In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].

https://www.cv-foundation.org/openaccess/content_cvpr_2014/papers/Zhang_Novel_Methods_for_2014_CVPR_paper.pdf

Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD

Novel methods for multilinear data completion and de-noising based on tensor-SVD

Image compression techniques: A survey in lossless and lossy algorithms

Electrical distribution systems have been experiencing many changes in recent times. Advances in metering system infrastructure and the deployment of a large number of smart meters in the grid will produce a big volume of data that will be required for many different applications. Despite the significant investments taking place in the communications infrastructure, this remains a bottleneck for the implementation of some applications. This paper presents a methodology for lossy data compression in smart distribution systems using the singular value decomposition technique. The proposed method is capable of significantly reducing the volume of data to be transmitted through the communications network and accurately reconstructing the original data. These features are illustrated by results from tests carried out using real data collected from metering devices at many different substations.

Data Compression in Smart Distribution Systems via Singular Value Decomposition

During the past couple of decades several proposals for image coders using singular value decomposition (SVD) have been put forward. The results using SVD in this context have never been spectacular. The main problem with the SVD is that the transform itself must be transmitted as side information. We demonstrate through some simple experiments that for a given image reconstruction quality, more scalar parameters must be transmitted using the SVD, than when using the discrete cosine transform (DCT). Also, using an alternative interpretation of the SVD we show that the SVD representation necessitates quantization of individual factors as compared to quantization of the associated product. This is clearly suboptimal.

A critique of SVD-based image coding systems

An image coder based on the singular value decomposition and vector quantization is presented. The singular values and singular vectors of the image subblocks are computed at the encoder and quantized using a novel variable bit-rate coding scheme. The performance of the coder is assessed by computer simulations.

http://ieeexplore.ieee.org/iel3/3238/9764/00465543.pdf

A. Bury

Papers

Image coding using the singular value decomposition and vector quantization