Discriminative reconstruction via simultaneous dense and sparse coding
Authors: Abiy Tasissa, Manos Theodosis, Bahareh Tolooshams, Demba E. Ba
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Experiments The codes for reproducing the experiments in this section can be found on Git Hub: https://github.com/ manosth/densae/ and https://github.com/btolooshams/densae. 5.1 Phase transition curves We generate phase transition curves and present how the success rate of the recovery, using the proposed model, changes under different scenarios. To generate the data, we sample random matrices A Rm p and B Rm n whose columns have expected unit norm and fix the number of columns of B to be n = 100. The vector u Rn has s randomly chosen indices, whose entries are drawn according to a standard normal distribution, and x Rp is generated as x = AT γ where γ Rm is a random vector. The construction ensures that x does not belong in the null space of A, and hence degenerate cases are avoided. We normalize both x and u to have unit norm, and generate the measurement vector y Rm as y = Ax + Bu. To generate the transition curves we vary the sampling ratio σ = m n+p [0.05, 0.95] and the sparsity ratio ρ = s m in the same range. Note that the sensing matrix in our model is [A B]; therefore, our definition of σ takes into account both the size of A and B. In the case where we revert to the compressive sensing scenario (p = 0), the sampling ratios coincide. We solve the convex optimization problem of (17) to obtain the numerical solution pair (ˆx, ˆu) using CVXPY (Diamond & Boyd, 2016; Agrawal et al., 2018), and register a successful recovery if both ˆx x 2 x 2 ϵ and ˆu u 2 u 2 ϵ, with ϵ = 10 3. For each choice of σ and ρ, we average 100 independent runs to estimate the success rate. |
| Researcher Affiliation | Academia | Abiy Tasissa EMAIL Department of Mathematics Tufts University Emmanouil Theodosis EMAIL School of Engineering and Applied Sciences Harvard University Bahareh Tolooshams EMAIL Computing + Mathematical Sciences California Institute of Technology Demba Ba EMAIL School of Engineering and Applied Sciences Harvard University |
| Pseudocode | No | The paper includes 'Figure 2: Flow chart that shows the construction of the measurement matrices.' which describes a procedure with numbered steps, but it is presented as a flow chart figure and not as a pseudocode or algorithm block. |
| Open Source Code | Yes | The codes for reproducing the experiments in this section can be found on Git Hub: https://github.com/manosth/densae/ and https://github.com/btolooshams/densae. |
| Open Datasets | Yes | The real data we consider is the MNIST database of handwritten digits (Le Cun, 1998; Le Cun et al., 1998). ... We trained Den Sa E for supervised image denoising when β = 0 using BSD432 and tested it on BSD68 (Martin et al., 2001). |
| Dataset Splits | Yes | Table 5: Network parameters for MNIST classification experiment. # training examples 50,000 MNIST # validation examples 10,000 MNIST # testing examples 10,000 MNIST ... Table 6: Network parameters for natural image denoising experiments. # training examples 432 BSD432 # testing examples 68 BSD68 |
| Hardware Specification | No | The paper does not explicitly mention specific hardware details such as GPU models, CPU types, or memory amounts used for running experiments. |
| Software Dependencies | No | The paper mentions using "CVXPY (Diamond & Boyd, 2016; Agrawal et al., 2018)", "ADAM optimizer (Kingma, 2014)", and "FISTA (Beck & Teboulle, 2009)", but it does not specify version numbers for these software components or any other libraries. |
| Experiment Setup | Yes | To generate the transition curves we vary the sampling ratio σ = m n+p [0.05, 0.95] and the sparsity ratio ρ = s m in the same range. ... For each choice of σ and ρ, we average 100 independent runs to estimate the success rate. ... In our experiments, we use µ = 3 and λ = 0.01. ... All the networks are trained for 250 epochs using the ADAM optimizer (Kingma, 2014) and the filters are initialized using the random Gaussian distribution. The initial learning rate is set to 10 4 and then decayed by 0.8 every 50 epochs. We set ϵ of the optimizer to be 10 3 for stability. At every iteration, a random patch of size 128 128 is cropped from the training image and zero-mean Gaussian noise is added to it with the corresponding noise level. ... The learning rate is set to 10 3. We set ϵ of the optimizer to be 10 15 and used batch size of 16. For disjoint classification training, we trained for 1,000 epochs, and for joint classification training, the network is trained for 500 epochs. |