Related papers: Quantizers with Parameterized Distortion Measures
We introduce a distortion measure for images, Wasserstein distortion, that simultaneously generalizes pixel-level fidelity on the one hand and realism or perceptual quality on the other. We show how Wasserstein distortion reduces to a pure…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
This paper considers the problem of transmitting the difference of two jointly Gaussian sources over a two-user additive Gaussian noise multiple access channel (MAC). The goal is to recover this difference within an average mean squared…
Compressing large neural networks is an important step for their deployment in resource-constrained computational platforms. In this context, vector quantization is an appealing framework that expresses multiple parameters using a single…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
The Grassmann manifold G_{n,p}(L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space L^{n}, where L is either R or C. This paper considers an unequal dimensional quantization in which a source…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
This paper examines the quantization methods used in large-scale data analysis models and their hyperparameter choices. The recent surge in data analysis scale has significantly increased computational resource requirements. To address…
We consider the k-encoder source coding problem with a quadratic distortion measure. We show that among all source distributions with a given covariance matrix K, the jointly Gaussian source requires the highest rates in order to meet a…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…
This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements. The main contributions include the…
We define a regularized size-shape distortion (quality) measure for curved high-order elements on a Riemannian space. To this end, we measure the deviation of a given element, straight-sided or curved, from the stretching, alignment, and…
We consider the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an…
Distance transforms are a central tool in shape analysis, morphometry, and curve evolution problems. This work describes and investigates an artifact present in distance maps computed from sampled signals. Namely, sampling reflects through…
Traditionally, quantization is designed to minimize the reconstruction error of a data source. When considering downstream classification tasks, other measures of distortion can be of interest; such as the 0-1 classification loss.…
Deep Neural Networks reached state-of-the-art performance across numerous domains, but this progress has come at the cost of increasingly large and over-parameterized models, posing serious challenges for deployment on resource-constrained…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
The distortion-rate function of output-constrained lossy source coding with limited common randomness is analyzed for the special case of squared error distortion measure. An explicit expression is obtained when both source and…