Missing Intensity Interpolation Using a Kernel PCA-Based POCS Algorithm and its Applications
Takahiro Ogawa,Miki Haseyama +1 more
TL;DR: Since the proposed missing intensity interpolation method can restore any images including arbitrary-shaped missing areas, its potential in two image reconstruction tasks, image enlargement and missing area restoration, is shown.
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Abstract: A missing intensity interpolation method using a kernel principal component analysis (PCA)-based projection onto convex sets (POCS) algorithm and its applications are presented in this paper. In order to interpolate missing intensities within a target image, the proposed method reconstructs local textures containing the missing pixels by using the POCS algorithm. In this reconstruction process, a nonlinear eigenspace is constructed from each kind of texture, and the optimal subspace for the target local texture is introduced into the constraint of the POCS algorithm. In the proposed method, the optimal subspace can be selected by monitoring errors converged in the reconstruction process. This approach provides a solution to the problem in conventional methods of not being able to effectively perform adaptive reconstruction of the target textures due to missing intensities, and successful interpolation of the missing intensities by the proposed method can be realized. Furthermore, since our method can restore any images including arbitrary-shaped missing areas, its potential in two image reconstruction tasks, image enlargement and missing area restoration, is also shown in this paper.
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Figures
![Fig. 6. Comparison of results (640 × 480 pixels) obtained by using different image enlargement methods (Test image 3): (a) Result of reconstruction by sinc interpolation, (b) Result of reconstruction by the local-PCA based method, (c) Result of reconstruction by the conventional method [16], (d) Result of reconstruction by the conventional method [12], (e) Result of reconstruction by the conventional method [29], (f) Result of reconstruction by the proposed method.](/figures/fig-6-comparison-of-results-640-x-480-pixels-obtained-by-22l87iz5.png)
Fig. 6. Comparison of results (640 × 480 pixels) obtained by using different image enlargement methods (Test image 3): (a) Result of reconstruction by sinc interpolation, (b) Result of reconstruction by the local-PCA based method, (c) Result of reconstruction by the conventional method [16], (d) Result of reconstruction by the conventional method [12], (e) Result of reconstruction by the conventional method [29], (f) Result of reconstruction by the proposed method. 
Fig. 7. (a) Zoomed portion of Fig. 2(c), (b) Zoomed portion of Fig. 2(g), (c) Zoomed portion of Fig. 6(a), (d) Zoomed portion of Fig. 6(b), (e) Zoomed portion of Fig. 6(c), (f) Zoomed portion of Fig. 6(d), (g) Zoomed portion of Fig. 6(e), (h) Zoomed portion of Fig. 6(f). ![Fig. 14. Comparison of results obtained by using different missing area restoration methods (Test image 3): (a) Corrupted image including text regions “Fall Harvest Sweet Chestnut” (11.3 % loss), (b) Image reconstructed by the conventional method [10], (c) Image reconstructed by the local-PCA based method, (d) Image reconstructed by the kernel PCA based method using [12], (e) Image reconstructed by the conventional method [32], (f) Image reconstructed by the proposed method.](/figures/fig-14-comparison-of-results-obtained-by-using-different-2cq0c8gi.png)
Fig. 14. Comparison of results obtained by using different missing area restoration methods (Test image 3): (a) Corrupted image including text regions “Fall Harvest Sweet Chestnut” (11.3 % loss), (b) Image reconstructed by the conventional method [10], (c) Image reconstructed by the local-PCA based method, (d) Image reconstructed by the kernel PCA based method using [12], (e) Image reconstructed by the conventional method [32], (f) Image reconstructed by the proposed method. 
Fig. 13. (a) Zoomed portion of Fig. 9(b), (b) Zoomed portion of Fig. 12(a), (c) Zoomed portion of Fig. 12(b), (d) Zoomed portion of Fig. 12(c), (e) Zoomed portion of Fig. 12(d), (f) Zoomed portion of Fig. 12(e), (g) Zoomed portion of Fig. 12(f). 
Fig. 15. (a) Zoomed portion of Fig. 9(c), (b) Zoomed portion of Fig. 14(a), (c) Zoomed portion of Fig. 14(b), (d) Zoomed portion of Fig. 14(c), (e) Zoomed portion of Fig. 14(d), (f) Zoomed portion of Fig. 14(e), (g) Zoomed portion of Fig. 14(f). ![Fig. 5. Comparison of results by the conventional and proposed methods (Test image 2): (a) Zoomed portion of Fig. 2(b), (b) Zoomed portion of Fig. 2(f), (c) Zoomed portion of reconstruction result by sinc interpolation, (d) Zoomed portion of reconstruction result by the local-PCA based method, (e) Zoomed portion of reconstruction result by the conventional method [16], (f) Zoomed portion of reconstruction result by the conventional method [12], (g) Zoomed portion of reconstruction result by the conventional method [29], (h) Zoomed portion of reconstruction result by the proposed method.](/figures/fig-5-comparison-of-results-by-the-conventional-and-proposed-3b94nl36.png)
Fig. 5. Comparison of results by the conventional and proposed methods (Test image 2): (a) Zoomed portion of Fig. 2(b), (b) Zoomed portion of Fig. 2(f), (c) Zoomed portion of reconstruction result by sinc interpolation, (d) Zoomed portion of reconstruction result by the local-PCA based method, (e) Zoomed portion of reconstruction result by the conventional method [16], (f) Zoomed portion of reconstruction result by the conventional method [12], (g) Zoomed portion of reconstruction result by the conventional method [29], (h) Zoomed portion of reconstruction result by the proposed method.
![Fig. 6. Comparison of results (640 × 480 pixels) obtained by using different image enlargement methods (Test image 3): (a) Result of reconstruction by sinc interpolation, (b) Result of reconstruction by the local-PCA based method, (c) Result of reconstruction by the conventional method [16], (d) Result of reconstruction by the conventional method [12], (e) Result of reconstruction by the conventional method [29], (f) Result of reconstruction by the proposed method.](/figures/fig-6-comparison-of-results-640-x-480-pixels-obtained-by-22l87iz5.webp){kind=tracking}
![Fig. 14. Comparison of results obtained by using different missing area restoration methods (Test image 3): (a) Corrupted image including text regions “Fall Harvest Sweet Chestnut” (11.3 % loss), (b) Image reconstructed by the conventional method [10], (c) Image reconstructed by the local-PCA based method, (d) Image reconstructed by the kernel PCA based method using [12], (e) Image reconstructed by the conventional method [32], (f) Image reconstructed by the proposed method.](/figures/fig-14-comparison-of-results-obtained-by-using-different-2cq0c8gi.webp)
![Fig. 5. Comparison of results by the conventional and proposed methods (Test image 2): (a) Zoomed portion of Fig. 2(b), (b) Zoomed portion of Fig. 2(f), (c) Zoomed portion of reconstruction result by sinc interpolation, (d) Zoomed portion of reconstruction result by the local-PCA based method, (e) Zoomed portion of reconstruction result by the conventional method [16], (f) Zoomed portion of reconstruction result by the conventional method [12], (g) Zoomed portion of reconstruction result by the conventional method [29], (h) Zoomed portion of reconstruction result by the proposed method.](/figures/fig-5-comparison-of-results-by-the-conventional-and-proposed-3b94nl36.webp)
Citations
Biclustering and classification analysis in gene expression using Nonnegative Matrix Factorization on multi-GPU systems
Edgardo Mejía-Roa,Carlos García,José Ignacio Gómez,Manuel Prieto,Francisco Tirado,R. Nogales,Alberto Pascual-Montano +6 more
- 01 Nov 2011
TL;DR: Two parallel implementations of Nonnegative Matrix Factorization are presented, one of which uses CUDA on a Graphics Processing Unit (GPU) and the other distributes data among multiple GPUs synchronized through MPI (Message Passing Interface).
14
Fast image inpainting using exponential- threshold POCS plus conjugate gradient
Shu-Qin Wang,Jinhai Zhang +1 more
TL;DR: In this article, an exponential-threshold projection onto convex sets (POCS) was proposed to improve the convergence of the traditional POCS, which can recover the image in about 20 iterations but it cannot reconstruct the image details very well even with hundreds of iterations.
Edge Halo Reduction for Projections onto Convex Sets Super Resolution Image Reconstruction
Huiqin Xi,Chuangbai Xiao,Chunxiao Bian +2 more
- 01 Dec 2012
TL;DR: In order to improve the blur edge caused by bilinear interpolation, the wavelet bi-cubic interpolation is proposed to obtain the initial image estimation for reconstruction algorithm based on POCS and the point spread function (PSF) with edge-preserving property is suggested to reduce the amount of edge Halo in reconstruction result.
8
Adaptive example-based super-resolution using kernel PCA with a novel classification approach
Takahiro Ogawa,Miki Haseyama +1 more
TL;DR: An adaptive example-based super-resolution (SR) using kernel principal component analysis (PCA) with a novel classification approach is presented, which can adaptively estimate the missing high-frequency components, and successful reconstruction of the HR image is realized.
Exemplar-based image completion via new quality measure based on phaseless texture features
Takahiro Ogawa,Miki Haseyama +1 more
- 01 Mar 2017
TL;DR: Since the phaseless texture features are robust to various changes such as spatial gaps and luminance changes, the newquality measure successfully provides the best matched patch from few training examples and accurate image completion using the new quality measure becomes feasible.
5
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