Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Adaptive Rates for Total Variation Image Denoising
Authors: Francesco Ortelli, Sara van de Geer
JMLR 2020 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We prove upper bounds on the mean squared error for image denoising with a total variation penalty promoting piecewise constant estimates on rectangular sets. These upper bounds are presented in the form of oracle inequalities, cf. Koltchinskii (2006); Lounici et al. (2011); Dalalyan and Salmon (2012); Stucky and van de Geer (2017); Bellec et al. (2017, 2018); Bellec (2018); Elsener and van de Geer (2019). Oracle inequalities are finite-sample theoretical guarantees on the performance of an estimator treating in a unified way both the cases of well-specified and misspecified models. ... Figure 3 shows some simulation results for denoising the image Y = f0 + ϵ with σ = 1, where, for n1 = n2 {4, 8, . . . , 196, 200}, f0 is taken as in Equation (1). For such images, f0 has 4 nonzero components. Therefore we chose s = 4. The estimator was computed via a detour through its synthesis formulation (see Section 5), which allowed to use the R package glmnet. The results of the simulation support our findings: if tuned with λ = p log(2n)/(2n), the estimator ˆ f converges at an almost parametric rate to the underlying piecewise rectangular image f0. |
| Researcher Affiliation | Academia | Acknowledgments We would like to acknowledge support for this project from the the Swiss National Science Foundation (SNF grant 200020 169011). We moreover thank the action editor and the referees for the careful reading of the manuscript and for their valuable comments. The paper mentions funding from the Swiss National Science Foundation, which is a public funding body. While direct author affiliations (university names, company names, email domains) are not explicitly stated in the provided text, funding from a national science foundation typically supports academic research. |
| Pseudocode | No | The paper describes methods mathematically and textually but does not contain any clearly labeled pseudocode blocks or algorithm sections. |
| Open Source Code | No | The estimator was computed via a detour through its synthesis formulation (see Section 5), which allowed to use the R package glmnet. The paper mentions using a third-party R package (glmnet) but does not state that the authors have made their own implementation code for the described methodology publicly available. |
| Open Datasets | Yes | The ANOVA decomposition of the image lg1 from the Leaf Shapes Database by Waghmare. The image (a) is the original image f, (b) represents the interaction terms f and (c) and (d) are the main effects f( , ) and f( , ), respectively. ... V. E. Waghmare. Leaf Shapes Database. URL http://imageprocessingplace. net/downloads_V3/root_downloads/image_databases/leafshapedatabase/leaf_ shapes_downloads.htm. |
| Dataset Splits | No | Figure 3 shows some simulation results for denoising the image Y = f0 + ϵ with σ = 1, where, for n1 = n2 {4, 8, . . . , 196, 200}, f0 is taken as in Equation (1). For such images, f0 has 4 nonzero components. Therefore we chose s = 4. The estimator was computed via a detour through its synthesis formulation (see Section 5), which allowed to use the R package glmnet. The results of the simulation support our findings: if tuned with λ = p log(2n)/(2n), the estimator ˆ f converges at an almost parametric rate to the underlying piecewise rectangular image f0. ... Plot (a) displays the logarithm of the average mean squared error of the estimator over 40 realizations of the noise term versus log(n), for n1 = n2 {4, 8, . . . , 196, 200}. The paper describes generating data for simulations (f0 + epsilon) and running 40 realizations of the noise term, but it does not specify any training/test/validation splits for a dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments or simulations. |
| Software Dependencies | No | The estimator was computed via a detour through its synthesis formulation (see Section 5), which allowed to use the R package glmnet. The paper mentions using the 'R package glmnet' but does not specify a version number for glmnet or R itself. |
| Experiment Setup | Yes | If we instead make the choice λ = 4σ p log(2n)/n, which does not depend on S, then, with probability at least 1 1/n, we have that ˆ f f0 2 2/n = O s2 log2(n)/n . ... The results of the simulation support our findings: if tuned with λ = p log(2n)/(2n), the estimator ˆ f converges at an almost parametric rate to the underlying piecewise rectangular image f0. However, the rate of convergence n 1 (up to log terms) is achieved only for n large enough and the tuning parameter has to be chosen smaller by a constant factor than the smallest theoretical choice λ = 4 p log(2n)/(2n) suggested by Theorem 6. ... Choose SM such that & 25/433/4 log3/8(2n)TV3/4(f0) and λ = 33/4σ5/4 log3/8(2n) / 21/12n5/8TV1/4(f0) γλ0(log(2n)). |