Graph-based Dequantization of Block-Compressed Piecewise Smooth Images

Hu, Wei; Cheung, Gene; Kazui, Masato

doi:10.1109/lsp.2015.2510379

Cited by 54 publications

(48 citation statements)

References 15 publications

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“…More importantly, we show next that ∇ 2 g(c t ) is invertible only if the feature functions f k (i) are linearly independent, so that the Newton's method (11) can be used to solve (10).…”

Section: B Newton's Descent Methodsmentioning

confidence: 90%

“…After a new set of feature weighs c t+1 has been computed using (11), the optimal graph-signal x given the graph can be solved again via (7). The procedure repeats until both the signal x and the feature weights c converge.…”

Section: B Newton's Descent Methodsmentioning

confidence: 99%

“…Assume that edge weight w i,j connecting vertices i and j is computed using K pre-selected feature functions f k ( ) evaluated at i and j and a Gaussian kernel, as done in [3][4][5][6][7][8][9][10][11]:…”

Section: A Problem Definitionmentioning

confidence: 99%

“…The ill-posed problem is regularized using a graph-signal smoothness prior: an assumption that the desired signal x is smooth with respect to an underlying similarity graph G with respective vertex and edge sets V and E. The graph-signal smoothness prior has been used successfully in many signal restoration problems, such as denoising [3][4][5], interpolation [6][7][8], bit-depth enhancement [9] and JPEG de-quantization [10,11]. Simulation results in [2] for two image datasets with varying amount of label noise show that the constructed graph-based classifier outperforms two competing learning approaches in the literature noticeably.…”

Section: Introductionmentioning

confidence: 99%

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Joint learning of similarity graph and image classifier from partial labels

Mao

Cheung

Lin

et al. 2016

2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)

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Learning of a binary classifier from partial labels is a fundamental and important task in image classification. Leveraging on recent advance in graph signal processing (GSP), a recent work poses classifier learning as a graph-signal restoration problem from partial observations, where the ill-posed problem is regularized using a graph-signal smoothness prior. In this paper, we extend this work by using the same smoothness prior to refine the underlying similarity graph also, so that the same graphsignal projected on the modified graph will be even smoother. Specifically, assuming an edge weight connecting two vertices i and j is computed as the exponential kernel of the weighted sum of feature function differences at the two vertices, we find locally "optimal" feature weights via iterative Newton's method. We show that the conditioning of the Hessian matrix reveals redundancy in the feature functions, which thus can be eliminated for improved computation efficiency. Experimental results show that our joint optimization of the classifier graph-signal and the underlying graph has better classification performance then the previous work and spectral clustering.

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“…More importantly, we show next that ∇ 2 g(c t ) is invertible only if the feature functions f k (i) are linearly independent, so that the Newton's method (11) can be used to solve (10).…”

Section: B Newton's Descent Methodsmentioning

confidence: 90%

Section: B Newton's Descent Methodsmentioning

confidence: 99%

Section: A Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Joint learning of similarity graph and image classifier from partial labels

Mao

Cheung

Lin

et al. 2016

2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA)

Self Cite

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show abstract

“…To reduce computation complexity, we first divide the pre-filtered image and the output of CNN graph into K non-overlapping pixel patches (i.e., {X k pre } K k=1 and {f k n } K k=1 , 1 ≤ k ≤ K) for individual processing, as done in [12,25,26]. Note that K and k are the number of patches and the index of patches, respectively.…”

Section: Graph Constructionmentioning

confidence: 99%

Graph Neural Net Using Analytical Graph Filters and Topology Optimization for Image Denoising

Cheung

Wildes

et al. 2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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While convolutional neural nets (CNN) have achieved remarkable performance for a wide range of inverse imaging applications, the filter coefficients are computed in a purely data-driven manner and are not explainable. Inspired by an analytically derived CNN by Hadji et al., in this paper we construct a new layered graph convolutional neural net (GCNN) using GraphBio as our graph filter. Unlike convolutional filters in previous GNNs, our employed GraphBio is analytically defined and requires no training, and we optimize the end-to-end system only via learning of appropriate graph topology at each layer. In signal filtering terms, it means that our linear graph filter at each layer is always intrepretable as low-pass with known biorthogonal conditions, while the graph spectrum itself is optimized via data training. As an example application, we show that our analytical GCNN achieves image denoising performance comparable to a state-of-the-art CNN-based scheme when the training and testing data share the same statistics, and when they differ, our analytical GCNN outperforms it by more than 1dB in PSNR.

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Graph Spectral Image Processing

Cheung

Magli

Tanaka

et al. 2021

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Graph-based Dequantization of Block-Compressed Piecewise Smooth Images

Cited by 54 publications

References 15 publications

Joint learning of similarity graph and image classifier from partial labels

Joint learning of similarity graph and image classifier from partial labels

Graph Neural Net Using Analytical Graph Filters and Topology Optimization for Image Denoising

Graph Spectral Image Processing

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