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 and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Convergence for nonconvex ADMM, with applications to CT imaging
Authors: Rina Foygel Barber, Emil Y. Sidky
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this work, our new theoretical results provide convergence guarantees under a restricted strong convexity assumption without requiring smoothness or differentiability, while still allowing differentiable terms to be treated approximately if needed. We validate these theoretical results empirically, with a simulated example where both f and g are nondifferentiable and thus outside the scope of existing theory as well as a simulated CT image reconstruction problem. |
| Researcher Affiliation | Academia | Rina Foygel Barber EMAIL Department of Statistics University of Chicago Chicago, IL 60637, USA; Emil Y. Sidky EMAIL Department of Radiology University of Chicago Chicago, IL 60637, USA |
| Pseudocode | Yes | Algorithm 1 ADMM with linear approximations Input: Functions f = fc+fd and g = gc+gd, with fc, gc convex, fd, gd twice differentiable; matrices A, B; vector c; penalty matrix Σ 0; step size matrices Hf, Hg 0. Initialize: x0, y0, u0. for t = 0, 1, 2, . . . do Update x: xt+1 = arg min x fc(x) + x, fd(xt) + A ut 2 Ax + Byt c 2 Σ + 1 2 x xt 2 Hf Update y: yt+1 = arg min y gc(y) + y, gd(yt) + B ut 2 Axt+1 + By c 2 Σ + 1 2 y yt 2 Hg o , Update u: ut+1 = ut + Σ(Axt+1 + Byt+1 c). until some convergence criterion is reached. |
| Open Source Code | Yes | Code reproducing the simulation and all figures is available at https://github. com/rinafb/ADMM_CT. |
| Open Datasets | No | The paper describes generating synthetic data for both the sparse quantile regression problem and the CT imaging application, but does not provide explicit access information (link, DOI, etc.) for the generated datasets themselves. For example, for quantile regression: 'The matrix Φ Rn d is constructed with i.i.d. N(0, 1) entries. We define wi = φ i x + zi, where φi is the ith row of Φ, and the true signal is given by x = (1, . . . , 1, 0, . . . , 0), with s = 10 nonzero entries. The noise terms zi are drawn i.i.d. from t5, the standard t distribution with 5 degrees of freedom...' For CT imaging: 'The ground truth... is a 10cm 10cm two-dimensional image discretized to a 25 25 grid... The simulated CT scanner has 50 detector cells...' |
| Dataset Splits | No | The paper uses simulated datasets for its experiments, which are generated according to specified parameters rather than being split from a larger, pre-existing dataset. Therefore, no explicit training/test/validation splits are provided. For example, for quantile regression: 'We choose dimension d = 2500 and sample size n = 2000...' For CT imaging: 'The ground truth... is a 10cm 10cm two-dimensional image discretized to a 25 25 grid...' |
| Hardware Specification | No | The paper mentions running simulations in Python but does not provide any specific hardware details such as CPU, GPU models, or memory specifications. For example: 'To demonstrate the algorithm s performance on the nononvex CT image reconstruction problem, we carry out a small-scale simulation in Python.' |
| Software Dependencies | No | The paper states that the CT simulation was carried out 'in Python' but does not specify any particular software libraries, frameworks, or their version numbers. While code is provided on GitHub, this information is not in the main paper text. |
| Experiment Setup | Yes | For sparse high-dimensional quantile regression: 'We choose dimension d = 2500 and sample size n = 2000... We choose the quantile q = 0.5... For the penalty term, we choose λ = 0.1 and β = 0.5... The parameter σ controlling the enforcement of the constraint in ADMM... is varied as σ {0.00005, 0.0001, 0.0002, 0.0005}. The results after running Algorithm 1 for 1000 iterations are displayed...' For CT simulation: 'The ground truth... is a 10cm 10cm two-dimensional image discretized to a 25 25 grid... The simulated CT scanner has 50 detector cells, and takes images from 50 angles... The beam intensity is set to 106 photons, and there are nw = 3 energy windows... Figure 6 displays the estimated image (shown at iteration 1000, at each value of the ADMM parameter σ {1, 10, 100})... In our implementation, at each iteration t we run N = 10 steps of the Newton Raphson method to compute the y update...' |