# Super-Resolution Lensless Imaging of Cells Using Brownian Motion
## 1 Introduction  
Since the late 2000s, the lensless imaging technique based on CIS has enabled the creation of integrated microscopes on a chip scale [1; 2]. Using this technique to collect cell micrographic images has become a novel technique in the cell analysis aspect of point-of-care testing (POCT), which plays an important role in biological research, disease diagnosis, and new drug development [3; 4; 5; 6; 7; 8; 9]. As lensless imaging is not focused and amplified by an optical lens, some problems are experienced, such as diffraction and low resolution, in the lensless imaging system. To solve the diffraction problem, two different methods have been researched. The [PERSON] research group (California Institute of Technology) produced a near-diffraction-free cell imaging system by narrowing the distance between the cells and the photosensitive surface of CIS [10; 11; 12; 13]. The [PERSON] research group (University of California) irradiated cell samples using a near-coherent light source to obtain holographic images and reconstruct the focused images using an iterative algorithm [14; 15; 16; 17; 18; 19; 20; 21; 22]. The [PERSON] research group made cells flow through a microchannel in the microfluidic chip and obtained sub-pixel displacement both horizontally and vertically, which can be used by multi-frame super-resolution reconstruction [23]. Due to the stable flow rate of the diluent in the microchannel, the motion of cells in the diluent is close to uniform motion in a straight line. The sub-pixel displacement of cells can be accurately estimated using the averaging method to accurately register multi-frame images of cells. However, [PERSON]'s group used a multi-light source scheme to achieve sub-pixel displacement for multi-frame super-resolution reconstruction [24; 25]. In this scheme, two framesof exposure have different positions of point light source, and the cell shadow image displays the corresponding displacement. The sub-pixel displacement achieving the multi-frame super-resolution can be obtained by adjusting the distance between the point light sources. These two methods can determine the inter-frame motion of the cell image using an external device, and then obtain multi-frame low resolution images with sub-pixel displacement information to synthetic a high resolution image. However, these additional devices inevitably increase the volume of the system. [PERSON] propose a clever method to extend the numerical aperture by synthetic Fourier transform light scattering in in-line holographic microscope [26]. Combining the advantages of above methods, the key to improving the resolution is to capture the sub-pixel displacement information of cells images. To improve the resolution of cell images, the multi-frame super-resolution algorithm is used. Because of the low signal-to-noise ratio (SNR) of the image captured by lensless imaging system, a robust algorithm is needed to suppress the noise. Among all kinds of multi-frame super-resolution algorithms, a non-linear interpolation algorithm, normalized convolution (normalize convolution) proposed by Kuntsson Group [27], performs strongly in anti-noise interference. However, the [PERSON]'s algorithm cannot be extended to the edge of the image. Subsequently, [PERSON] [28] proposed a robust normalized convolution algorithm based on tensor, which uses the Gaussian kernel function to represent the size and direction of the neighborhood. The literature shows that all tiny objects make Brownian motion in fluid, and the cells are no exception in liquid [29]. According to the characteristics of Brownian motion direction and random displacement, we present a super-resolution method for a lensless imaging system based on Brownian motion. Using the inherent Brownian motion, the super-resolution of cell images in a lensless system can be realized without additional devices, such as an injection pump and a matrix light source.