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Manifold Graph Signal Restoration using Gradient Graph Laplacian Regularizer
We generalize previous signal-dependent Graph Laplacian Regularizer
(GLR) that promotes piecewise constant (PWC) signal reconstruction to
Gradient Graph Laplacian Regularizer (GGLR) that promotes
piecewise planar (PWP) signal reconstruction for graph signal
restoration tasks, such as image interpolation and 3D point cloud
denoising. For image interpolation examples, download
software HERE.
See the following paper for details.
- Fei Chen, Gene Cheung, Xue Zhang, "Manifold Graph Signal Restoration using Gradient Graph Laplacian Regularizer," submitted to IEEE Transactions on Signal Processing, June 2022. (arXiv)
Graph
Sampling Set Selection Using Gershgorin Disc Alignment
We propose an eigen-decomposition-free graph samping set selection
algorithm via a novel use of the Gershgorin circle theorem.
Specifically, we maximize the smallest eigenvalue of a coefficient
matrix by shifting and scaling Gershgorin discs via sample
selection. The algorithm runs in roughly linear time. Download
software HERE.
See the following paper for details.
- Yuanchao Bai, Fen Wang, Gene
Cheung, Yuji Nakatsukasa, Wen Gao, "Fast
Graph Sampling Set Selection Using Gershgorin Disc Alignment," vol. 68, pp. 2419-2434, IEEE Transactions on Signal Processing, March 2020. (arXiv)
Graph-based
3D Point Cloud Denoising using Low-Dimensional Manifold Model
Using the dimensionality of a manifold as a signal prior, we denoise a
3D point cloud using a graph Laplacian regularizer (GLR) to efficiently
compute the manifold dimension.
Download software HERE.
See the following paper for details.
- Jin Zeng, Gene Cheung, Michael Ng, Jiahao Pang,
Cheng Yang, "3D Point Cloud Denoising
using Graph Laplacian Regularization of a Low Dimensional Manifold Model," IEEE Transactions on
Image Processing, vol. 29, pp. 3474-3489, December 2019. (arXiv)
Blind
Image Deblurring using Reweighted Graph Total Variation (RGTV)
Blind deblur a natural image spectrally: use Reweighted Graph Total
Variation (RGTV) to first construct an ultra-sharp skeleton image, then
deduce the blur kernel for deconvolution.
Download software HERE.
See the following paper for details.
- Yuanchao Bai, Gene Cheung, Xianming Liu, Wen
Gao, "Graph-Based Blind Image
Deblurring from a Single Photograph," IEEE Transactions on Image Processing,
vol. 28, no.3, pp.1404-1418, March 2019. (arXiv)
Left
Eigenvectors of the Random Walk Graph Laplacian (LeRAG) for Soft
Decoding of JPEG Images
Soft decode a JPEG encoded image using Left Eigenvectors of the Random
Walk Graph Laplacian (LeRAG) as signal prior.
Download software HERE.
See the following paper for details.
- Xianming Liu, Gene Cheung, Xiaolin Wu, Debin
Zhao, "Random Walk Graph Laplacian
based Smoothness Prior for Soft Decoding of JPEG Images," IEEE Transactions on Image Processing,
vol.26, no.2, pp.509-524, February 2017. (arXiv)
Optimal
Graph Laplacian Regularization (OGLR) for Image Denoising
Denoise an input natural / depth image patch-by-patch by constructing
an optimal graph and coresponding graph Laplacian regularizer.
Download software HERE.
See the following paper for details.
- Jiahao Pang, Gene Cheung, "Graph Laplacian Regularization for Inverse
Imaging: Analysis in the Continuous Domain," IEEE Transactions on Image Processing,
vol. 26, nol.4, pp.1770-1785, April 2017. (arXiv)
Context
Tree based
Contour Coding (CTCC)
Encode contiguous contours in an image via construction of a
variable-lenght context tree (VCT) given small training data.
Download software HERE.
See the following paper for details.
- Amin Zheng, Gene Cheung, Dinei
Florencio, "Context Tree based Image
Contour Coding using A Geometric Prior," IEEE Transactions on Image Processing,
vol.26, no.2, pp.574-589, February 2017. (arXiv)
Arithmetic
Edge Coding (AEC)
Encode contiguous contours in an image using arithmetic coding.
Download version 1 HERE. See the
following papers for details.
- Ismael Daribo, Dinei Florencio, Gene Cheung, "Arbitrarily Shaped Motion Prediction
for Depth Video Compression Using Arithmetic Edge Coding," IEEE Transactions on Image Processing,
vol.23, no.11, pp.4696-4708, November 2014.
- Ismael Daribo, Gene Cheung, Dinei Florencio, "Arithmetic Edge Coding for Arbitrarily
Shaped Sub-block Motion Prediction in Depth Video Coding (accepted
version)," IEEE International
Conference on Image Processing, Orlando, FL, September 2012.
Non-local
Graph-based Transform (NLGBT) for Depth Image Denoising
Denoise AWGN-corrupted depth images exploiting non-local
self-similarity in images and sparsity in graph transform. Download
version 1 HERE.
See the following
paper for details.
- Wei Hu, Xin Li, Gene Cheung, Oscar Au, "Depth Map Denoising using Graph-based
Transform and Group Sparsity (accepted
version)," IEEE International
Workshop on Multimedia Signal Processing, Pula (Sardinia),
Italy, October, 2013.(Top 10% paper award.)
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