Homomorphic Sensing: Sparsity and Noise
Authors: Liangzu Peng, Boshi Wang, Manolis Tsakiris
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | On the algorithmic level, we solve unlabeled compressed sensing by an iterative algorithm validated by synthetic data experiments. Finally, under the unifying homomorphic sensing framework we connect unlabeled sensing to other important practical problems. |
| Researcher Affiliation | Academia | 1School of Information Science and Technology, Shanghai Tech University, Shanghai, China. Correspondence to: Liangzu Peng, Boshi Wang, Manolis C. Tsakiris <penglz,wangbsh,mtsakiris@shanghaitech.edu.cn>. |
| Pseudocode | Yes | The iterative update is given as: x(t+1) Proj K x(t) µA sgn(Ax(t+1) y) (17) J the support {i : x(t+1) i = 0} of x(t+1) x(t+1) J argmin x Rn y AJx 1 (18) |
| Open Source Code | No | The paper does not include an explicit statement about releasing its source code or a link to a code repository for the methodology described. |
| Open Datasets | No | Data generation. We generate data by i) randomly sampling the entries of A Rm n from the standard normal distribution N(0, 1), ii) randomly selecting a support of the k-sparse x Rn whose non-zero entries are randomly sampled also from N(0, 1), iii) randomly producing a psparse permutation Π , and iv) computing y = Π Ax . |
| Dataset Splits | No | The paper generates synthetic data for its experiments but does not specify train/validation/test splits for a fixed dataset, nor does it refer to predefined splits with citations. It evaluates the algorithm over '100 trials' of newly generated data. |
| Hardware Specification | Yes | We evaluate the algorithm with µ := 10 4 and with the number of iterations set to T := 20 on an Intel(R) i7-8650 U, 1.9 GHz, 16 GB machine. |
| Software Dependencies | No | The paper mentions using 'an ADMM algorithm implemented in the FOM toolbox of Beck & Guttmann-Beck (2019)' but does not provide specific version numbers for the FOM toolbox or any other software dependencies such as Python, PyTorch, or CUDA. |
| Experiment Setup | Yes | We evaluate the algorithm with µ := 10 4 and with the number of iterations set to T := 20 on an Intel(R) i7-8650 U, 1.9 GHz, 16 GB machine. We generate data by i) randomly sampling the entries of A Rm n from the standard normal distribution N(0, 1), ii) randomly selecting a support of the k-sparse x Rn whose non-zero entries are randomly sampled also from N(0, 1), iii) randomly producing a psparse permutation Π , and iv) computing y = Π Ax . In Figure 1a we set p := 0.2m. Keeping m = 1400, n = 2000, k = 25, p = 0.2m fixed, we furthermore evaluated the robustness of the algorithm to noise. We added noise to the measurements y as per the SNR. |