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Robust Low-Tubal-Rank Tensor Recovery From Binary Measurements

Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor X from incomplete linear measurements M(X) . However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of M(X) . We still hope to recover X from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed—the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real n1×n2×n3 tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor λ:=m/((n1+n2)n3r) . To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of λ . Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.

Ketersediaan

Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE; Vol.44 No.8 August 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 4355-4373

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ADAPTIVITY
ONE-BIT TENSOR RECOVERY
LOW-TUBAL-RANK TENSOR
TENSOR HARD SINGULAR TUBE THRESHOLDING
TENSOR NUCLEAR NORM MINIMIZATION

Info Detail Spesifik

DOI: 10.1109/TPAMI.2021.3063527

Pernyataan Tanggungjawab

Jingyao Hou, Feng Zhang, Haiquan Qiu, Jianjun Wang, Yao Wang, Deyu Meng

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