## 1 Introduction  
A microscope allows researchers to visualize and study the structures and functions of specimens at a cellular and subcellular level. It is a device that combines an optical lens and a mechanical device and comprises a system that can achieve high magnification. Among the types of microscopes, light microscope is the most basic and is configured to directly observe the light passing through the specimen. Light microscope images often appear blurry because light from one point on the sample is not detected in a single pixel. This is caused by the fundamental limitation that light from a very small point cannot be detected from a similar point. Therefore, light can be detected only in a small area when the image is in focus [1]. In a non-ideal case, the obtained image is convolved with a point spread function (PSF) that provides the imaging system response with a degraded resolution. In particular, blurring should be removed through pre-calibration by considering the theoretical resolution and cross sectional capacity of the imaging system [2]. However, there is a limit to completely removing the PSF. Therefore, PSF estimation and deconvolution to the image acquisition condition are essential for high-quality restoration [3]. Deblurring approaches are divided into non-blind deblurring (performs deconvolution by knowing the PSF in advance) and blind deblurring (estimates the PSF and performs deconvolution without relying on ancillary measurements). Non-blind deblurringmethods have previously been investigated using various approaches, including the image-formation model [4; 5], inverse filtering [6], Tihkonov regularization [7], Landweber [8], fast iterative soft-thresholding [9], Richardson-Lucy [10; 11; 12], and maximum a posteriori method [13]. The corresponding representative algorithms are described in detail in the literature [1; 14]. Unfortunately, these methods depend on a prior PSF that is based on the laws of optics using the theory and knowledge of the optical components, and the PSF is unlikely to match the current experimental conditions [1]. Accurate PSF estimation is the key to successful image restoration in blind deblurring. Typical blind deblurring methods include parametric form-based methods [15; 16], joint image restoration and blur identification methods [17; 18], Bayesian-based methods [19; 20], prior-knowledge-based methods [21; 22], and the adaptive image deconvolution algorithm [13; 23]. Various studies have shown that these methods effectively estimate the PSF and exhibit outstanding image restoration results, even in ill-posed problems. However, the presence of noise in the microscope image is still a problem. The degraded image can be modeled by convolving a clean image, which is artifact free, and the blur kernel (or PSF) of a light microscope imaging system, as follows:  
\[g(x,y)=f(x,y)\bigotimes\bigotimes pgf(x,y)+n(x,y), \tag{1}\]  
where _g(x,y)_ and _f(x,y)_ are degraded and clean images, respectively; _psf(x,y)_ represents the blur kernel; and _n(x,y)_ is the added background noise. The noise that can be generated in an optical microscopic image includes Poisson noise from the number of photons, Gaussian noise from image sensor and ambient noise, quantization noise from the analog-to-digital conversion, and speckle noise from coherent light sources [24]. Image restoration based on a model that comprehensively considers various noises will produce accurate results. However, it is not feasible to implement a degradation model takes all noise components. Among the various noise degradation models, the additive noise model of the Gaussian distribution, which is universally assumed by transmitted-light microscopy, was selected in this study. For instance, [PERSON] et al. [25] assumed that white Gaussian noise was added to the original image (artifact free) in the process of performing 3D image reconstruction in transmitted light bright-field microscopy, and [PERSON] et al.