Related papers: Lossy Compression of General Random Variables
A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized…
JPEG is still the most widely used image compression algorithm. Most image compression algorithms only consider uncompressed original image, while ignoring a large number of already existing JPEG images. Recently, JPEG recompression…
Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression…
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…
This paper considers the use of total variation regularization in the recovery of approximately gradient sparse signals from their noisy discrete Fourier samples in the context of compressed sensing. It has been observed over the last…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Image compression is a fundamental research field and many well-known compression standards have been developed for many decades. Recently, learned compression methods exhibit a fast development trend with promising results. However, there…
With the increasing number of images and videos consumed by computer vision algorithms, compression methods are evolving to consider both perceptual quality and performance in downstream tasks. Traditional codecs can tackle this problem by…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Recent work has shown that Variational Autoencoders (VAEs) can be used to upper-bound the information rate-distortion (R-D) function of images, i.e., the fundamental limit of lossy image compression. In this paper, we report an improved…
This paper outlines an end-to-end optimized lossy image compression framework using diffusion generative models. The approach relies on the transform coding paradigm, where an image is mapped into a latent space for entropy coding and, from…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
Contemporary lossy image and video coding standards rely on transform coding, the process through which pixels are mapped to an alternative representation to facilitate efficient data compression. Despite impressive performance of…
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…
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…
Lossy compression algorithms are typically designed and analyzed through the lens of Shannon's rate-distortion theory, where the goal is to achieve the lowest possible distortion (e.g., low MSE or high SSIM) at any given bit rate. However,…
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…