Consistency Analysis of Generative Priors and Sparse Optimization for Signal Reconstruction
DOI:
https://doi.org/10.66238/sqjffx50Keywords:
generative prior, sparse optimization, signal reconstruction, compressed sensing, variational autoencoder, MRI reconstruction, data consistencyAbstract
Signal reconstruction from incomplete or noisy measurements is still challenging when signals contain complex structures and small details. Traditional sparse methods, including LASSO and total variation, are easy to explain, but they often rely on fixed sparse assumptions. This study presents a generative-sparse reconstruction method that combines a variational autoencoder prior, an L1 sparse term, and a data-consistency term. The VAE learns a compact latent representation of high-dimensional signals. The L1 term helps control unstable latent activation during reconstruction. Experiments were conducted on FastMRI for MRI reconstruction and BSD500 for compressed sensing image recovery. The sampling rates were set to 10% and 20%. Compared with LASSO and total variation, the proposed method increased PSNR by 2.8–4.3 dB, improved SSIM by 0.05–0.09, and reduced NMSE by about 18.7%. Under Gaussian noise with σ = 25, the model remained stable and preserved useful image details. These results show that the learned prior improves structural recovery, while the sparse term improves stability and noise resistance. The method provides a useful approach for MRI reconstruction and compressed sensing image recovery with limited measurements.
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