1 / 23

Understanding Principal Component Analysis (PCA) and Its Applications in Image Reconstruction

Principal Component Analysis (PCA) explores the intrinsic dimensionality of datasets, enhancing data visualization and noise reduction. In this guide, we detail two practical examples of PCA applications using the "noisy.mat" dataset, which contains distorted images. We demonstrate how to apply PCA, extract top eigenvectors, and reconstruct images, while using Singular Value Decomposition (SVD) for dimensionality reduction. Learn how to visualize original and reconstructed images and understand the benefits of PCA in image processing.

garnet
Télécharger la présentation

Understanding Principal Component Analysis (PCA) and Its Applications in Image Reconstruction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Principal Component Analysis (PCA)

  2. Principal Component Analysis (PCA)

  3. Principal Component Analysis (PCA)

  4. Principal Component Analysis (PCA)

  5. Principal Component Analysis (PCA)

  6. Principal Component Analysis (PCA)

  7. Principal Component Analysis (PCA)

  8. Principal Component Analysis (PCA)

  9. Principal Component Analysis (PCA)

  10. Principal Component Analysis (PCA)

  11. Alternative Derivation (PCA)

  12. Alternative Derivation (PCA)

  13. Alternative Derivation (PCA)

  14. Alternative Derivation (PCA)

  15. Singular Value Decomposition

  16. Singular Value Decomposition

  17. Singular Value Decomposition

  18. Example 1 • Use the data set "noisy.mat" available on your CD. The data set consists of 1965, 20-pixel-by-28-pixel grey-scale images distorted by adding Gaussian noises to each pixel with s=25.

  19. Example 1 • Apply PCA to the noisy data. Suppose the intrinsic dimensionality of the data is 10. Compute reconstructed images using the top d = 10 eigenvectors and plot original and reconstructed images

  20. Example 1 • If original images are stored in matrix X (it is 560 by 1965 matrix) and reconstructed images are in matrix X_hat , you can type in • colormap gray and then • imagesc(reshape(X(:,10),2028)’) • imagesc(reshape(X_hat(:,10),2028)’) to plot the 10th original image and its reconstruction.

  21. Example 2

  22. Example 2 • Load the sample data, which includes digits 2 and 3 of 64 measurements on a sample of 400. load 2_3.mat • Extract appropriate features by PCA [u s v]=svd(X','econ'); • Create data Low_dimensional_data=u(:,1:2); • Observe low dimensional data Imagesc(Low_dimensional_data)

More Related