“Application of FISTA and ISTA for Sparse Recovery in Compressed Sensing and Signal Denoising”
Step-by-Step Approach:
1. Review Literature: Start by thoroughly reviewing Beck and Teboulle’s paper and other literature on ISTA and FISTA, particularly in the context of compressed sensing and signal denoising.
2. Mathematical Formulation: Clearly formulate the optimization problems for both compressed sensing and signal denoising, including the sparse regularization term.
3. Implementation:
• Implement ISTA and FISTA for sparse signal recovery and denoising. You can follow the algorithms discussed in the reference paper but apply them to new datasets and problems.
• For compressed sensing, simulate a situation where a sparse signal is recovered from few measurements (undersampled data).
• For denoising, apply both algorithms to noisy signals or images and measure how well the algorithms remove noise while maintaining signal integrity.
4. Experimentation and Analysis:
• Compare ISTA and FISTA on different datasets.
• Measure convergence speed, accuracy, and how well the recovered signal matches the original.
5. Writing the Paper: Organize your paper according to the outline provided, ensuring that each section builds logically on the previous one.
Tools and Resources:
• Python: For implementation, using libraries like NumPy, PyWavelets, and scikit-learn will be helpful for matrix operations, wavelet transforms, and data analysis.
• MATLAB: If you prefer, MATLAB has excellent built-in functions for signal processing, sparse optimization, and wavelet analysis.
• Datasets: You can generate synthetic data for compressed sensing or use open-source datasets (e.g., for signal or image denoising tasks).