A Comprehensive Study of Blind and Non-blind Deconvolution Methods Applied to Spectrum Extraction

The detection of rolling bearing faults is essential to ensure the operational safety of rotating machinery. An effective method for diagnosing rolling bearing faults is the maximum second-order cyclostationarity blind deconvolution (CYCBD) method, which has the ability to extract weak fault periodic pulse features. However, blind deconvolution methods such as CYCBD often fail when composite bearing faults occur in the presence of strong background noise. To overcome this issue, an adaptive blind deconvolution (ABDD) method based on improved CYCBD is proposed. In this method, a finite impulse response (FIR) filter bank is constructed to cover the entire frequency band of the signal, enabling fault frequency segmentation. The improved CYCBD is then used to obtain a filter pattern that locks on the fault frequency. These filter patterns are arranged in descending order based on the correlation kurtosis (CK). The required filtering mode is selected according to the sorting mode, and a spectrum analysis is performed to extract fault features of single and compound faults in the bearing. Simulation and experimental results demonstrate that ABDD effectively extracts bearing composite fault features and outperforms classic feature decomposition and blind deconvolution methods in extracting single and composite fault features.

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.

Total variation minimizing blind deconvolution with shock filter reference

A new blind deconvolution method with additional phase spectral constraints for the blurred image is discussed in this paper. The blurred image is a convolution of an original image and a point-spread function (PSF). The proposed method is based on the following iterative procedures, i.e., a projection onto a frequency space satisfying phase spectrum constraints, a minimization of a cost function and a projection onto an image space satisfying the support and nonnegativity constraints. This method restores the original image and the PSF stably with high accuracy. The effectiveness of the proposed method is verified by applying it to some blind deconvolution problems of images. The experimental results show that the performance of the proposed method is drastically improved in comparison with the conventional blind deconvolution method.

A weighted total variation algorithm was proposed for solving some blind deconvolution problems,and then we got the existence of energy functional minimum and educed corresponding thermal flow.In computer simulations,the algorithm performs well even when we have no more accurate prior knowledge about point spread function and the original true image,besides some other constrains.Experiments show that the proposed algorithm is more effective and performs better than the total variation blind deconvolution method proposed.

We use blind deconvolution methods in optical diffusion tomography to reconstruct images of objects imbedded in or located behind turbid media from continuous-wave measurements of the scattered light transmitted through the media. In particular, we use a blind deconvolution imaging algorithm to determine both a deblurred image of the object and the depth of the object inside the turbid medium. Preliminary results indicate that blind deconvolution produces better reconstructions than can be obtained using backpropagation techniques. Moreover, it does so without requiring prior knowledge of the characteristics of the turbid medium or of what the blur-free target should look like: important advances over backpropagation.

When imaging through layered media such as walls, the contents and thickness of the wall layers are generally not known a priori. Furthermore, compensating for their effects can be computationally intensive, as this generally requires modelling the transmission and reflection of complex fields through layered media. We propose a blind deconvolution method that does not require knowledge of the wall layers by directly estimating a circularly symmetric Green’s function that models the transmission through the wall layers, simultaneously addressing both problems. We experimentally demonstrate this technique by measuring the reflection through a multilayered structure of building materials at the K-band microwave frequencies, and using the blind deconvolution method to find the image of a reflective object behind the layers.

Detection of an incipient internal defect from a measurement point on the surface of a machine is often made difficult due to the corruption of the source signal by background noise usually through the transmission path. In order to detect or recover the source signal, it is essential to suppress or remove this background noise. With the advancement of digital signal processing techniques, this removal can be achieved using fixed or adaptive filters. The main problem with the application of filtering techniques is that one has to know the characteristics of the noise in advance or may require more than two channels of data if using an adaptive filter. This paper reports on the application of Blind Deconvolution method to recover fault information from the measured (observed) signals of a damaged bearing through the transmission channel and which was also corrupted by noise. The Blind Deconvolution method manages to recover the fault signal by estimating the inverse of the transmission (channel transfer function) path using the eigenvector algorithm (EVA). Modified crest factor (MCF) and Arithmetic Mean (AM) algorithms were used to optimise the equaliser parameters. Computer simulation and experimental studies were used to verify the applicability of the technique.

Blind image deconvolution plays a very important role in the fields such as astronomical observation and fluorescence microscopy imaging, in which the noise follows Poisson distribution. However, due to the ill-posedness, it is a very challenging task to reach a satisfactory result from a single blurred image especially when the power of the Poisson noise is at a high level. Therefore, in this paper, we try to achieve high-quality restoration results with multi-blurred images which are contaminated by Poisson noise. Firstly, we design a novel sparse log-step gradient prior which adopts a mixture of logarithm and step functions to regularize the image gradients and combine it with the Poisson distribution to formulate the blind multi-image deconvolution problem. Secondly, we incorporate the methods of variable splitting and Lagrange multiplier to convert the original problem into sub-problems, then we alternately solve them to achieve the estimation of all the blur kernels of corresponding blurred images. Besides, we also design a non-blind multi-image deconvolution algorithm which is based on the log-step gradient prior to reach the final restored image. Experimental results on both synthetic and real-world blurred images show that the proposed prior is very capable of suppressing negative artifacts caused by ill-posedness. The algorithm can achieve restored image of very high quality which is competitive with some state-of-the-art methods.

We propose a new method of blind deconvolution (BD) suitable for the recovery of truncated blurred images. In practical cases we often encounter truncated images, but they are difficult to treat properly with conventional BD algorithms, since nontruncated blurred images are assumed. The proposed method is based on simulated annealing (SA), to which we introduce an adaptive masking process. After a truncated segment is cut out from the blurred image, the sharp edges surrounding the segment are removed by multiplying the initial window, whose shape is determined with the initial estimate of the point spread function (PSF). A more appropriate estimate for the PSF is obtained from the masked segment based on the SA algorithm, and according to the new estimate of the PSF, the shape of the window is varied. These procedures are iterated until we finally obtain the best possible estimate of the PSF. In the last step, the entire blurred image is deconvolved with the final estimate of the PSF to obtain the recovered image. The effectiveness of the proposed method is confirmed by computer simulation.

A blind deconvolution problem is newly stated with the following conditions: the point-spread function is band limited, both the object and the point-spread function are nonnegative, and the solution is to be a diffraction-limited object. A blind deconvolution method was developed that can easily be applied to problems in optics because of the conditions used. The performance of the method is investigated with computer simulations.

A blind deconvolution method using the concept of subband filter banks has been proposed. This method makes possible the speedy convergence of solution, due to estimation of supports of the reconstructed images by a deconvolution in the lower layer. We apply the method to blind deconvolution by a simulated annealing algorithm and confirm its usefulness.

Blind deconvolution subject to sparse representation for fluorescence microscopy

Blind deconvolution is a challenging problem of recovering a signal from their noisy convolution and it is prevalent in various fields including astronomical imaging, medical imaging, signal processing and computational optics. This paper discusses a more practical blind deconvolution problem which copes with the noisy convolution by spatially variant kernels. We found that the simple scheme used to participate the blurred images into regions for estimating spatially variant kernels is inaccurate. Otherwise, without using efficient kernel refinement and boundary condition, most of the current algorithms suffer more artifacts. In this paper, we proposed a double pyramid field-aware blind deconvolution framework. The proposed framework divides the given image to several patches by different field and estimate the coarse kernels of those patches by total variation-based algorithm. Then a new kernel refinement algorithm is proposed to refine the coarse kernels. After that, the non-blind deconvolution method with Hyper-Laplacian priors is used to get the deconvoluted whole image by their own refined kernels. Finally, the high-quality image is reconstructed by interpolating the several patch-kernel restored images together with the field-weighted interpolation method. Experiments illustrated that this framework can alleviate the restoration inaccuracy by single kernel, handle the unknown distortions to kernels and significantly improve visual quality.

In this paper, a method for MIMO blind deconvolution is proposed. The method is applicable to the case of non-Gaussian i.i.d. input signals. The core of the method is an algorithm which extracts one of the input signals from the information of the output signals only. This algorithm is an non-trivial generalization of the Shalvi-Weinstein algorithm for SISO blind deconvolution and converges in super-exponential rate possibly after finite iterations. By recursive use of this algorithm, extraction of all input signals can be achieved.