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Multiplexed Barcoding Image Analysis for Immunoprofiling and Spatial Mapping Characterization in the Single-Cell Analysis of Paraffin Tissue Samples

Multiplexed Barcoding Image Analysis for Immunoprofiling and Spatial Mapping Characterization in the Single-Cell Analysis of Paraffin Tissue Samples

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Multiplex Transformed Tensor Decomposition for Multidimensional Image Recovery.

Lanlan Feng, Ce Zhu, Zhen Long

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|June 14, 2023

Summary

This summary is machine-generated.

This study introduces a novel multiplex transformed tensor decomposition (MTTD) for low-rank tensor completion. MTTD effectively recovers missing multi-way data in any order-N tensor, outperforming existing methods in accuracy and efficiency.

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Area of Science:

Multi-way data analysis
Tensor decomposition
Signal processing and computer vision

Background:

Low-rank tensor completion is crucial for multi-way data analysis.
Existing methods like t-SVD have limitations in handling higher-order tensors and rotation sensitivity.
There is a need for a more generalized and robust tensor completion framework.

Purpose of the Study:

To develop a novel tensor decomposition framework, Multiplex Transformed Tensor Decomposition (MTTD), for generalized low-rank tensor completion.
To address the limitations of existing methods, particularly for higher-order tensors.
To improve the accuracy and computational efficiency of tensor completion.

Main Methods:

Proposed Multiplex Transformed Tensor Decomposition (MTTD) framework for any order-N tensor.
Developed a multi-dimensional square model for low-rank tensor completion incorporating MTTD.
Integrated a total variation term to leverage piecewise smoothness of tensor data.
Employed the alternating direction method of multipliers to solve the optimization problem.
Evaluated performance using Fast Fourier Transform (FFT), Discrete Cosine Transform (DCT), and unitary transforms.

Main Results:

The proposed MTTD framework effectively characterizes global low-rank structures across all modes of any order-N tensor.
The multi-dimensional square model with MTTD and total variation demonstrated superior recovery accuracy.
Experiments showed significant improvements in computational efficiency compared to state-of-the-art methods.
Validated through simulations and real-world data experiments.

Conclusions:

The novel MTTD framework offers a robust and generalized approach to low-rank tensor completion.
The proposed method overcomes limitations of previous techniques, handling higher-order tensors effectively.
MTTD provides a promising solution for applications requiring accurate and efficient multi-way data recovery.