Magnetic Resonance Imaging plays a crucial role in modern medicine, helping doctors diagnose a wide range of health issues. Signal denoising methods are powerful tools for increasing the quality of MRI signals to reduce acquisition time. However, existing methods often provide inadequate denoising and fail to recover the minute structures present in MR images. We developed a pixel-wise thresholding method based on Srivastava-Freed singular value decomposition that effectively removes noise from MR images while preserving these minute structures. To validate our method, we applied it to ACR phantom data. Additionally, the pixel-wise method was applied to volunteer MRI data from two brain scans and one lumbar spine scan to demonstrate MRI scan time reduction. The denoised results display superior visual quality, recover minute structures, and reduce MRI scan time by 50%. Another application of the method is constructing 2D distance distributions from pulsed dipolar ESR spectroscopy. Currently, distance distribution reconstruction methods are limited to one dimension and require prior information. Additionally, these methods provide inconclusive results for multimodal distributions. The developed method is an extension of the SF-SVD method to two dimensions. To validate our method, we applied it to a two-dimensional simulated bimodal distribution. For comparison with current methods, we applied the method to the pH titration DEER spectroscopy dataset for bimodal and multimodal distance distribution. The comparative results establish the superior performance of our method.