Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.05802 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911424683442176 |
|---|---|
| author | Führling, Niclas Rexhepi, Getuar Abreu, Giuseppe |
| author_facet | Führling, Niclas Rexhepi, Getuar Abreu, Giuseppe |
| contents | We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries represent the RGB values. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN) minimization-based low-rank TC paradigm, through the addition of a discrete-aware regularizer, which enforces discreteness in the objective of the problem, by an $\ell_0$-norm regularizer that is approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework, in order to solve the proposed problem. Simulation results demonstrate the superior performance of the new method both in terms of normalized mean square error (NMSE) and convergence, compared to the conventional state of-the-art (SotA) techniques, including NN minimization approaches, as well as a mixture of the latter with a matrix factorization approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete Aware Tensor Completion via Convexized $\ell_0$-Norm Approximation Führling, Niclas Rexhepi, Getuar Abreu, Giuseppe Signal Processing Information Theory We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries represent the RGB values. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN) minimization-based low-rank TC paradigm, through the addition of a discrete-aware regularizer, which enforces discreteness in the objective of the problem, by an $\ell_0$-norm regularizer that is approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework, in order to solve the proposed problem. Simulation results demonstrate the superior performance of the new method both in terms of normalized mean square error (NMSE) and convergence, compared to the conventional state of-the-art (SotA) techniques, including NN minimization approaches, as well as a mixture of the latter with a matrix factorization approach. |
| title | Discrete Aware Tensor Completion via Convexized $\ell_0$-Norm Approximation |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2602.05802 |