Villota Santiago, Inga Esteban
Biomedical Engineering Program, Universidad Politécnica Salesiana, Quito EC170525, Ecuador.
Master in ICT for Education, Smart Grid Research Group (GIREI), Universidad Politécnica Salesiana, Quito EC170525, Ecuador.
Sensors (Basel). 2025 Aug 19;25(16):5137. doi: 10.3390/s25165137.
This paper explores the application of transform-domain sparsification and compressed sensing (CS) techniques to improve the efficiency and quality of magnetic resonance imaging (MRI). We implement and evaluate three sparsifying methods-discrete wavelet transform (DWT), fast Fourier transform (FFT), and discrete cosine transform (DCT)-which are used to simulate subsampled reconstruction via inverse transforms. Additionally, one accurate CS reconstruction algorithm, basis pursuit (BP), using the L-MAGIC toolbox, is implemented as a benchmark based on convex optimization with L-norm minimization. Emphasis is placed on basis pursuit (BP), which satisfies the formal requirements of CS theory, including incoherent sampling and sparse recovery via nonlinear reconstruction. Each method is assessed in MATLAB R2024b using standardized DICOM images and varying sampling rates. The evaluation metrics include peak signal-to-noise ratio (PSNR), root mean square error (RMSE), structural similarity index measure (SSIM), execution time, memory usage, and compression efficiency. The results show that although discrete cosine transform (DCT) outperforms the others under simulation in terms of PSNR and SSIM, it is inconsistent with the physics of MRI acquisition. Conversely, basis pursuit (BP) offers a theoretically grounded reconstruction approach with acceptable accuracy and clinical relevance. Despite the limitations of a controlled experimental setup, this study establishes a reproducible benchmarking framework and highlights the trade-offs between the quality of transform-based reconstruction and computational complexity. Future work will extend this study by incorporating clinically validated CS algorithms with L and nonconvex Lp (0 < < 1) regularization to align with state-of-the-art MRI reconstruction practices.
本文探讨了变换域稀疏化和压缩感知（CS）技术在提高磁共振成像（MRI）效率和质量方面的应用。我们实现并评估了三种稀疏化方法——离散小波变换（DWT）、快速傅里叶变换（FFT）和离散余弦变换（DCT）——用于通过逆变换模拟欠采样重建。此外，使用L-MAGIC工具箱实现了一种精确的CS重建算法——基追踪（BP），作为基于L范数最小化的凸优化的基准。重点放在基追踪（BP）上，它满足CS理论的形式要求，包括非相干采样和通过非线性重建进行稀疏恢复。每种方法都在MATLAB R2024b中使用标准化的DICOM图像和不同的采样率进行评估。评估指标包括峰值信噪比（PSNR）、均方根误差（RMSE）、结构相似性指数测量（SSIM）、执行时间、内存使用和压缩效率。结果表明，尽管在模拟中离散余弦变换（DCT）在PSNR和SSIM方面优于其他方法，但它与MRI采集的物理原理不一致。相反，基追踪（BP）提供了一种具有理论依据的重建方法，具有可接受的准确性和临床相关性。尽管受控实验设置存在局限性，但本研究建立了一个可重复的基准框架，并突出了基于变换的重建质量与计算复杂性之间的权衡。未来的工作将通过纳入具有L和非凸Lp（0 < p < 1）正则化的临床验证CS算法来扩展本研究，以与最新的MRI重建实践保持一致。
