Multi-resolution analysis enables fidelity-ensured deconvolution for fluorescence microscopy

Abstract Fluorescence microscopic imaging is essentially a convolution process distorted by random noise, limiting critical parameters such as imaging speed, duration, and resolution. Though algorithmic compensation has shown great potential to enhance these pivotal aspects, its fidelity remains questioned. Here we develop a physics-rooted computational resolution extension and denoising method with ensured fidelity. Our approach employs a multi-resolution analysis (MRA) framework to extract the two main characteristics of fluorescence images against noise: across-edge contrast, and along-edge continuity. By constraining the two features in a model-solution framework using framelet and curvelet, we develop MRA deconvolution algorithms, which improve the signal-to-noise ratio (SNR) up to 10 dB higher than spatial derivative based penalties, and can provide up to two-fold fidelity-ensured resolution improvement rather than the artifact-prone Richardson-Lucy inference. We demonstrate our methods can improve the performance of various diffraction-limited and super-resolution microscopies with ensured fidelity, enabling accomplishments of more challenging imaging tasks.