Research map / Learning theory and algorithms / Matrix and tensor methods
Non-Convex Tensor Recovery from Tube-Wise Sensing
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Proposes a tube-wise local tensor compressed sensing model and recovers low-rank tensors by minimizing a non-convex Burer–Monteiro factorized objective via gradient descent with spectral initialization, with a proof of exact recovery.
Problem
Recovering a low-rank third-order tensor from measurements when sensing operators are applied independently to each tube of the tensor.
Approach
Replaces global tensor sensing with tube-wise local sensing operators and solves the resulting problem with a Burer–Monteiro non-convex factorization optimized by gradient descent from spectral initialization, rather than convex nuclear-norm relaxation.
Key results
- Proves that gradient descent with spectral initialization on the non-convex Burer–Monteiro objective achieves exact recovery of the low-rank tensor under tube-wise local sensing (abstract truncated before the rate is stated).
Limitations
- Full text unavailable; the abstract is truncated, so the convergence rate and assumptions are not stated.
Experimental setup
Builds on: Burer–Monteiro factorization tensor compressed sensing
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