Sparsity-based computational three dimensional microscopic imaging

He, Kuan

doi:https://doi.org/10.21985/n2-4e8c-9016

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Sparsity-based computational three dimensional microscopic imaging

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Recovering three-dimensional (3D) structural information of a specimen from a single two-dimensional (2D) measurement remains an important but challenging task in microscopic imaging. A conventional 2D microscopic image has a shallow depth-of-focus (DoF). Thus, recovering 3D information usually requires sequentially z-scanning the focal planes. This process is time consuming and requires precise mechanical control. The long acquisition time of focal scanning microscopy fundamentally prevents the applications in \emph{in vivo} imaging, especially when the 3D movement of biomedical objects is desired. To realize snapshot 3D microscopy, a standard microscope has to be modified in such a way that 3D information can be encoded onto a 2D plane. In this thesis, I explore and discuss three different snapshot 3D microscopic imaging techniques: (1) multifocal microscopy (MFM); (2) multifocal light field microscopy (MFLFM); (3) and digital holographic micrsocopy (DHM). I analyze and investigate each of those imaging systems in terms of their implementation setups, the point spread functions (PSFs), resolution, field-of-view (FOV), noise and image formation models. For inverse 3D image reconstructions, I explore the sparsity-based optimization methods under compressed sensing (CS) or Richardson-Lucy (RL) deconvolution frameworks. In particular, I consider 2D/3D total variation (TV) regularization for the image reconstruction. MFM extends DoF by recording a focal stack simultaneously by placing a diffractive optical element (DOE) in the Fourier plane of a standard microscope. The chromatic aberration due to DOE is analyzed. The image formation modeling under Poisson noise curruption is derived and the joint RL algorithm is proposed which automatically recovers the background noise, the optimal regularizer parameter and a high resolution 3D image from a single captured 2D MFM image. In addition, a dual-objective interferometric MFM (iMFM) system is designed and simulated to achieve axial super resolution in a single shot. LFM extends DoF by capturing the light field of the 3D sample based on which a focal stack can be constructed. Here, I propose and implement an MFLFM by combining MFM and LFM. MFLFM is capable of recording differently focused light field simultaneously. By stacking those light field, MFLFM can achieve an extended DoF over MFM/LFM. In addition, I show that MFLFM can produce the uniform lateral resolution across depth, overcoming the lateral resolution fall-off problem in a conventinal LFM. DHM encodes 3D information into a 2D hologram via interference between object field and reference field. Unlike MFM and LFM where incoherent illumination is used, DHM requires coherent illumination. Here I develope a CS-based method for digital Fourier transform holography and coherent diffraction imaging to tackle the missing data problem in the Fourier domain measurements.

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