Gray-Wyner lossy source coding system is investigated. For the case of jointly Gaussian distributed sources, we establish an expression for the rate-distortion function under the constraint…
3D Gaussian Splatting (3DGS) has become an emerging technique with remarkable potential in 3D representation and image rendering. However, the substantial storage overhead of 3DGS significantly impedes its practical applications. In this…
In this paper we invoke a nonanticipative information Rate Distortion Function (RDF) for sources with memory, and we analyze its importance in probabilistic matching of the source to the channel so that transmission of a symbol-by-symbol…
The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the…
Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
We establish a single-letter characterization of the fundamental distortion-rate-perception tradeoff with limited common randomness under the squared error distortion measure and the squared Wasserstein-2 perception measure. Moreover, it is…
This paper deals with the computation of a non-asymptotic lower bound by means of the nonanticipative rate-distortion function (NRDF) on the discrete-time zero-delay variable-rate lossy compression problem for discrete Markov sources with…
In this paper we consider the rate distortion problem of discrete-time, ergodic, and stationary sources with feed forward at the receiver. We derive a sequence of achievable and computable rates that converge to the feed-forward rate…
In this paper, we propose a novel function named Rate Distortion-in-Distortion (RDD) function as an extension of the classical rate-distortion (RD) function, where the expected distortion constraint is replaced by a Gromov-type distortion.…
We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components…
We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the…
For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar…
This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function…
Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it operates on sampled versions of the CT signals. When sampling is applied to a CT…
In lossy compression, the classical tradeoff between compression rate and reconstruction distortion has traditionally guided algorithm design. However, Blau and Michaeli [5] introduced a generalized framework, known as the…
Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…
The Gauss-Markov source produces $U_i = aU_{i-1} + Z_i$ for $i\geq 1$, where $U_0 = 0$, $|a|<1$ and $Z_i\sim\mathcal{N}(0, \sigma^2)$ are i.i.d. Gaussian random variables. We consider lossy compression of a block of $n$ samples of the…