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OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems

AAAI 2025 · Learning theory and algorithms › Matrix and tensor methods · approach: Low-rank tensor completion · 3 citations (OpenAlex)

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Proposes OTLRM, a generative t-SVD low-rank model whose transform is a learnable endogenous orthogonal matrix built from Householder reflections, solved by gradient descent instead of SVT, and applied to tensor completion, CASSI spectral reconstruction, and MSI denoising.

Problem

Existing t-SVD low-rank methods use fixed or pre-given transforms and rely on SVT, whose SVD derivatives are numerically unstable when integrated into deep networks, limiting data adaptivity for multi-dimensional inverse problems.

Approach

Construct a learnable orthogonal transform from products of Householder reflections (guaranteed orthogonal and invertible), parameterize the t-SVD factors and a dense rank estimation operator, and optimize the low-rank tensor directly by gradient descent within a DNN framework, replacing explicit SVT.

Key results

• On CAVE MSI tensor completion at SR=0.05, OTLRM reaches 40.20 dB PSNR on Balloons versus 38.35 dB for the best baseline LS2T2NN, per the Table 1 comparison.
• On KAIST CASSI simulation (scene01-05), OTLRM averages 36.41 dB PSNR, above HLRTF's 36.02 dB and HDNet's 36.07 dB is slightly higher, so the claimed gain is over supervised methods in the paper's text.
• On MSI denoising with N(0,0.2) on scene10, OTLRM gets 30.82 dB PSNR, below DDS2M's 32.80 dB, but runs in 45 s.

Measured effects reported in the paper

Surprising findings

• The model deliberately drops the semi-orthogonality constraints on U and V; the paper reports that adding a semi-orthogonal penalty decreases performance as its weight grows.

Limitations

• Denoising results on scene10 lag diffusion-based DDS2M in PSNR and SSIM.
• Transform construction costs O(n3^4), and the paper reports a runtime of 118 s versus 415 s for DTNN on the same tensor completion task.
• Only self-reported results on MSI, video, and MRI data; no theoretical convergence analysis is given for the gradient-based solver.

Experimental setup

Datasets: CAVE NTT video database KAIST Brain MRI

Benchmarks: CAVE NTT KAIST

Metrics: PSNR SSIM FSIM time (s)

Baselines: TNN TQRTNN UTNN DTNN LS2T2NN HLRTF DeSCI λ-Net TSA-Net HDNet DGSMP ADMM-Net

Builds on: tensor nuclear norm t-SVD singular value thresholding DTNN HLRTF

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