Multiscale Adaptive Representation of Signals: I. The Basic Framework
Authors: Cheng Tai, Weinan E
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we discuss some examples of applications of the multi-scale adaptive frames, the Ada Frames. A thorough comparison of the proposed model and other existing models will be postponed to future publications. ... In this section, we discuss some examples of applications of the multi-scale adaptive frames, the Ada Frames. ... In section 8, we discuss applications to image processing and image classification. |
| Researcher Affiliation | Academia | Cheng Tai EMAIL PACM, Princeton University Princeton, NJ 08544, USA Weinan E EMAIL School of Mathematical Sciences and BICMR Peking University and Department of Mathematics and PACM Princeton University Princeton, NJ 08544, USA |
| Pseudocode | Yes | Algorithm 1 Adaptive construction of frames 1: Input: x. 2: Initialize k = 0, B = 0, A = A0, D = WA0x. 3: while not converge do 4: Dk+1 arg min D D 1,1 + η 2 D WAkx Bk 2 F 5: Ak+1 arg min A WAx Dk+1 + Bk 2 F s.t. A Q. 6: Bk+1 Bk + WAk+1 Dk+1. 7: k k + 1 8: return Ak |
| Open Source Code | No | The software we use is downloaded from http://www.cs.technion.ac.il/~ronrubin/software. This refers to the software for the K-SVD algorithm, not the authors' own implementation for Ada Frame. |
| Open Datasets | Yes | Our next example is the fingerprint dataset (Maltoni et al., 2009). ... We tested this idea on the extended Yale human face dataset B (Lee et al., 2005). ... The dataset we used is MNIST (Le Cun et al., 1998). |
| Dataset Splits | Yes | The dataset we used is MNIST (Le Cun et al., 1998). It contains 70000 28 28 images of digits from 0 to 9, 60000 for training and 10000 for testing. |
| Hardware Specification | No | In our laptop with the same setup, the K-SVD algorithm takes 25s to train a dictionary with 256 atoms of support size 8 8 and 6.5s to denoise the image. The Ada Frame takes 3.7s to train 64 filters with support size 8 8 and takes 0.6s to denoise. This mentions a 'laptop' but lacks specific details (CPU, GPU, RAM, etc.). |
| Software Dependencies | No | The paper mentions 'MATLAB syntax' but does not specify a version. It also mentions 'K-SVD algorithm' and a URL to download its software, but does not provide version numbers for K-SVD or any other libraries/frameworks used for their own implementation. |
| Experiment Setup | Yes | We use Algorithm 1 to learn the filters with η = 102. ... The filters are learned using Algorithm 2 with parameters η = 102, λ = 103. ... 4 filters of support size 6 6 are learned using Algorithm 1 with η = 102. ... Initialization is done using the Daubechies filters db3. ... 7 levels of decompositions are performed. ... we train the filters both from the noisy image and the clean image with m = 36, r = 6, η = 102, λ = 103. A two-level decomposition is performed. The soft thresholding parameter is set to be 0.14. Initialization is done by setting the filters to be random orthogonal vectors. |