Papers › Enhanced image approximation using shifted rank-1 reconstruction
Enhanced image approximation using shifted rank-1 reconstruction
Florian Boßmann, Jianwei Ma
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Low rank approximation has been extensively studied in the past. It is most suitable to reproduce rectangular like structures in the data. In this work we introduce a generalization using shifted rank-1 matrices to approximate A∈ℂ^(M×N). These matrices are of the form S_λ(uv^*) where u∈ℂᴹ, v∈ℂᴺ and λ∈ℤᴺ.The operator S_λ circularly shifts the k-th column of uv^* by λₖ. These kind of shifts naturally appear in applications, where an object u is observed in N measurements at different positions indicated by the shift λ. The vector v gives the observation intensity. Exemplary, a seismic wave can be recorded at N sensors with different time of arrival λ; Or a car moves through a video changing its position in every frame. We present theoretical results as well as an efficient algorithm to calculate a shifted rank-1 approximation in O(NM logM). The benefit of the proposed method is demonstrated in numerical experiments. A comparison to other sparse approximation methods is given. Finally, we illustrate the utility of the extracted parameters for direct information extraction in several applications including video processing or non-destructive testing.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections