Compressed sensing and learning-based methods for super-resolution structured illumination microscopy

Official URL: https://risc01.sabanciuniv.edu/record=b2553601_(Table of contents)

Using an optical microscope, most viruses, proteins, and small molecules cannot be successfully imaged because of Abbe’s diffraction limit. The super-resolution structured illumination microscopy (SIM) technique overcomes this issue and expands the lateral resolution to the half of the diffraction limit. The cost of the SIM technique results from the need to record at least nine raw images to reconstruct a single super-resolution image. This requirement has two consequences: photobleaching and motion artifacts. To alleviate these problems, we need a system that is extremely fast for recording raw images (to observe high dynamic processes) and projects less excitation light onto the sample (to avoid photobleaching). Compressed sensing (CS) can be a candidate for achieving these objectives. First, CS allows us to record an object scene with a photomultiplier tube (PMT) instead of a camera. The acquisition speed of a PMT is much higher than a scientific complementary metaloxide- semiconductor (sCMOS) camera. Second, the scene in the CS framework is sampled faster (thanks to the higher frame rate of a digital micromirror device - DMD), and also sampled with lower excitation light (because of sampling patterns). Third, the CS framework can recover the scene reliably with few measurements, reducing the overall data collection time further. The main objective of this dissertation is to combine CS and SIM techniques, but we also make various contributions to this framework. The main contributions of this dissertation are (1) proposing a dictionary learning method based on the multi-layer convolutional sparse coding (ML-CSC) model to improve the performance of a CS recovery algorithm; and (2) proposing a method for the combination of CS and SIM and demonstrating the method with simulation-based studies as well as real data collection experiments. In early attempts in the sparse representation theory, some off-the-shelf dictionaries were utilized. However, training dictionaries instead of using a known transform significantly improved signal reconstruction quality. On the other hand, the success of a CS recovery algorithm is directly related to the sparsity level of a signal. The sparsity level of a signal depends on the sparsifying transform or dictionary. With that perspective, we need to learn a sparsifying transform or dictionary that is compatible with a signal of interest. Therefore, we propose a dictionary learning method based on ML-CSC. The method does not depend on any parameters or the success of a CS recovery algorithm involved in the dictionary learning steps although the ancestor of the proposed algorithm depends on some parameters and the recovery algorithm. We also implement the learned dictionaries into a CS recovery algorithm and discuss the performance of the proposed learning algorithm. The other main contribution of this dissertation is to combine the CS framework and the SIM technique. We demonstrate this combination utilizing a simulation-based study. The mathematical foundation of the proposed study is demonstrated. Then, experimental results for both stationary and non-stationary objects are presented. We utilize some CS recovery algorithms presented previously and compare the reconstruction results for the case of the combination of CS and SIM. We propose an optical configuration for the data collection problem with the photomultiplier tube (PMT), and then we discuss the limitations of the DMD in the laboratory. Then, an optical configuration for the combination of CS and SIM is introduced. Using the proposed configuration, an experimental study is performed for both stationary and non-stationary objects. The normalized intensity profiles of the reconstructions and the other conventional microscopy methods for the same object are compared. The proof-of-principle solution for the photobleaching issue is evaluated for the real optical configuration. We also present a CS approach for holography and demonstrate the extraction of depth information from a single hologram. An optical configuration for holographic data collection is first presented. The depths of the variety of digital holograms (include compressive ones) are obtained using the stereo disparity method. The proposed method does not require the phase information of the hologram but two perspectives of the scene, which are easily obtained by dividing the hologram into two parts (two apertures) before the reconstruction. We investigated the effects of gradual and sharp divisions of the holograms for the disparity map calculations, specifically for divisions in the vertical, horizontal, and diagonal directions. After obtaining the depth map from the stereo images, a regular two-dimensional image of the object is merged with the depth information to form 3D visualization of the object.