Optimized Subspace Iteration Methods for Spectral Decomposition and Image Compression

Description

This repository contains the implementation of advanced Subspace Iteration Methods for spectral decomposition of matrices, with a focus on applying these methods to image compression.

Project Overview

We explore various versions of the Subspace Iteration Method, starting from the Power Method and extending to optimized versions including Rayleigh Projection and acceleration techniques. The project includes a performance comparison of custom algorithms against MATLAB’s built-in eig function for eigenvalue computations, particularly applied to image compression tasks.

Key Features

• Subspace Iteration: Various implementations for improved spectral decomposition.
• Rayleigh Projection: Faster convergence for eigenvalue computation.
• Image Compression: Using matrix decomposition for efficient image compression.
• Performance Metrics: Comparative analysis with MATLAB’s eig function.

Methods Implemented

1. Power Method: A basic iterative method for eigenvalue computation.
2. Subspace Iteration (v1): A refined method without projection.
3. Subspace Iteration with Rayleigh Projection (v2): Enhanced with Rayleigh projection.
4. Subspace Iteration with Rayleigh Projection and Acceleration (v3): Further optimized for large matrices.

Results

• The MATLAB eig function is generally the fastest and most efficient.
• The accelerated subspace iteration method performs well for large matrices in image compression applications.