Efficient Coding of Signal Distances Using Universal Quantized Embeddings

Abstract

Traditional rate-distortion theory is focused on how to best encode a signal using as few bits as possible and incurring as low a distortion as possible. However, very often, the goal of transmission is to extract specific information from the signal at the receiving end, and the distortion should be measured on that extracted information. In this paper we examine the problem of encoding signals such that sufficient information is preserved about their pairwise distances. For that goal, we consider randomized embeddings as an encoding mechanism and provide a framework to analyze their performance. We also propose the recently developed universal quantized embeddings as a solution to that problem and experimentally demonstrate that, in image retrieval experiments, universal embedding can achieve up to 25% rate reduction over the state of the art.I. INTRODUCTION Source coding theory and practice has primarily focused on how to best encode a signal for transmission using the fewest possible bits while incurring the smallest possible distortion. For example, in image or video compression, the encoder aims to reduce the bit-rate for a given visual reconstruction quality. This goal is dictated by the end user of the signal: an image or a video will be viewed by a human being. Quite often, however, the end user of a signal is not a human being observing the distorted signal per se, but a server extracting information. In this case, the goal is different: encoding must happen in a way that does not destroy the information that the server wants to extract, even if the signal itself cannot be completely recovered. In particular, we examine applications in which the server is interested in extracting only the information about the distance of a signal from its nearest neighbors. This paper examines how to efficiently encode signals for transmission such that the receiver can approximately determine the distance between signals up to a specified radius. Our encoding exploits the recently developed theory for efficient universal quantization and universal quantized embeddings [1]. We demonstrate that, using universal quantized embeddings, we are able to improve compression performance up to 25% over previous embedding-based approaches [2], [3], including our own earlier work [4]. The main advantage of universal embeddings is that they preserve distance information only up to a certain radius, as required to determine the near neighbors, and not any farther. Thus, rate is not wasted in coding distances larger than necessary.Our main-but not the only-motivating example is image retrieval, with emphasis on augmented reality (AR) applications. As we discuss in [4], AR and more general image retrieval applications can benefit significantly by efficient coding of distances to a signal's nearest neighbors. In typical cloud-based image retrieval applications, a client transmits

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“…For ≥ 14, which is near the maximum original distance values, distances are in the utility region R − leading to a high accuracy above 90 %. Accuracy does not increase significantly with further increases in (see also [11]). …”

“…Rane and Boufounos [6] and Boufounos and Rane [11] propose the use of distance-preserving embeddings for privacy-preserving matching and nearest-neighbor searches in the context of image retrieval. We apply these distance-preserving embeddings as one step in our proposed protocol and make use of their privacy-preserving properties.…”

“…uniform elements in the range [ 0, ]. is both a quantization and a security parameter and described in detail in [6,11]. The values of k and m are discussed in Section 5.…”

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“…In addition, recent work has demonstrated that if the application does not require accurately preserving the full range of distances but only a small range, then the bit-rate can be further reduced. 17 …”

“…Existing techniques in the literature enable us to characterize the ambiguity in this transformation, 17 although we do not attempt this in this paper.…”