Sparse blind deconvolution: What cannot be done

Single-image blind deconvolution is one of the most challenging fields in image processing which restores a sharp image from its blurred version. Nowadays blind deconvolution algorithms have made significant progress. However, the restoration of blurred images with little scale edges and periodic textures is still a hard work. To solve this problem, this paper proposes a new normalized sparse regularization blind deconvolution algorithm, which uses a gradient saliency map to prohibit the image small structures on image blurry kernel estimation. Firstly, salient detection is performed to select the important area which conforms with the human vision system and generates a binary mask to screen out useful gradients. Secondly, the normalized sparse regularization blind deconvolution method is applied to obtain accurate blur kernel and recover the sharp image. Finally, the experiment results show that the algorithm can effectively deblur the degraded image on different scenarios.

The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method that enables blind recovery from much fewer measurements with respect to the full received signal in time. The proposed compression measures the signal through a filter followed by a subsampling, allowing for a significant reduction in implementation cost. We derive theoretical guarantees for the identifiability and recovery of a sparse filter from compressed measurements. Our results allow for the design of a wide class of compression filters. We, then, propose a data-driven unrolled learning framework to learn the compression filter and solve the S-MBD problem. The encoder is a recurrent inference network that maps compressed measurements into an estimate of sparse filters. We demonstrate that our unrolled learning method is more robust to choices of source shapes and has better recovery performance compared to optimization-based methods. Finally, in data-limited applications (fewshot learning), we highlight the superior generalization capability of unrolled learning compared to conventional deep learning.

We study the multichannel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel $a$ and multiple sparse inputs $\{x_i\}_{i=1}^p$ from their circulant convolu...

In many real-life situations, we need to reconstruct a blurred image in situations when no information about the blurring is available. This problem is known as the problem of blind deconvolution. There exist techniques for solving this problem, but these techniques are not rotation-invariant. Thus, the result of using this technique may change with rotation. So, if we rotate the image a little bit, the method, in general, leads to a different deconvolution result. Therefore, even when the original reconstruction is optimal, the reconstruction of a rotated image will be different and, thus, not optimal. To improve the quality of image decomposition, it is desirable to modify the current state-of-the art techniques by making them rotation-invariant. In this paper, we show how this can be done, and we show that this indeed improves the quality of blind deconvolution.

Resolution enhancement of deconvolved ground penetrating radar images using singular value decomposition

Blind deconvolution, which comprises simultaneous blur and image estimations, is a strongly ill-posed problem. It is by now well known that if multiple images of the same scene are acquired, this multichannel (MC) blind deconvolution problem is better posed and allows blur estimation directly from the degraded images. We improve the MC idea by adding robustness to noise and stability in the case of large blurs or if the blur size is vastly overestimated. We formulate blind deconvolution as an l(1) -regularized optimization problem and seek a solution by alternately optimizing with respect to the image and with respect to blurs. Each optimization step is converted to a constrained problem by variable splitting and then is addressed with an augmented Lagrangian method, which permits simple and fast implementation in the Fourier domain. The rapid convergence of the proposed method is illustrated on synthetically blurred data. Applicability is also demonstrated on the deconvolution of real photos taken by a digital camera.

Publication in the conference proceedings of EUSIPCO, Toulouse, France, 2002

In view of band-limited seismic data with a low dominant frequency and short data records, this paper proposes a new approach to the seismic blind deconvolution problem, a new criterion for blind deconvolution is constructed, by which we can measure the independency of output signals. The optimization program for new criterion of blind deconvolution is performed by applying Neidell's wavelet model to the inverse filter, which then makes the optimization program for multivariate reduce to univariate case. The proposed method can broaden the spectrum of seismic data effectively resulting in the improved resolution even in the case of band-limited seismic data with a low dominant frequency and short data records. The simulation test and actual seismic data processing results show that the correctness of the method.

The cross-correlation is an effective tool for estimating a time delay between two signals. Unfortunately, in practical world, there always exist problems of multi-path time delay estimation (MTDE). The cross-correlation fails to deal with the MTDE case. In this paper, a novel technique for high-resolution multi-path time delay estimation (HMTDE) is proposed. The new method is based on 2D blind deconvolution and the slice selection on the third order cross-moment (TOCM) of the two signals. To get a high resolution estimation of the multi-path time delay, it is necessary to remove the component of transmitted signal. Instead of solving a one-dimensional blind deconvolution problem in original signals domain, the proposed method solves a two-dimensional blind deconvolution problem in their TOCM domain. It recovers a scaled and time-shifted version of the reflectivity sequence with the maximum time delay slices (MTDS) of TOCM of the reflectivities corresponding to the two signals. The only information of the transmitted signal needed in this method is its third order moment(TOM), which can be estimated only using the two received signals. It is well known that higher order statistics (HOS) carry more information and be insensitive to additive Gaussian noise than does the second order statistics (SOS). These properties lead to a robust and unique solution of HMTDE by using our TOCM based approach.

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 35821, “A Mobile Platform for AI-Powered Underwater Image Processing,” by Chenyu Zhou, University of Houston; Lily Walker, William & Mary; and Xin Fu, University of Houston, et al. The paper has not been peer reviewed. Copyright 2025 Offshore Technology Conference. _ Timely inspection of subsea infrastructure—particularly pipelines—is crucial for preventing oil spills and protecting the environment. This paper introduces a technology for offshore pipeline inspection centered on an autonomous robotic system equipped with underwater computer vision and edge-computing capabilities. The aim is to create a fast, cost-effective solution for inspecting underwater structures, enabling early detection of environmental hazards. Introduction Autonomous underwater vehicles (AUVs) have revolutionized the ability to explore and monitor marine environments. The cornerstone of AUV capabilities lies in their imaging systems, although the underwater environment poses unique and complex challenges for these systems. Additional image-processing and correction ability remains a goal for AUVs, creating computational demands that must be balanced against limited onboard power and processing capabilities (Fig. 1). Recently, advancements in deep learning have enabled deep neural networks (DNNs) to achieve remarkable success in solving a wide range of image-processing challenges, significantly surpassing the performance of traditional methods. In this research, the authors build upon foundational work in the literature to present a comprehensive workflow for adapting and deploying pretrained DNN models onto mobile computing platforms suitable for integration with AUVs. The described approach examines and documents the transition from powerful desktop systems to resource-constrained mobile platforms. Underwater Image Enhancement Motion blur is a common challenge in underwater image processing, especially when the camera is mounted on a moving platform such as an AUV. The lack of adequate lighting in underwater environments often requires longer exposure times, further exacerbating motion blur. The blurring process can be mathematically described as a convolution of the sharp image with a blur kernel, plus noise. If the blur kernel is known beforehand, the problem becomes one of nonblind deconvolution. However, when the blur kernel is unknown—common in dynamic underwater settings—it becomes a blind deconvolution problem. This problem is inherently ill-posed because multiple combinations of sharp images and blur kernels can explain the same blurred image. To resolve this ambiguity, assumptions or previous knowledge about the blur kernel or image structure typically are introduced. Traditional blind deconvolution methods often use iterative algorithms, refining the blur kernel and sharp image estimates over multiple steps. These classical approaches, however, often suffer from artifacts such as ringing and struggling with large motions or noise. To address these limitations, researchers have explored regularization techniques that incorporate priors to constrain the solution space. For example, sparsity priors in the temporal domain encourage smooth results, while Bayesian frameworks provide probabilistic formulations of the problem. One promising direction involves leveraging domain-specific priors for underwater imagery. By incorporating this property into optimization frameworks, researchers have developed more-effective and -robust blind deblurring methods tailored to underwater scenarios.

The problem of multichannel blind signal deconvolution is considered. The mixing system is supposed to be stable and invertible and the input signals, also called sources, are assumed zero-mean independent and identically distributed (IID) random signals. Using the hypothesis that sources are statistically independent, we propose a generalization to the convolutive case of some separation criteria available in the instantaneous one. Hence, we obtain a new generalized class of criteria for signal deconvolution.

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.

Previous research presented by the author and others into maximum-likelihood image restoration for incoherent imagery is extended to consider problems of blind deconvolution in which the impulse response of the system is assumed to be unknown. Potential applications that motivate this study are wide-field and confocal fluorescence microscopy, although applications in astronomy and infrared imaging are foreseen as well. The methodology incorporates the iterative expectation-maximization algorithm. Although the precise impulse response is assumed to be unknown, some prior knowledge about characteristics of the impulse response is used. In preliminary simulation studies that are presented, the circular symmetry and the band-limited nature of the impulse response are used as such. These simulations demonstrate the potential utility and present limitations of these methods.

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.

The main inherent property of medical ultrasound imaging is speckle noise which generally obscures and reduces the diagnostic image resolution and contrast. Consequently, the substantial improvement of ultrasound images is an important prerequisite, whenever ultrasound is used as one of the most utilized diagnostic modalities. The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as a prerequisite in ultrasound imaging processing in the recent decades. Recently, the Total Variation (TV) regularization method has become extremely effective approach for image reconstruction, especially for restoring edges of the blurring image. In this paper, we present a new blind iterative TV deconvolution algorithm for reconstructing ultrasound images from blurry and noisy observations. First, it proposes the initial estimation of the point-spread function (PSF) based on a generalization of two-dimensional homomorphic filtering in cepstrum domain. It is demonstrated that the initial PSF can be effectively estimated by applying a proper smoothing low-pass filtering in cepstrum domain. Second, it introduces a novel blind iterative TV deconvolution which is derived from an alternating minimization algorithm. Fast Fourier Transform (FFT) is used in the pre-iteration computation. The innovative blind deconvolution is based on either concurrent or successive estimation of the PSF function and the image of interest. The iterative scheme is devised to recover the image and simultaneously identify the PSF function. The estimated PSF and restored image will be close to real values in the subsequent iterative deconvolution. Final, tests on phantom and clinical images have proven our novel blind iterative TV deconvolution gives more positive results of higher spatial resolution and better defined tissue structures than other deconvolution methods.