Out-of-focus blur estimation for blind image deconvolution: Using particle swarm optimization

PurposeHow to model blind image deblurring that arises when a camera undergoes ego-motion while observing a static and close scene. In particular, this paper aims to detail how the blurry image can be restored under a sequence of the linear model of the point spread function (PSF) that are derived from the 6-degree of freedom (DOF) camera’s accurate path during the long exposure time.Design/methodology/approachThere are two existing techniques, namely, an estimation of the PSF and a blind image deconvolution. Based on online and short-period inertial measurement unit (IMU) self-calibration, this motion path has discretized a sequence of the uniform speed of 3-DOF rectilinear motion, which unites with a 3-DOF rotational motion to form a discrete 6-DOF camera’s path. These PSFs are evaluated through the discrete path, then combine with a blurry image to restoration through deconvolution.FindingsThis paper describes to build a hardware attachment, which is composed of a consumer camera, an inexpensive IMU and a 3-DOF motion mechanism to the best of the knowledge, together with experimental results demonstrating its overall effectiveness.Originality/valueFirst, the paper proposes that a high-precision 6-DOF motion platform periodically adjusts the speed of a three-axis rotational motion and a three-axis rectilinear motion in a short time to compensate the bias of the gyroscope and the accelerometer. Second, this paper establishes a model of 6-DOF motion and emphasizes on rotational motion, translational motion and scene depth motion. Third, this paper addresses a novel model of the discrete path that the motion during long exposure time is discretized at a uniform speed, then to estimate a sequence of PSFs.

Generally, blind super-resolution with unknown blurs is treated as an optimization problem. This involves a cost function, composed of terms accounting for changes in image and point spread function (PSF), which usually undergoes regularization due to the ill-posedness of the problem. In this paper, we introduce a novel regularization term for the PSF such that the spectral change in the image caused by degradation is also included. This is based on the fact that the presence of PSF in images affects the frequency component concentration. This cost function is optimized with respect to the image and the PSF in an alternating manner. Experiment results show that the proposed method is effective based on an objective evaluation method and that its PSF estimation accuracy is competitive in comparison with the recently proposed parametric method.

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.

Point spread function (PSF) estimation plays an important role in blind image deconvolution. It has been shown that incorporating Wiener filter, minimization of the predicted Stein’s unbiased risk estimate (p-SURE)—unbiased estimate of predicted mean squared error—could yield an accurate PSF estimate. In this paper, we provide a theoretical analysis for the PSF estimation error, which shows that the better deconvolution leads to more accurate PSF estimate. It motivates us to incorporate an \(\ell _1\)-penalized sparse deconvolution into the p-SURE minimization, instead of the Wiener-type filtering. In particular, based on FISTA—one of the most popular iterative \(\ell _1\)-solvers, we evaluate the p-SURE for each update, by Jacobian recursion and Monte Carlo simulation. Numerical results of both synthetic and real experiments demonstrate the improvements in PSF estimate, and therefore, deconvolution performance.

BackgroundThe maximum standardized uptake value (SUVmax) is a common clinical parameter for quantification in F18-fluorodeoxyglucose positron emission tomography/computed tomography (FDG-PET/CT), but it is influenced by image reconstruction. The aim of this study was to analyze the association of SUVmax deviations related to point spread function (PSF) and time-of-flight (TOF) reconstruction with tumor-to-background ratios (TBR) in colorectal liver metastases (CRLM).MethodsFifteen patients (f, 6; m, 9; median age, 59 years; range, 32 to 72 years) with 28 liver metastases were included retrospectively. FDG-PET/CT imaging (median activity, 237 MBq; range, 231 to 252 MBq; median uptake, 61 min; range, 55 to 67 min) was performed on a Siemens Biograph mCT 64 followed by image reconstruction using 3D-ordered subset expectation maximization (3D-OSEM) or 3D-OSEM with PSF modeling - both with and without TOF information. Differences in SUVmax were analyzed using the Friedman test and Wilcoxon test for paired non-parametric data. The correlation of inter-method differences with the lesions’ TBR was studied using Spearman’s rank correlation coefficient (rho). Differences between lesions with low (<4.8) and high (>4.8) TBR were analyzed using the Mann-Whitney U test (TBR measured with 3D-OSEM; binarized by its median).ResultsThere was a significant correlation of the lesions’ TBR with relative SUVmax differences related to PSF (PSF + TOF vs. 3D-OSEM + TOF, rho = 0.61; PSF vs. 3D-OSEM, rho = 0.52) or TOF (PSF + TOF vs. PSF, rho = −0.58; 3D-OSEM + TOF vs. 3D-OSEM, rho = −0.61). Accordingly, PSF algorithms only showed higher SUVmax than non-PSF algorithms in lesions with a high TBR (median differences at low/high TBR, +2.6%/+9.1% [PSF + TOF vs. 3D-OSEM + TOF]; +0.7%/+6.4% [PSF vs. 3D-OSEM]). TOF integration also led to higher SUVmax but mainly at low TBR (low/high TBR, +10.4%/+1.8% [PSF + TOF vs. PSF]; +8.6%/−0.1% [3D-OSEM + TOF vs. 3D-OSEM]).ConclusionsBoth PSF and TOF reconstruction resulted in a substantial alteration of SUVmax in CRLM. TOF provided the highest SUVmax increase in low-contrast lesions while - vice versa - PSF showed the most relevant increase in high-contrast lesions. Thus, one should be aware that quantitative analyses of lesions with varying TBR, e.g., in radiotherapy or follow-up studies, may be mainly affected by either PSF or TOF reconstruction, respectively.

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 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 propose to use the blind deconvolution and its modification to extract the point spread function (PSF) of layered metamaterials from a SNOM measurement. The measurement results are processed using the blind deconvolution algorithm to reconstruct the real-valued non-coherent PSF, or using the modified blind deconvolution introduced in this paper to reconstruct the complex-valued coherent PSF. The two algorithms are tested in simulations with a layered metamaterial deposited on a thin metallic mask with test apertures. We show that the modified algorithm is capable of recovering the approximate shape of complex PSF with a sub-wavelength full width at half maximum from a measurement in which the apertures are larger than the wavelength.

Direct exoplanet detections are limited by the speckle noise of the point spread function (PSF). This noise can be reduced by subtracting PSF images obtained simultaneously in adjacent narrow spectral bands using a multichannel camera (MCC). Experiments have shown that speckle attenuation performances are severely degraded by differential optical aberrations between channels that decorrelate the PSFs of the different spectral bands. We present a new technique which can greatly alleviate this problem: the introduction of a holographic diffuser at the focal plane of the MCC. The holographic diffuser converts the PSF image into an incoherent illumination scene that is then re-imaged with the MCC. This imaging process is equivalent to a convolution of the scene with the PSF of each channel of the MCC. The optical aberrations in the MCC then affect only the convolution kernel of each channel and not the PSF globally, resulting in more correlated images. We report laboratory measurements with a dual channel prototype (1.575 &#956;m and 1.625 &#956;m) to validate this approach. We achieved a speckle noise suppression factor of 12-14, which is ~4-6 times better than what has been achieved by existing MCCs.

The paper describes the three basic functions used to describe the image forming properties of photographic materials. The functions are the line spread function, the point spread function, and the transfer function (spatial frequency response). Only one of the three functions is independent, and therefore three pairs of conjugate relations exist among them. All six relations are given explicitly.The relations are exemplified by deriving the point and line spread functions of Super-XX, Kodachrome, and Microfile film from the transfer function measurements of Schade. The results are given in Figs. 2 and 3. Four different characteristic lengths associated with the spread functions are defined, and their numerical values are given in Table I.

It is important to measure the spatial performance of an in-flight satellite sensor to determine if any spatial resolution degradations occur over time; then some compensation methods can be adopted to improve the image quality. In satellite on-orbit measurements of spatial resolution, the performance of the sensors can be objectively evaluated through the point spread function (PSF) or modulation transfer function (MTF). The well-known image-based PSF derivation method of sampling along a slanted linear step structure from the degraded image is widely used in the satellite image restoration area. Due to the non-uniformity of the linear ground objects, generally, the operators have to pick out good profiles from all the profiles along the edge in order to increase the estimation accuracy. However, only some qualitative criteria have been proposed in the literature to instruct researchers how to pick out good profiles. In this article, we propose a method to quantitatively measure the homogeneity and contrast of the candidate linear structures in order to extract the optimal profiles. This method first automatically detects and locates the slanted linear step edge object in the image. Then it measures the homogeneity and the contrast at each location along the edge by using two adjacent square regions on both sides of the linear step structure. The locations that have high measurement values are regarded as the optimal locations. Finally, the optimal profiles can be extracted at these edge locations to derive an accurate PSF estimation by differentiation. This method makes an automatic optimal step edge detection method for PSF derivation to be practical. Experiment results on simulated and real images are provided. This article shows that using only the ‘optimal’ profiles can play a real and important role and can achieve a good PSF estimation result.

Blind color deconvolution, normalization, and classification of histological images using general super Gaussian priors and Bayesian inference

Context. Weak gravitational lensing requires precise measurements of galaxy shapes and therefore accurate knowledge of the point spread function (PSF) model. The latter can be a source of systematics that affect the shear two-point correlation function. A key aspect of weak-lensing analysis is the forecasting of the systematics due to the PSF. Aims. Correlation functions of galaxies and the PSF, the so-called ρ and τ statistics, are used to evaluate the level of systematics coming from the PSF model and PSF corrections and contributing to the two-point correlation function used to perform cosmological inference. Our goal is to introduce a fast and simple method to estimate this level of systematics and to assess its agreement with state-of-the-art approaches. Methods. We introduce a new way to estimate the covariance matrix of τ statistics using analytical expressions. The covariance allows us to estimate parameters directly related to the level of systematics associated with the PSF and provides us with a tool to validate the PSF model used in a weak-lensing analysis. We applied these methods to data from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). Results. We show that semi-analytical covariance yields results comparable to those obtained by using covariances obtained from simulations or jackknife resampling. The approach requires less computation time and is therefore well suited to rapid comparison of the systematic level obtained from different catalogues. We also show how one can break degeneracies between parameters with a redefinition of the τ statistics. Conclusions. The methods developed in this work will be useful tools in the analysis of current weak-lensing data but also of Stage IV surveys such as Euclid, LSST, and Roman. They provide fast and accurate diagnostics on PSF systematics that are crucial in the context of cosmic shear studies.

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.

In this paper we propose a blind deconvolusion method to enhance the resolution of images obtained by near-field microwave nondestructive techniques using an open ended rectangular waveguide probe. In fact, we model such imags to be the result of a convolution of the real input images with a point spread function (PSF). This PSF depends mainly on the dimensions of the waveguide, the operating frequency, the nature of the object under test and standoff distance between the waveguide and the object. Unfortunately, it is very difficult to model this PSF from the physical data. For this reason, we consider the problem as a blind deconvolution. The proposed method is based on regularization, and the solution is obtained iteratively, by successive estimation of the input and the PSF. The algorithm is initialized with a PSF obtained from a very simplified physical model. The performance of the proposed method is evaluated on some real data. Several examples of real image enhancement will be presented.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.