Point Spread Function Estimation Research Articles

Super-resolution of hyperspectral images using sparse representation and Gabor prior

Super-resolution (SR) as a postprocessing technique is quite useful in enhancing the spatial resolution of hyperspectral (HS) images without affecting its spectral resolution. We present an approach to increase the spatial resolution of HS images by making use of sparse representation and Gabor prior. The low-resolution HS observations consisting of large number of bands are represented as a linear combination of a small number of basis images using principal component analysis (PCA), and the significant components are used in our work. We first obtain initial estimates of SR on this reduced dimension by using compressive sensing-based method. Since SR is an ill-posed problem, the final solution is obtained by using a regularization framework. The novelty of our approach lies in: (1) estimation of optimal point spread function in the form of decimation matrix, and (2) using a new prior called “Gabor prior” to super-resolve the significant PCA components. Experiments are conducted on two different HS datasets namely, 31-band natural HS image set collected under controlled laboratory environment and a set of 224-band real HS images collected by airborne visible/infrared imaging spectrometer remote sensing sensor. Visual inspections and quantitative comparison confirm that our method enhances spatial information without introducing significant spectral distortion. Our conclusions include: (1) incorporate the sensor characteristics in the form of estimated decimation matrix for SR, and (2) preserve various frequencies in super-resolved image by making use of Gabor prior.

The DES Science Verification weak lensing shear catalogues

We present weak lensing shear catalogues for 139 square degrees of data taken during the Science Verification (SV) time for the new Dark Energy Camera (DECam) being used for the Dark Energy Survey (DES). We describe our object selection, point spread function estimation and shear measurement procedures using two independent shear pipelines, IM3SHAPE and NGMIX, which produce catalogues of 2.12 million and 3.44 million galaxies respectively. We detail a set of null tests for the shear measurements and find that they pass the requirements for systematic errors at the level necessary for weak lensing science applications using the SV data. We also discuss some of the planned algorithmic improvements that will be necessary to produce sufficiently accurate shear catalogues for the full 5-year DES, which is expected to cover 5000 square degrees.

多帧距离选通图像点扩散函数估计的超分辨率重建

多帧距离选通图像点扩散函数估计的超分辨率重建

Point spread function estimation from projected speckle illumination.

The resolution of an imaging apparatus is ideally limited by the diffraction properties of the light passing through the system aperture, but in many practical cases, inhomogeneities in the light propagating medium or imperfections in the optics degrade the image resolution. Here we introduce a powerful and practical new approach for estimating the point spread function (PSF) of an imaging system on the basis of PSF Estimation from Projected Speckle Illumination (PEPSI). PEPSI uses the fact that the speckles’ phase randomness cancels the effects of the aberrations in the illumination path, thereby providing an objective pattern for measuring the deformation of the imaging path. Using this approach, both wide-field-of-view and local-PSF estimation can be obtained by calibration-free, single-speckle-pattern projection. Finally, we demonstrate the feasibility of using PEPSI estimates for resolution improvement in iterative maximum likelihood deconvolution.

Mallows’ statistics CL: A novel criterion for parametric PSF estimation

Considering blind image deconvolution as a statistical estimation problem, we propose an unbiased estimator of the prediction error – Mallows’ statistics CL – as a novel criterion for estimating a point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of smoother filterings (with frequency-dependent regularization term). We then perform non-blind deconvolution using the popular BM3D algorithm. The CL-based framework is exemplified with a number of parametric PSF’s, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel.The experimental results show that the CL-minimization yields highly accurate estimates of the PSF parameters, which also result in a negligible loss of visual quality, compared to that obtained with the exact PSF. The highly competitive results demonstrate the great potential of developing more powerful blind deconvolution algorithms based on the CL-estimator.

Localizing edges for estimating point spread function by removing outlier points

This paper presents an approach to detect sharp edges for estimating point spread function (PSF) of a lens. A category of PSF estimation methods detect sharp edges from low-resolution (LR) images and estimate PSF with the detected edges. Existing techniques usually rely on accurate detection of ending points of the profile normal to an edge. In practice, however, it is often very difficult to localize profiles accurately. Inaccurately localized profiles generate a poor PSF estimation. We employ the Random Sample Consensus (RANSAC) algorithm to rule out outlier points. In RANSAC, prior knowledge about a pattern shape is incorporated, and the edge points lying far away from the pattern shape will be removed. The proposed method is tested on images of saddle patterns. Experimental results show that the proposed method can robustly localize sharp edges from LR saddle pattern images and yield accurate PSF estimation.

SURE-Type Functionals as Criteria for Parametric PSF Estimation

Point spread function (PSF) estimation plays an important role in blind image deconvolution. This paper proposes two novel criteria for parametric PSF estimation, based on Stein's unbiased risk estimate (SURE), namely, prediction-SURE and its variant. We theoretically prove the SURE-type functionals incorporating exact (complementary) smoother filtering as the valid criteria for PSF estimation. We also provide the theoretical error analysis for the regularizer approximations, by which we show that the proposed frequency-adaptive regularization term yields more accurate PSF estimate than others. In particular, the proposed SURE-variant enables us to avoid estimation of noise variance, which is a key advantage over the traditional SURE-like functional. Finally, we propose an efficient algorithm for the minimizations of the criteria. Not limited to the examples we show in this paper, the proposed SURE-based framework has a great potential for other imaging applications, provided the parametric PSF form is available.

Slant edge method for point spread function estimation

The traditional edge method (TEM) is applicable only in areas whose knife edges are horizontal or vertical. The slant edge method (SEM) requires using the approximate function in the edge spread function (ESF) fitting. The ESF sample is uneven and therefore affects the accuracy of the estimated point spread function (PSF). This study proposes a novel slant edge method (NSEM), including a knife-edge area extraction algorithm that ensures the evenness of the ESF sample and a PSF estimation algorithm that directly fits the line spread function, to improve the accuracy of the estimated PSF. The validity and applicability of the NSEM have been proven in theory and practice, respectively. Compared with the TEM and SEM, the NSEM exhibits a clear improvement in accuracy and stability across the three experiments conducted in this study.

Reconstruction of images degraded by aerosol scattering and measurement noise

Images measured through the atmosphere are degraded by scattering and absorption from aerosols along the path and by atmospheric turbulence. In the presence of heavy scattering at visible and infrared wavelengths, the distances over which reasonable observations are possible are quite short compared to astronomical imaging paradigms, and aerosol scattering effects dominate the degradation of the point spread function (PSF) due to atmospheric effects. In addition to aerosol-induced blurring, measurement noise effects are present in observed images. We examine the problem of reconstructing images degraded by aerosol blur and measurement noise using estimates of the overall PSF, which account for unscattered and scattered radiation detected by the imaging system. Representative images of a spoke target acquired under various conditions of scattering and photon flux levels were simulated, and reconstruction of the degraded images is performed using two linear reconstruction algorithms: a Wiener filter and a constrained least squares filter. Results of the reconstructions show that spatial resolution can be recovered in badly blurred images up to the limit imposed by the noise effective cutoff spatial frequency of the measurement.

PSF Estimation via Gradient Cepstrum Analysis for Image Deblurring in Hybrid Sensor Network

In hybrid sensor networks, information fusion from heterogeneous sensors is important, but quite often information such as image is blurred. Single image deblurring is a highly ill-posed problem and usually regularized by alternating estimating point spread function (PSF) and recovering blur image, which leads to high complexity and low efficiency. In this paper, we first propose an efficient PSF estimation algorithm based on gradient cepstrum analysis (GCA). Then, to verify the accuracy of the strategy, estimated PSFs are used for image deconvolution step, which exploits a novel total variation model coupling with a gradient fidelity term. We also adopt an alternating direction method (ADM) numerical algorithm with rapid convergence and high robustness to optimize the energy function. Both synthetic and real blur experiments show that our scheme can estimate PSF rapidly and produce comparable results without involving long time consuming.

The Restoration of Motion Blurred Images Based on the Background Modeling

For the mutual effects of camera shake and subject movement, the image generation space varying motion blur. In order to achieve image restoration, firstly dividing the image area using the Gaussian background modeling, and updated model adaptive to improve the speed and convergence accuracy. Then use the total variation (TV) of the L1 model to estimate the regional point spread function (PSF), and adopted the edge density weight to reduce small edge’s interference for the PSF estimates. Eventually to restored image by Wiener filter. Through experimental analysis, compared with other algorithms, our algorithms get better results in the space varies motion-blurred image.

Estimation method of point spread function based on Kalman Filter for accurately evaluating real optical properties of photonic crystal fibers

The evaluation accuracy of real optical properties of photonic crystal fibers (PCFs) is determined by the accurate extraction of air hole edges from microscope images of cross sections of practical PCFs. A novel estimation method of point spread function (PSF) based on Kalman filter is presented to rebuild the micrograph image of the PCF cross-section and thus evaluate real optical properties for practical PCFs. Through tests on both artificially degraded images and microscope images of cross sections of practical PCFs, we prove that the proposed method can achieve more accurate PSF estimation and lower PSF variance than the traditional Bayesian estimation method, and thus also reduce the defocus effect. With this method, we rebuild the microscope images of two kinds of commercial PCFs produced by Crystal Fiber and analyze the real optical properties of these PCFs. Numerical results are in accord with the product parameters.

Estimation of PSF for a Shaking Blurred Image Restoration

SUMMARYThe development of downsized digital cameras has caused numerous undesirable shaking‐blurred images. In order to restore these images, we need to estimate the PSF (point spread function) from them. It has been proposed to estimate the PSF using cepstrum images. There are PSF features in the cepstrum images of blurred images. We can estimate the PSF by searching pixels in the cepstrum images. However cepstrum images also show features of ground‐truth images, so that we cannot estimate the PSF accurately. We propose a method of PSF estimation using a genetic algorithm (GA). We use the cepstrum images as a fitness function, so that the estimation results are not affected by other features in the cepstrum images. The effectiveness of our proposed method is confirmed by simulations.

방향성 직사각형 열화 영상을 사용한 초해상도 영상복원

본 논문에서는 저해상도 영상들 사이의 움직임 정보를 사용하지 않고 서로 다른 형태의 열화영상들로부터 초해상도 영상을 복원하는 기술을 제안한다. 초해상도 영상 복원을 위해서 직사각형 조리개 마스크를 90도 회전하여 두 장의 영상을 취득하기 위한 렌즈시스템을 제안한다. 제안한 기술은 저해상도 영상에서 발생한 초점열화를 프레임마다 추정할 필요가 없고, 조리개 마스크 형태에 해당하는 초점열화만 추정하면 된다. 취득한 영상 간에는 평행 이동이 없기 때문에 영상정합이 필요하지 않다. 직사각형 조리개 마스크를 직교하여 취득한 두 장만의 영상으로 충분히 배타적인 정보를 얻을 수 있다. 따라서 저해상도 영상들 사이의 정합오류와 정합을 위한 계산량을 감소시킬 수 있기 때문에 고해상도 영상을 추정하기에 용이하다. 또한 기존의 카메라 렌즈 시스템에 조리개 마스크를 추가하여 적용할 수 있기 때문에 새로운 형태의 렌즈 시스템을 제작할 필요 없이 초해상도 영상을 복원할 수 있는 카메라 시스템으로 확장 가능하다. 마지막으로 본 논문에서 제안한 방향성 직사각형 열화를 사용한 초해상도 영상복원 기술의 성능을 검증하기 위해서 기존의 초해상도 영상복원 기술과 비교하였으며, 그 결과 해상도가 상당히 개선되었음을 보였다. This paper presents a superresolution restoration technique that can restore high-resolution images from differently blurred low resolution images rather than using the motion information between low-resolution images. In order to restore the super-resolution image the rotatable aperture mask lens system is proposed. The proposed technique does not need to estimate point spread function at each frame. In addition, it does not require image registration because there is no global translational motion between low resolution images. By using a rotatable rectangular aperture, two consecutive captured images provide sufficiently exclusive information for superresolution. Therefore, the proposed method can reduce the registration error between the low-resolution image as well as the calculation amount for superresolution restoration. The existing lens system of the camera can be extended to obtain a superresolution image by only adding an rotatable rectangular aperture mask. Finally, in order to verify the performance of the proposed system, experimental results are performed. By comparing with the existing superresolution methods, the proposed method showed the significant improvements in the sense of spatial resolution.

Restoration of retinal images with space-variant blur

Retinal images are essential clinical resources for the diagnosis of retinopathy and many other ocular diseases. Because of improper acquisition conditions or inherent optical aberrations in the eye, the images are often degraded with blur. In many common cases, the blur varies across the field of view. Most image deblurring algorithms assume a space-invariant blur, which fails in the presence of space-variant (SV) blur. In this work, we propose an innovative strategy for the restoration of retinal images in which we consider the blur to be both unknown and SV. We model the blur by a linear operation interpreted as a convolution with a point-spread function (PSF) that changes with the position in the image. To achieve an artifact-free restoration, we propose a framework for a robust estimation of the SV PSF based on an eye-domain knowledge strategy. The restoration method was tested on artificially and naturally degraded retinal images. The results show an important enhancement, significant enough to leverage the images' clinical use.

运动模糊图像点扩散函数的频谱估计法

运动模糊图像点扩散函数的频谱估计法

Model-based PSF and MTF estimation and validation from skeletal clinical CT images

A method was developed to correct for systematic errors in estimating the thickness of thin bones due to image blurring in CT images using bone interfaces to estimate the point-spread-function (PSF). This study validates the accuracy of the PSFs estimated using said method from various clinical CT images featuring cortical bones. Gaussian PSFs, characterized by a different extent in the z (scan) direction than in the x and y directions were obtained using our method from 11 clinical CT scans of a cadaveric craniofacial skeleton. These PSFs were estimated for multiple combinations of scanning parameters and reconstruction methods. The actual PSF for each scan setting was measured using the slanted-slit technique within the image slice plane and the longitudinal axis. The Gaussian PSF and the corresponding modulation transfer function (MTF) are compared against the actual PSF and MTF for validation. The differences (errors) between the actual and estimated full-width half-max (FWHM) of the PSFs were 0.09 ± 0.05 and 0.14 ± 0.11 mm for the xy and z axes, respectively. The overall errors in the predicted frequencies measured at 75%, 50%, 25%, 10%, and 5% MTF levels were 0.06 ± 0.07 and 0.06 ± 0.04 cycles/mm for the xy and z axes, respectively. The accuracy of the estimates was dependent on whether they were reconstructed with a standard kernel (Toshiba's FC68, mean error of 0.06 ± 0.05 mm, MTF mean error 0.02 ± 0.02 cycles/mm) or a high resolution bone kernel (Toshiba's FC81, PSF FWHM error 0.12 ± 0.03 mm, MTF mean error 0.09 ± 0.08 cycles/mm). The method is accurate in 3D for an image reconstructed using a standard reconstruction kernel, which conforms to the Gaussian PSF assumption but less accurate when using a high resolution bone kernel. The method is a practical and self-contained means of estimating the PSF in clinical CT images featuring cortical bones, without the need phantoms or any prior knowledge about the scanner-specific parameters.

A phase model for point spread function estimation in ground-based astronomy

In ground-based astronomy, images of objects in outer space are acquired via ground-based telescopes. However, the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function (PSF). To restore the observed images, aberration of the wavefront at the telescope’s aperture, i.e., the phase, is utilized to derive the PSF. However, the phase is not readily available. Instead, its gradients can be collected by wavefront sensors. Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy. Here, we develop a model that reconstructs the phase directly. The proposed model uses the tight frame regularization and it can be solved efficiently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established. Numerical results illustrate that our new model is efficient and gives more accurate estimation for the PSF.

Depth-variant blind restoration with pupil-phase constraints for 3D confocal microscopy

Three-dimensional images of confocal laser scanning microscopy suffer from a depth-variant blur, due to refractive index mismatch between the different mediums composing the system as well as the specimen, leading to optical aberrations. Our goal is to develop an image restoration method for 3D confocal microscopy taking into account the blur variation with depth. The difficulty is that optical aberrations depend on the refractive index of the biological specimen. The depth-variant blur function or the Point Spread Function (PSF) is thus different for each observation. A blind or semi-blind restoration method needs to be developed for this system. For that purpose, we use a previously developed algorithm for the joint estimation of the specimen function (original image) and the 3D PSF, the continuously depth-variant PSF is approximated by a convex combination of a set of space-invariant PSFs taken at different depths. We propose to add to that algorithm a pupil-phase constraint for the PSF estimation, given by the the optical instrument geometry. We thus define a blind estimation algorithm by minimizing a regularized criterion in which we integrate the Gerchberg-Saxton algorithm allowing to include these physical constraints. We show the efficiency of this method relying on some numerical tests.

Method for Large-Area Satellite Image Quality Enhancement With Local Aerial Images Based on Non-Target Multi-Point Calibration

This paper designed a non-target multi-point calibration method for the quality enhancement of large-area satellite images by using local aerial images. Satellite images are more sensitive to atmospheric effects compared with aerial images. Atmospheric effects on aerial images are even negligible in fine weather. Given that aerial remote sensing has high spatial resolution and geometric fidelity, more spatial details can be recorded in aerial images. However, the scan bandwidth of aerial images is limited compared with that of satellite images. Thus, taking high-quality aerial images of a neighborhood as reference can provide prior knowledge for point spread function (PSF) estimation and for the quality enhancement of large-area satellite images. The least square method and interpolation are used for the PSF estimation of spatial variation, and then total variation minimization is used for recovery. The results show that the designed method can effectively enhance the quality of large-area satellite images.