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In this paper, we focus on the problem of completion of multidimensional arrays (also referred to as tensors), in particular three-dimensional (3-D) arrays, from limited sampling. Our approach is based on a recently proposed tensor algebraic framework where 3-D tensors are treated as linear operators over the set of 2-D tensors. In this framework, one can obtain a factorization for 3-D data, referred...
This article presents a VLSI (Very Large Scale of Integration) architecture for the QR decomposition (QRD) based on the Modified Complex Givens Rotations (MCGR) algorithm. Being the QRD a fundamental matrix-computation tool for factorizing matrices (matrix decomposition), its vast set of applications is extended to solve several engineering problems in many areas. For example, in the context of Spatial-Multiplexing...
Maximum distance separable (MDS) array codes are XOR-based optimal erasure codes that are particularly suitable for use in disk arrays. This paper develops an innovative method to build MDS array codes from an elegant class of nested graphs, termed complete-graph-of-rings (CGR). We discuss a systematic and concrete way to transfer these graphs to array codes, unveil an interesting relation between...
In this paper we study the R-way Parallel Factor Analysis (also referred to as R-way PARAFAC) problem. This branch of multi-way signal processing has received increased attention recently which is due to the versatility of the model as well as the identifiability results demonstrating its superiority to matrix-only (2-way) approaches. In R-way PARAFAC analysis, the goal is to decompose an R-dimensional...
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