Holographic sensing

Abstract

Holographic representations of data enable distributed storage with progressive refinement when the stored packets of data are made available in any arbitrary order. In this paper, we propose and test patch-based transform coding holographic sensing of image data. Our proposal is optimized for progressive recovery under random order of retrieval of the stored data. The coding of the image patches relies on the design of distributed projections ensuring best image recovery, in terms of the 2 norm, at each retrieval stage. The performance depends only on the number of data packets that has been retrieved thus far.Several possible options to enhance the quality of the recovery while changing the size and number of data packets are discussed and tested. This leads us to examine several interesting bit-allocation and rate-distortion trade offs, highlighted for a set of natural images with ensemble estimated statistical properties.

Patch-Based Holographic Image Sensing

“…Notice that L = r i=1 y r . For example, entry 3 in Table 2 for the aggregate's statistics has the distribution [8] 3 [4][2] 2 in Mode 1. We read this as L = 6 with s 1 = s 2 = s 3 = 8, s 4 = 4, and s 5 = s 6 = 2, when all N packets are available.…”

“…Recently we provided an in-depth analysis of a holographic sensing paradigm, in the classical setting of Wiener filtering, on general random vector data in [4]. In the proposal, probings are performed by projection operators that eventually enable graceful successive refinement of the random vectors.…”

“…In this paper, we apply the paradigm in [4] on images, seen as ensembles of smaller patches which are interpreted as realizations of a random process, in place of random vectors. In this important application, instead of merely repeating the relevant process in [4], we carefully and A. BRUCKSTEIN, M. EZERMAN, A. FAHREZA, AND S. LING deeply exploit special statistical properties of image data vectors. Furthermore, we formulate explicit probing policies guided by either estimated or modeled statistical image properties.…”