Fast & Robust Image Interpolation using Gradient Graph Laplacian Regularizer
Bibliographic record
Abstract
In the graph signal processing (GSP) literature, it has been shown that signal-dependent graph Laplacian regularizer (GLR) can efficiently promote piecewise constant (PWC) signal reconstruction for various image restoration tasks. However, for planar image patches, like total variation (TV), GLR may suffer from the well-known "staircase" effect. To remedy this problem, we generalize GLR to gradient graph Laplacian regularizer (GGLR) that provably promotes piecewise planar (PWP) signal reconstruction for the image interpolation problem -- a 2D grid with random missing pixels that requires completion. Specifically, we first construct two higher-order gradient graphs to connect local horizontal and vertical gradients. Each local gradient is estimated using structure tensor, which is robust using known pixels in a small neighborhood, mitigating the problem of larger noise variance when computing gradient of gradients. Moreover, unlike total generalized variation (TGV), GGLR retains the quadratic form of GLR, leading to an unconstrained quadratic programming (QP) problem per iteration that can be solved quickly using conjugate gradient (CG). We derive the means-square-error minimizing weight parameter for GGLR, trading off bias and variance of the signal estimate. Experiments show that GGLR outperformed competing schemes in interpolation quality for severely damaged images at a reduced complexity.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".