DeepAI AI Chat
Log In Sign Up

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

by   Ren Wang, et al.

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements. Leveraging the low-rank property of the tensor, this paper proposes a nonconvex optimization problem for tensor recovery. We provide a theoretical upper bound of the recovery error, which diminishes to zero when the sizes of dimensions increase to infinity. Our error bound significantly improves over the existing results in one-bit tensor recovery and quantized matrix recovery. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee is proposed to solve the nonconvex problem. Our recovery method can handle data losses and do not need the information of the quantization rule. The method is validated on synthetic data, image datasets, and music recommender datasets.


Cross: Efficient Low-rank Tensor Completion

The completion of tensors, or high-order arrays, attracts significant at...

Optimal Low-Rank Tensor Recovery from Separable Measurements: Four Contractions Suffice

Tensors play a central role in many modern machine learning and signal p...

Noisy Tensor Completion via Low-rank Tensor Ring

Tensor completion is a fundamental tool for incomplete data analysis, wh...

Iterative Hard Thresholding for Low CP-rank Tensor Models

Recovery of low-rank matrices from a small number of linear measurements...

Modewise Operators, the Tensor Restricted Isometry Property, and Low-Rank Tensor Recovery

Recovery of sparse vectors and low-rank matrices from a small number of ...

STARK: Structured Dictionary Learning Through Rank-one Tensor Recovery

In recent years, a class of dictionaries have been proposed for multidim...

Sparse tensor recovery via N-mode FISTA with support augmentation

A common approach for performing sparse tensor recovery is to use an N-m...