Blind Deconvolution Framework Research Articles

Luminosity rectified blind Richardson-Lucy deconvolution for single retinal image restoration

Background and objectiveDue to imperfect imaging conditions, retinal images can be degraded by uneven/insufficient illumination, blurriness caused by optical aberrations and unintentional motions. Degraded images reduce the effectiveness of diagnosis by an ophthalmologist. To restore the image quality, in this research we propose the luminosity rectified Richardson-Lucy (LRRL) blind deconvolution framework for single retinal image restoration. MethodsWe established an image formation model based on the double-pass fundus reflection feature and developed a differentiable non-convex cost function that jointly achieves illumination correction and blind deconvolution. To solve this non-convex optimization problem, we derived the closed-form expression of the gradients and used gradient descent with Nesterov-accelerated adaptive momentum estimation to accelerate the optimization, which is more efficient than the traditional half quadratic splitting method. ResultsThe LRRL was tested on 1719 images from three public databases. Four image quality matrixes including image definition, image sharpness, image entropy, and image multiscale contrast were used for objective assessments. The LRRL was compared against the state-of-the-art retinal image blind deconvolution methods. ConclusionsOur LRRL corrects the problematic illumination and improves the clarity of the retinal image simultaneously, showing its superiority in terms of restoration quality and implementation efficiency. The MATLAB code is available on Github.

Spatially adaptive blind deconvolution methods for optical coherence tomography

Optical coherence tomography (OCT) is a powerful noninvasive imaging technique for detecting microvascular abnormalities. Following optical imaging principles, an OCT image will be blurred in the out-of-focus domain. Digital deconvolution is a commonly used method for image deblurring. However, the accuracy of traditional digital deconvolution methods, e.g., the Richardson-Lucy method, depends on the prior knowledge of the point spread function (PSF), which varies with the imaging depth and is difficult to determine. In this paper, a spatially adaptive blind deconvolution framework is proposed for recovering clear OCT images from blurred images without a known PSF. First, a depth-dependent PSF is derived from the Gaussian beam model. Second, the blind deconvolution problem is formalized as a regularized energy minimization problem using the least squares method. Third, the clear image and imaging depth are simultaneously recovered from blurry images using an alternating optimization method. To improve the computational efficiency of the proposed method, an accelerated alternating optimization method is proposed based on the convolution theorem and Fourier transform. The proposed method is numerically implemented with various regularization terms, including total variation, Tikhonov, and l1 norm terms. The proposed method is used to deblur synthetic and experimental OCT images. The influence of the regularization term on the deblurring performance is discussed. The results show that the proposed method can accurately deblur OCT images. The proposed acceleration method can significantly improve the computational efficiency of blind demodulation methods.

Overcomplete Order-3 Tensor Decomposition, Blind Deconvolution, and Gaussian Mixture Models

We expand the family of tensors that can be efficiently decomposed and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our basic contribution is an efficient algorithm to decompose certain symmetric overcomplete order-3 tensors, that is, three dimensional arrays of the form $T = \sum_{i=1}^n a_i \otimes a_i \otimes a_i$ where the $a_i$s are not linearly independent. Our second contribution builds on top of our tensor decomposition algorithm to expand the family of Gaussian mixture models whose parameters can be estimated efficiently. These ideas are also presented in a much more general framework of blind deconvolution that makes them applicable to mixture models of identical but very general distributions, including all centrally symmetric distributions with finite 6th moment.

Photon-Limited Blind Deconvolution Using Unsupervised Iterative Kernel Estimation

Blind deconvolution is a challenging problem, but in low-light it is even more difficult. Existing algorithms, both classical and deep-learning based, are not designed for this condition. When the photon shot noise is strong, conventional deconvolution methods fail because (1) the image does not have enough signal-to-noise ratio to perform the blur estimation; (2) While deep neural networks are powerful, many of them do not consider the forward process. When the noise is strong, these networks fail to simultaneously deblur and denoise; (3) While iterative schemes are known to be robust in the classical frameworks, they are seldom considered in deep neural networks because it requires a differentiable non-blind solver. This paper addresses the above challenges by presenting an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised</i> blind deconvolution method. At the core of this method is a reformulation of the general blind deconvolution framework from the conventional image-kernel alternating minimization to a purely kernel-based minimization. This kernel-based minimization leads to a new iterative scheme that backpropagates an unsupervised loss through a pre-trained non-blind solver to update the blur kernel. Experimental results show that the proposed framework achieves superior results than state-of-the-art blind deconvolution algorithms in low-light conditions.

Blind Deconvolution Based on Compressed Sensing with bi-l0-l2-norm Regularization in Light Microscopy Image.

Blind deconvolution of light microscopy images could improve the ability of distinguishing cell-level substances. In this study, we investigated the blind deconvolution framework for a light microscope image, which combines the benefits of bi-l0-l2-norm regularization with compressed sensing and conjugated gradient algorithms. Several existing regularization approaches were limited by staircase artifacts (or cartooned artifacts) and noise amplification. Thus, we implemented our strategy to overcome these problems using the bi-l0-l2-norm regularization proposed. It was investigated through simulations and experiments using optical microscopy images including the background noise. The sharpness was improved through the successful image restoration while minimizing the noise amplification. In addition, quantitative factors of the restored images, including the intensity profile, root-mean-square error (RMSE), edge preservation index (EPI), structural similarity index measure (SSIM), and normalized noise power spectrum, were improved compared to those of existing or comparative images. In particular, the results of using the proposed method showed RMSE, EPI, and SSIM values of approximately 0.12, 0.81, and 0.88 when compared with the reference. In addition, RMSE, EPI, and SSIM values in the restored image were proven to be improved by about 5.97, 1.26, and 1.61 times compared with the degraded image. Consequently, the proposed method is expected to be effective for image restoration and to reduce the cost of a high-performance light microscope.

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.

Investigation of a blind-deconvolution framework after noise reduction using a gamma camera in nuclear medicine imaging

A gamma camera system using radionuclide has a functional imaging technique and is frequently used in the field of nuclear medicine. In the gamma camera, it is extremely important to improve the image quality to ensure accurate detection of diseases. In this study, we designed a blind-deconvolution framework after a noise-reduction algorithm based on a non-local mean, which has been shown to outperform conventional methodologies with regard to the gamma camera system. For this purpose, we performed a simulation using the Monte Carlo method and conducted an experiment. The image performance was evaluated by visual assessment and according to the intensity profile, and a quantitative evaluation using a normalized noise-power spectrum was performed on the acquired image and the blind-deconvolution image after noise reduction. The result indicates an improvement in image performance for gamma camera images when our proposed algorithm is used.

Iteratively reweighted blind deconvolution for passive millimeter-wave images

Passive millimeter-wave (PMMW) imaging frequently suffers from blurring and low resolution due to the diffraction limits and the long wavelengths compared with visual and infrared radiation. Moreover, the observed image is inevitably degraded by the system noise and natural clutter noise. The blur and noise limit the capability of PMMW images in practical applications. In this study, we propose an iteratively reweighted blind deconvolution method for obtaining high quality PMMW images. A weighted least-squares data-fidelity term that is robust to modeling error and a weighted bilateral total variation regularization term are incorporated into the variational blind deconvolution framework. Furthermore, we impose an appropriate smooth constraint for the point spread function of the imaging system. In addition, to improve the practicality of the method, we derive a formula to automatically update the regularization parameter from the data. Comparative experimental results on simulated and real images show that the proposed method is superior to the state-of-the-art methods in terms of both subjective measure and visual quality.

Multi-frame partially saturated images blind deconvolution

When blurred images have saturated or over-exposed pixels, conventional blind deconvolution approaches often fail to estimate accurate point spread function (PSF) and will introduce local ringing artifacts. In this paper, we propose a method to deal with the problem under the modified multi-frame blind deconvolution framework. First, in the kernel estimation step, a light streak detection scheme using multi-frame blurred images is incorporated into the regularization constraint. Second, we deal with image regions affected by the saturated pixels separately by modeling a weighted matrix during each multi-frame deconvolution iteration process. Both synthetic and real-world examples show that more accurate PSFs can be estimated and restored images have richer details and less negative effects compared to state of art methods.

Single-Image Refocusing and Defocusing

In this paper, we present a postprocessing method to tackle the single-image refocusing-and-defocusing problem. The proposed method can accomplish the tasks of focus-map estimation and image refocusing and defocusing. Given an image with a mixture of focused and defocused objects, we first detect the edges and then estimate the focus map based on the edge blurriness, which is depicted explicitly by a parametric model. The image refocusing problem is addressed in a blind deconvolution framework, where the image prior is modeled by using both global and local constraints. In particular, we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a local prior to ensure the sharpness of the refocused image. Experimental results demonstrate that the proposed method performs well in producing visually plausible images with different focus effects from a single input.

Blind Image Deconvolution Using Machine Learning for Three-Dimensional Microscopy

In this work, we propose a novel method for the regularization of blind deconvolution algorithms. The proposed method employs example-based machine learning techniques for modeling the space of point spread functions. During an iterative blind deconvolution process, a prior term attracts the point spread function estimates to the learned point spread function space. We demonstrate the usage of this regularizer within a Bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction, thus creating a complete blind deconvolution method. The application of the proposed algorithm is demonstrated on synthetic and real-world three-dimensional images acquired by a wide-field fluorescence microscope, where the need for blind deconvolution algorithms is indispensable, yielding excellent results.

Wavelet-based deconvolution of ultrasonic signals in nondestructive evaluation

In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in the nondestructive evaluation field, which is based on the theory of Fourier-Wavelet regularized deconvolution (ForWaRD). This new approach can be viewed as a solution to the open problem of adaptation of the ForWaRD framework to perform the convolution kernel estimation and deconvolution interdependently. The results indicate stable solutions of the estimated pulse and an improvement in the radio-frequency (RF) signal taking into account its signal-to-noise ratio (SNR) and axial resolution. Simulations and experiments showed that the proposed approach can provide robust and optimal estimates of the reflectivity function.

Adaptive blind separation of independent sources: A deflation approach

In this paper, we address the adaptive blind source separation of independent sources using higher order statistics. Although this problem was considered in numerous works, none of the existing algorithms is guaranteed to converge to a relevant solution. Here, we propose a new separation scheme whose convergence is proved analytically. It is based on the observation that it is possible to extract one of the source signals by a simple algorithm obtained by extending to the source separation context some of the ideas developed by Shalvi-Weinstein in the framework of blind deconvolution. A low cost deflation procedure allows the extraction of the other source signals by means of the same algorithm. A statistical study of the performance of the new method is also presented.