Basic Bayesian Transform for Compressed Sensing

This article introduces a basic compressed sensing method using Bayesian transform. The implementation includes complete source code along with practical examples: one demonstrating 1D signal processing and two showcasing 2D image applications. Bayesian transform is widely adopted in signal processing for enhancing compressed sensing capabilities through frequency-domain transformations. This method enables significant signal compression while preserving critical features by strategically representing signals in reduced-dimensional spaces. The 1D signal example demonstrates Bayesian transform implementation for audio file compression, illustrating how to maintain audio quality while reducing storage requirements through sparse representation algorithms. The 2D image examples showcase image compression techniques using Bayesian priors, where key functions handle wavelet transformations and optimization algorithms to preserve visual features while minimizing file size. Through this material, you'll learn to implement basic Bayesian compressed sensing and understand its practical applications in signal processing, including code structure for handling different data dimensions and parameter optimization techniques.