Image Reconstruction Algorithm Based on Compressed Sensing

Compressed Sensing (CS) represents a groundbreaking signal acquisition and reconstruction technique that transcends traditional Nyquist sampling theorem limitations, demonstrating remarkable potential in image reconstruction applications. Its core principle leverages signal sparsity to achieve high-quality reconstruction from observational data acquired at significantly lower rates than conventional sampling requirements.

Core Principles Sparse Representation: Natural images exhibit sparsity in specific transform domains (e.g., wavelet, DCT), where most coefficients approach zero. Implementation typically involves applying sparsifying transforms like `dct2()` or `wavedec2()` in MATLAB. Incoherent Measurements: Linear projection of images through random measurement matrices (e.g., Gaussian matrices) captures limited observations. Code implementation often uses `randn()` for matrix generation with orthogonality validation. Reconstruction Optimization: Reformulates reconstruction as sparsity-constrained optimization problems. Common algorithms include Basis Pursuit (BP) and Orthogonal Matching Pursuit (OMP), where OMP implementations iteratively select atoms using correlation maximization.

Key Advantages Low Sampling Rate: Achieves image reconstruction with only 10%-30% of traditional sampling data. Noise Resilience: Demonstrates robustness against measurement noise, particularly suitable for low-SNR scenarios like medical imaging through regularized optimization techniques.

Typical Applications Accelerated MRI Imaging in Medical Diagnostics Single-Pixel Camera Design Data Transmission in Wireless Sensor Networks

Learning Recommendations Beginners should start with 1D signal reconstruction before advancing to 2D images. Focus on practical integration of measurement matrix design, sparsifying transform selection, and reconstruction algorithm parameter tuning through hands-on coding exercises.