The primary objective of the project is to systematically assess the efficacy and performance of some of these methods which enable building of low-order representations of image data. For a detailed project report, please refer to the Complete Project Report
The dataset under assessment for performance evaluation is a multi-channel (color) image.
The dataset has been reduced in size for performance evaluation using neural networks for a smaller training time with the limited computaitonal resources.
Low-order representations of the image data can be obtained by storing data upto different value of rank r (All the three channels have the same value of r) after the singular vector decomposition of the data matrix (which is an image in this case). For a more accurate reconstruction with lower storage, different value of r can be set for each of the three channels based on the amount of cumulative energy that is captured.
This transformation shifts an image from its spatial domain into the frequency domain, allowing for the segregation of high-frequency and low-frequency coefficients. Low-order representations of the image data can be obtained by storing data upto different value of frequencies on the bases of the magnitude of their fourier coefficients. It also permits the attenuation or modification of specific frequencies, resulting in an image with reduced data but retaining a satisfactory level of quality.
Neural networks’ ability to learn nonlinear relationships makes autoencoders a powerful extension of PCA. Convolutional Neural Networks (CNN) based autoencoders extend the basic autoencoder architecture by incorporating convolutional layers. This enables them to capture spatial hierarchies and features within the image data, which improves image compression and reconstruction. In the context of image data, this latent space captures the most salient features of the input.
Convolutional Neural Network (CNN)-based Hierarchical Autoencoders (HAE) represent a powerful neural network architecture designed for hierarchical feature learning, particularly well-suited for tasks involving complex spatial data, such as image analysis, computer vision, and deep learning applications. Hierarchical autoencoders extend the principles of traditional autoencoders to enable the extraction of increasingly abstract and informative features through multiple layers of stacked autoencoders. Furthermore, the CNN-HAE architecture can order the AE modes following their contributions to the reconstructed field while achieving efficient order reduction.
