Noise-robust, physical microscopic deconvolution algorithm enabled by multi-resolution analysis regularization

Despite the grand advances in fluorescence microscopy, the photon budget of fluorescent molecules remains the fundamental limiting factor for major imaging parameters, such as temporal resolution, duration, contrast, and even spatial resolution. Computational methods can strategically utilize the fluorescence photons against the imaging noise, to break the abovementioned limits. Here, we propose a multi-resolution analysis (MRA) approach to recharacterize and extract the two main characteristics of fluorescence images: (1) high contrast across the edge, and (2) high continuity along the edge. By regularizing the solution using framelet and curvelet domain sparsity, we develop MRA deconvolution algorithm for fluorescence image, which allows fine detail recovery even with negative signal-to-noise-ratio (SNR), and can provide more than 2-fold physical resolution enhancement with conspicuously fewer artifacts than maximum likelihood estimation (MLE) methods. Furthermore, we develop DeepMRA deconvolution algorithm that can provide computational background inhibition through a bias thresholding mechanism while deconvolving a fluorescence image. Compared with conventional background mitigation schemes, this novel deconvolution canonical form can deal with severer background and better preserve the high-frequency and low-intensity details, which are commonly disrupted by other algorithms. We demonstrate that the MRA and DeepMRA deconvolution algorithms can improve the SNR and resolution of biological images in various microscopies, such as wide-field, confocal, spinning-disk confocal (SD-confocal), light-sheet, structured illumination microscopy (SIM), and stimulated excitation depletion (STED) microscopy.