A vector quantization approach to universal noiseless coding and quantization

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions

A Progressive Universal Noiseless Coder

The authors combine pruned tree-structured vector quantization (pruned TSVQ) with Itoh's (1987) universal noiseless coder. By combining pruned TSVQ with universal noiseless coding, they benefit from the “successive approximation” capabilities of TSVQ, thereby allowing progressive transmission of images, while retaining the ability to noiselessly encode images of unknown statistics in a provably asymptotically optimal fashion. Noiseless compression results are comparable to Ziv-Lempel and arithmetic coding for both images and finely quantized Gaussian sources

Quantized Estimation of Gaussian Sequence Models in Euclidean Balls

A central result in statistical theory is Pinsker's theorem, which characterizes the minimax rate in the normal means model of nonparametric estimation. In this paper, we present an extension to Pinsker's theorem where estimation is carried out under storage or communication constraints. In particular, we place limits on the number of bits used to encode an estimator, and analyze the excess risk in terms of this constraint, the signal size, and the noise level. We give sharp upper and lower bounds for the case of a Euclidean ball, which establishes the Pareto-optimal minimax tradeoff between storage and risk in this setting.Comment: Appearing at NIPS 201

Generative Adversarial User Privacy in Lossy Single-Server Information Retrieval

We propose to extend the concept of private information retrieval by allowing for distortion in the retrieval process and relaxing the perfect privacy requirement at the same time. In particular, we study the tradeoff between download rate, distortion, and user privacy leakage, and show that in the limit of large file sizes this trade-off can be captured via a novel information-theoretical formulation for datasets with a known distribution. Moreover, for scenarios where the statistics of the dataset is unknown, we propose a new deep learning framework by leveraging a generative adversarial network approach, which allows the user to learn efficient schemes from the data itself, minimizing the download cost. We evaluate the performance of the scheme on a synthetic Gaussian dataset as well as on both the MNIST and CIFAR-10 datasets. For the MNIST dataset, the data-driven approach significantly outperforms a non-learning based scheme which combines source coding with multiple file download, while the CIFAR-10 performance is notably better.Comment: Submitted to IEEE for possible publication. This paper was presented in part at the NeurIPS 2020 Workshop on Privacy Preserving Machine Learning - PRIML and PPML Joint Editio

Generative Compression

Traditional image and video compression algorithms rely on hand-crafted encoder/decoder pairs (codecs) that lack adaptability and are agnostic to the data being compressed. Here we describe the concept of generative compression, the compression of data using generative models, and suggest that it is a direction worth pursuing to produce more accurate and visually pleasing reconstructions at much deeper compression levels for both image and video data. We also demonstrate that generative compression is orders-of-magnitude more resilient to bit error rates (e.g. from noisy wireless channels) than traditional variable-length coding schemes

Lexicographic Bit Allocation for MPEG Video

We consider the problem of allocating bits among pictures in an MPEG video coder to equalize the visual quality of the coded pictures, while meeting bu er and channel constraints imposed by the MPEG Video Bu ering Veri er. We address this problem within a framework that consists of three components: 1) a bit production model for the input pictures, 2) a set of bit-rate constraints imposed by the Video Bu ering Veri er, and 3) a novel lexicographic criterion for optimality. Under this framework, we derive simple necessary and su cient conditions for optimality that lead to e cient algorithms

Effects of discrete wavelet compression on automated mammographic shape recognition

At present early detection is critical for the cure of breast cancer. Mammography is a breast screening technique which can detect breast cancer at the earliest possible stage. Mammographic lesions are typically classified into three shape classes, namely round, nodular and stellate. Presently this classification is done by experienced radiologists. In order to increase the speed and decrease the cost of diagnosis, automated recognition systems are being developed. This study analyses an automated classification procedure and its sensitivity to wavelet based image compression; In this study, the mammographic shape images are compressed using discrete wavelet compression and then classified using statistical classification methods. First, one dimensional compression is done on the radial distance measure and the shape features are extracted. Second, linear discriminant analysis is used to compute the weightings of the features. Third, a minimum distance Euclidean classifier and the leave-one-out test method is used for classification. Lastly, a two dimensional compression is performed on the images, and the above process of feature extraction and classification is repeated. The results are compared with those obtained with uncompressed mammographic images

Rate-Distortion Analysis of Multiview Coding in a DIBR Framework

Depth image based rendering techniques for multiview applications have been recently introduced for efficient view generation at arbitrary camera positions. Encoding rate control has thus to consider both texture and depth data. Due to different structures of depth and texture images and their different roles on the rendered views, distributing the available bit budget between them however requires a careful analysis. Information loss due to texture coding affects the value of pixels in synthesized views while errors in depth information lead to shift in objects or unexpected patterns at their boundaries. In this paper, we address the problem of efficient bit allocation between textures and depth data of multiview video sequences. We adopt a rate-distortion framework based on a simplified model of depth and texture images. Our model preserves the main features of depth and texture images. Unlike most recent solutions, our method permits to avoid rendering at encoding time for distortion estimation so that the encoding complexity is not augmented. In addition to this, our model is independent of the underlying inpainting method that is used at decoder. Experiments confirm our theoretical results and the efficiency of our rate allocation strategy