Reconstruction Using Compressive Sensing Technology

Compressive sensing is a revolutionary signal sampling and reconstruction technique that breaks the limitations of traditional Nyquist sampling theorem. It enables high-quality reconstruction by acquiring signals at sampling rates far below the Nyquist frequency while leveraging signal sparsity. Filter-based reconstruction algorithms, as one important implementation approach, effectively enhance reconstruction efficiency and accuracy through the combination of filtering techniques and sparse optimization methods.

In compressive sensing, signals typically require sparse representation in certain transform domains (such as Fourier transform, wavelet transform, etc.). The core concept of filter-based reconstruction algorithms involves utilizing prior information to perform filtering operations on signals, suppressing noise and irrelevant components. Simultaneously, optimization algorithms (like iterative thresholding methods, convex optimization, etc.) are employed to solve for sparse representation coefficients, ultimately recovering the original signal. This method achieves a good balance between computational efficiency and reconstruction quality, making it suitable for applications in medical imaging, wireless communications, and remote sensing.

Compared to traditional reconstruction algorithms, filter-based reconstruction demonstrates stronger noise resistance and faster convergence speed. However, its performance depends on filter design and optimization of sparse regularization parameters. In the future, adaptive filtering methods incorporating deep learning may further enhance the reconstruction performance of compressive sensing.