Quadratic optimal functional quantization of stochastic processes and numerical applications

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a Hilbert-valued random variable, using a nearest neighbour projection on a finite codebook. A special emphasis is made on the computational aspects and the numerical applications, in particular the pricing of some path-dependent European options.Comment: 41 page

Distributed video coding for wireless video sensor networks: a review of the state-of-the-art architectures

Distributed video coding (DVC) is a relatively new video coding architecture originated from two fundamental theorems namely, Slepian–Wolf and Wyner–Ziv. Recent research developments have made DVC attractive for applications in the emerging domain of wireless video sensor networks (WVSNs). This paper reviews the state-of-the-art DVC architectures with a focus on understanding their opportunities and gaps in addressing the operational requirements and application needs of WVSNs

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning

A two-stage video coding framework with both self-adaptive redundant dictionary and adaptively orthonormalized DCT basis

In this work, we propose a two-stage video coding framework, as an extension of our previous one-stage framework in [1]. The two-stage frameworks consists two different dictionaries. Specifically, the first stage directly finds the sparse representation of a block with a self-adaptive dictionary consisting of all possible inter-prediction candidates by solving an L0-norm minimization problem using an improved orthogonal matching pursuit with embedded orthonormalization (eOMP) algorithm, and the second stage codes the residual using DCT dictionary adaptively orthonormalized to the subspace spanned by the first stage atoms. The transition of the first stage and the second stage is determined based on both stages' quantization stepsizes and a threshold. We further propose a complete context adaptive entropy coder to efficiently code the locations and the coefficients of chosen first stage atoms. Simulation results show that the proposed coder significantly improves the RD performance over our previous one-stage coder. More importantly, the two-stage coder, using a fixed block size and inter-prediction only, outperforms the H.264 coder (x264) and is competitive with the HEVC reference coder (HM) over a large rate range