Structure-Blind Signal Recovery
Authors: Dmitry Ostrovsky, Zaid Harchaoui, Anatoli Juditsky, Arkadi S. Nemirovski
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present preliminary results on simulated data of the proposed adaptive signal recovery methods in several application scenarios. We compare the performance of the penalized ℓ2-recovery of Sec. 3 to that of the Lasso recovery of [1] in signal and image denoising problems. Implementation details for the penalized ℓ2-recovery are given in Sec. 6. Discussion of the discretization approach underlying the competing Lasso method can be found in [1, Sec. 3.6]. We follow the same methodology in both signal and image denoising experiments. For each level of the signal-to-noise ratio SNR {1, 2, 4, 8, 16}, we perform N Monte-Carlo trials. In each trial, we generate a random signal x on a regular grid with n points, corrupted by the i.i.d. Gaussian noise of variance σ2. The signal is normalized: x 2 = 1 so SNR 1 = σ n. We set the regularization penalty in each method as follows. For penalized ℓ2-recovery (8), we use λ = 2σ2 log[63n/α] with α = 0.1. For Lasso [1], we use the common setting λ = σ 2 log n. We report experimental results by plotting the ℓ2-error bx x 2, averaged over N Monte-Carlo trials, versus the inverse of the signal-to-noise ratio SNR 1. |
| Researcher Affiliation | Academia | LJK, University of Grenoble Alpes, 700 Avenue Centrale, 38401 Domaine Universitaire de Saint-Martind H eres, France. University of Washington, Seattle, WA 98195, USA. Georgia Institute of Technology, Atlanta, GA 30332, USA. |
| Pseudocode | No | The paper discusses solving optimization problems using methods like Mirror-Prox and Nesterov’s accelerated gradient algorithms, but it does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper states: 'Extensive theoretical discussions and numerical experiments will be presented in the follow-up journal paper.' It does not provide a link to source code or explicitly state its release. |
| Open Datasets | No | The paper describes generating synthetic data for its experiments: 'In each trial, we generate a random signal x on a regular grid with n points, corrupted by the i.i.d. Gaussian noise of variance σ2.' This is not a publicly available or open dataset. |
| Dataset Splits | No | The paper mentions performing 'N Monte-Carlo trials' and generating random signals for denoising experiments, but it does not specify train, validation, or test dataset splits with percentages or counts. |
| Hardware Specification | No | The paper does not specify any hardware used for running the experiments (e.g., CPU, GPU, memory, or specific computing clusters). |
| Software Dependencies | No | The paper mentions using 'Mirror-Prox and Nesterov s accelerated gradient algorithms' for solving optimization problems and compares to 'Lasso [1]', but it does not provide specific version numbers for any software libraries or dependencies. |
| Experiment Setup | Yes | We set the regularization penalty in each method as follows. For penalized ℓ2-recovery (8), we use λ = 2σ2 log[63n/α] with α = 0.1. For Lasso [1], we use the common setting λ = σ 2 log n. We present additional numerical illustrations in the supplementary material. For the penalized ℓ2-recovery, we implement the blockwise denoising strategy (see Appendix for the implementation details) with just one block for the entire image. |