A Kalman filter approach for denoising and deblurring 3-D microscopy images

Distortion Correction and Denoising of Light Sheet Fluorescence Images

Light Sheet Fluorescence Microscopy (LSFM) has emerged as a valuable tool for neurobiologists, enabling the rapid and high-quality volumetric imaging of mice brains. However, inherent artifacts and distortions introduced during the imaging process necessitate careful enhancement of LSFM images for optimal 3D reconstructions. This work aims to correct images slice by slice before reconstructing 3D volumes. Our approach involves a three-step process: firstly, the implementation of a deblurring algorithm using the work of K. Becker; secondly, an automatic contrast enhancement; and thirdly, the development of a convolutional denoising auto-encoder featuring skip connections to effectively address noise introduced by contrast enhancement, particularly excelling in handling mixed Poisson-Gaussian noise. Additionally, we tackle the challenge of axial distortion in LSFM by introducing an approach based on an auto-encoder trained on bead calibration images. The proposed pipeline demonstrates a complete solution, presenting promising results that surpass existing methods in denoising LSFM images. These advancements hold potential to significantly improve the interpretation of biological data.

A New Framework of Designing Iterative Techniques for Image Deblurring

In this work we present a framework of designing iterative techniques for image deblurring in inverse problem. The new framework is based on two observations about existing methods. We used Landweber method as the basis to develop and present the new framework but note that the framework is applicable to other iterative techniques. First, we observed that the iterative steps of Landweber method consist of a constant term, which is a low-pass filtered version of the already blurry observation. We proposed a modification to use the observed image directly. Second, we observed that Landweber method uses an estimate of the true image as the starting point. This estimate, however, does not get updated over iterations. We proposed a modification that updates this estimate as the iterative process progresses. We integrated the two modifications into one framework of iteratively deblurring images. Finally, we tested the new method and compared its performance with several existing techniques, including Landweber method, Van Cittert method, GMRES (generalized minimal residual method), and LSQR (least square), to demonstrate its superior performance in image deblurring.

Application of Blind Deconvolution Based on the New Weighted L1-norm Regularization with Alternating Direction Method of Multipliers in Light Microscopy Images

This study aimed to develop and evaluate a blind-deconvolution framework using the alternating direction method of multipliers (ADMMs) incorporated with weighted L1-norm regularization for light microscopy (LM) images. A presimulation study was performed using the Siemens star phantom prior to conducting the actual experiments. Subsequently, the proposed algorithm and a total generalized variation-based (TGV-based) method were applied to cross-sectional images of a mouse molar captured at 40× and 400× on-microscope magnifications and the results compared, and the resulting images were compared. Both simulation and experimental results confirmed that the proposed deblurring algorithm effectively restored the LM images, as evidenced by the quantitative evaluation metrics. In conclusion, this study demonstrated that the proposed deblurring algorithm can efficiently improve the quality of LM images.

Efficient and Fast Real-World Noisy Image Denoising by Combining Pyramid Neural Network and Two-Pathway Unscented Kalman Filter

Recently, image prior learning has emerged as an effective tool for image denoising, which exploits prior knowledge to obtain sparse coding models and utilize them to reconstruct the clean image from the noisy one. Albeit promising, these prior-learning based methods suffer from some limitations such as lack of adaptivity and failed attempts to improve performance and efficiency simultaneously. With the purpose of addressing these problems, in this paper, we propose a Pyramid Guided Filter Network (PGF-Net) integrated with pyramid-based neural network and Two-Pathway Unscented Kalman Filter (TP-UKF). The combination of pyramid network and TP-UKF is based on the consideration that the former enables our model to better exploit hierarchical and multi-scale features, while the latter can guide the network to produce an improved (a posteriori) estimation of the denoising results with fine-scale image details. Through synthesizing the respective advantages of pyramid network and TP-UKF, our proposed architecture, in stark contrast to prior learning methods, is able to decompose the image denoising task into a series of more manageable stages and adaptively eliminate the noise on real images in an efficient manner. We conduct extensive experiments and show that our PGF-Net achieves notable improvement on visual perceptual quality and higher computational efficiency compared to state-of-the-art methods.

PURE-LET Image Deconvolution

We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson or mixed Poisson-Gaussian noise. Many applications involve such a problem, ranging from astronomical to biological imaging. We parameterize the deconvolution process as a linear combination of elementary functions, termed as linear expansion of thresholds. This parameterization is then optimized by minimizing a robust estimate of the true mean squared error, the Poisson unbiased risk estimate. Each elementary function consists of a Wiener filtering followed by a pointwise thresholding of undecimated Haar wavelet coefficients. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations, which has a fast and exact solution. Simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state-of-the-art techniques, in terms of both restoration quality and computational complexity. Finally, we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images.We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson or mixed Poisson-Gaussian noise. Many applications involve such a problem, ranging from astronomical to biological imaging. We parameterize the deconvolution process as a linear combination of elementary functions, termed as linear expansion of thresholds. This parameterization is then optimized by minimizing a robust estimate of the true mean squared error, the Poisson unbiased risk estimate. Each elementary function consists of a Wiener filtering followed by a pointwise thresholding of undecimated Haar wavelet coefficients. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations, which has a fast and exact solution. Simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state-of-the-art techniques, in terms of both restoration quality and computational complexity. Finally, we present some results on real confocal fluorescence microscopy images and demonstrate the potential applicability of the proposed method for improving the quality of these images.

Feature-based filter design for resolution enhancement of known features in microscopy

We present a new feature-based design concept for filter design in which a filter is designed specifically to image a known feature with dimensions lower than the optical resolution of the system. Unlike the conventional filter design based on focal spot engineering, we use the complete response of the microscope to form a resolution factor and consider minimizing the resolution factor as the design goal. We consider three design goals (i.e., resolution factors) based on the system response and show that a feature matching approach is more suitable in practice. It is shown that a three-bar pattern and grid of square dots of critical dimension, 0.08λ, can be resolved using a simple two-layer feature-based filter designed for radially polarized illumination in aplanatic solid immersion lens microscopy. An example that requires a more complex filter is also shown. Applicability of the concept of feature-based filter design in diverse microscopy scenarios is discussed as well.