Unlabelled Compressive Sensing under Sparse Permutation and Prior Information
Authors: Garweet Sresth, Satish Mulleti, Ajit Rajwade
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical Experiments In order to assess the impact made by knowledge of known correspondences, we compare Ar-Lasso from equation 6 and A-Htp from Alg. 1 to the following estimators, none of which use the prior information of known correspondences.: (i) The robust Lasso (R-Lasso) estimator given by arg min β Rp,e Rn 1 2N y Aβ ne 2 2 +λβ β 1 +λe e 1, which is effectively Ar-Lasso with m = 0 and N = n. (ii) The ℓ1-norm hard thresholding pursuit approach in Peng et al. (2021) that minimizes y Aβ 1 w.r.t. β Rp such that β 0 k. We refer to this approach as ℓ1-Htp. (iii) The ℓ1 ℓ1 estimator motivated from Candes & Tao (2005); Candes et al. (2005) that is posed as arg min β Rp y Aβ 1 + λβ β 1. |
| Researcher Affiliation | Academia | Garweet Sresth EMAIL Department of Electrical Engineering IIT Bombay Satish Mulleti EMAIL Department of Electrical Engineering IIT Bombay Ajit Rajwade EMAIL Department of Computer Science and Engineering IIT Bombay |
| Pseudocode | Yes | Algorithm 1 Augmented Hard-Thresholding Pursuit Input: Measurement vector y, augmented matrix H, sparsity level k and number of permutations s (both k and s can be estimated via cross-validation see Sec. 5 under Choice of parameters ) Parameter: Learning rate µ Output: Estimate of β |
| Open Source Code | No | The paper does not provide an explicit statement about releasing code or a link to a code repository for the methodology described. |
| Open Datasets | No | Data generation: In all the experiments, the entries of A and the non-zero values of β are sampled from N(0, 1). P2 is generated by randomly sampling from the family of s-sparse permutation matrices. The entries of w are independently sampled from N(0, σ2) where σ := fr the mean absolute value of the entries of the noiseless measurement vector P Aβ with fraction fr (0, 1). Experiment: Consider two grayscale images I and R from row 1 of Fig. 4 respectively. The image I was chosen arbitrarily as the reference image. Image R was generated synthetically by warping I using a displacement vector field that was sparse in the 2D-DCT basis (for both X and Y components of the motion) following the model in equation 19. |
| Dataset Splits | No | The paper describes a cross-validation strategy for parameter selection, splitting available measurements into 95% for reconstruction and 5% for validation error computation. However, this is for hyperparameter tuning, not a fixed train/test/validation split of a publicly available dataset for direct model evaluation and reproduction. The main evaluation uses synthetically generated data instances. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments, such as GPU or CPU models. |
| Software Dependencies | No | We use CVXPY (Diamond & Boyd, 2016) to solve all the optimization problems, except for Sbl which is implemented via EM. |
| Experiment Setup | Yes | Data generation: In all the experiments, the entries of A and the non-zero values of β are sampled from N(0, 1). P2 is generated by randomly sampling from the family of s-sparse permutation matrices. The entries of w are independently sampled from N(0, σ2) where σ := fr the mean absolute value of the entries of the noiseless measurement vector P Aβ with fraction fr (0, 1). Choice of parameters: The regularization parameters λβ and λe in Ar-Lasso, R-Lasso, Lasso and ℓ1 ℓ1 algorithms are chosen through cross-validation on a held-out set of measurements. ... In our experiments, we observe that cross-validation overestimates (k, s) by a factor of 2. Hence, we directly set (k, s) to twice of their true value in the ℓ1-Htp and ℓ2-Htp algorithms. We select the learning rate in ℓ1-Htp and ℓ2-Htp through cross-validation. The number of iterations in ℓ1-Htp is set to 200, and that in ℓ2-Htp is set to 100. We always observed convergence within these iteration counts. |