Point Spread Function Estimation Research Articles

Incoherent Point Spread Function Estimation and Multipoint Deconvolution for Active Incoherent Millimeter-Wave Imaging

We present an approach to image deconvolution in active incoherent millimeter-wave (AIM) imaging. While traditional incoherent imaging systems capture thermal radiation from the scene, AIM imaging uses the transmission of noise signals to increase the signal-to-noise ratio (SNR) while maintaining the necessary space–time incoherence required for image reconstruction. Images formed by any imaging technique are corrupted by the impulse response, or point spread function (PSF), of the imaging system; however, the degradation of the image due to the PSF can be alleviated significantly via deconvolution if the PSF is characterized. Typically, estimation of the PSF is challenging due to spatial undersampling and the impact of noise. In this work, we experimentally demonstrate an approach to estimate the PSF of AIM imaging systems by averaging PSF estimates from multiple point targets using a shift-and-add method in a 38-GHz imaging system. We demonstrate image deconvolution using the CLEAN algorithm to reconstruct a scene with multiple targets.

Dynamic PSF-based jitter compensation and quality improvement for push-broom optical images considering terrain relief and the TDI effect.

Platform attitude jitter is inevitable during a satellite flight. The jitter reduces the quality of push-broom optical images, resulting in geometric deformation and image blur. This paper proposes an approach that offers jitter effect compensation and quality improvement for push-broom optical images based on dynamic point spread function (PSF) estimation and iterative image restoration considering the effect of terrain relief and time delay integration (TDI). First, the attitude jitter is precisely detected and estimated by considering the terrain relief. The jitter information is then used to establish the dynamic PSF of each image line considering the changing jitter values and TDI effect. Finally, based on the constructed PSF, the image is improved by iterative restoration using the optimal-window Richardson-Lucy algorithm. The method is validated by both simulation and real data experiments. In the simulation experiment, we apply jitter with different amplitudes and frequencies to generate the degraded images and then restore the image using the proposed restoration method. The results show that the proposed method can effectively restore images affected by jitter. In addition, real data experiments are carried out with multispectral remote sensing images from the ZY-3 satellite. The results show that in addition to the improvement of the radiometric quality, the geometric quality is also significantly improved in both the across-track and the along-track directions. The experimental results validated that the proposed method outperformed other methods without considering the terrain and TDI effect.

Point spread function estimation for blind image deblurring problems based on framelet transform

One of the most important issues in image processing is the approximation of the image that has been lost due to the blurring process. These types of matters are divided into non-blind and blind problems. The second type of problem is more complex in terms of calculations than the first problem due to the unknown of original image and point spread function estimation. In the present paper, an algorithm based on coarse-to-fine iterative by \(l_{0}-\alpha l_{1}\) regularization and framelet transform is introduced to approximate the spread function estimation. Framelet transfer improves the restored kernel due to the decomposition of the kernel to different frequencies. Also, in the proposed model, a fraction gradient operator is used instead of the ordinary gradient operator. The proposed method is investigated on different kinds of images such as text, face and natural. The output of the proposed method reflects the effectiveness of the proposed algorithm in restoring images from blind problems.

Optical satellite image MTF compensation for remote-sensing data production

Modulation Transfer Function (MTF) compensation had been widely used in Remote-Sensing (RS) imagery processing for texture feature enhancement and high-frequency details restoration. In this paper, we propose an optical satellite MTF Compensation (MTFC) method for engineering applications and RS data production. The framework mainly includes Point Spread Function (PSF) model estimation and non-blind image deconvolution. In PSF estimation, we used the iterative total variation algorithm and 2D Gaussian model fitting to reduce the dependence on slant-edge quality and improve the efficiency of PSF measurement. The PSF model estimation error is less than 3% using the results from standard commercial software as an evaluation benchmark. In image deconvolution, we adopted a regularisation-based non-blind deconvolution method using hyper-Laplacian prior. Compared with the widely used methods, the MTF has been improved more than double in high-frequency part. Its processing efficiency and image quality can meet the requirements of RS image products. These results can effectively prove the engineering application value of our proposed method.

Point Spread Function Estimation of Defocus

Point Spread Function Estimation of Defocus

Point-spread function of the BOLD response across columns and cortical depth in human extra-striate cortex.

Columns and layers are fundamental organizational units of the brain. Well known examples of cortical columns are the ocular dominance columns (ODCs) in primary visual cortex and the column-like stripe-based arrangement in the second visual area V2. The spatial scale of columns and layers is beyond the reach of conventional neuroimaging, but the advent of high field magnetic resonance imaging (MRI) scanners (UHF, 7 Tesla and above) has opened the possibility to acquire data at this spatial scale, in-vivo and non-invasively in humans. The most prominent non-invasive technique to measure brain function is blood oxygen level dependent (BOLD) fMRI, measuring brain activity indirectly, via changes in hemodynamics. A key determinant of the ability of high-resolution BOLD fMRI to accurately resolve columns and layers is the point-spread function (PSF) of the BOLD response in relation to the spatial extent of neuronal activity. In this study we take advantage of the stripe-based arrangement present in visual area V2, coupled with sub-millimetre anatomical and gradient-echo BOLD (GE BOLD) acquisition at 7 T to obtain PSF estimates and along cortical depth in human participants. Results show that the BOLD PSF is maximal in the superficial part of the cortex (1.78 mm), and it decreases with increasing cortical depth (0.83 mm close to white matter).

Image Deblurring using Wiener Filtering and Siamese Neural Network

Blurred images are difficult to avoid in situations when minor Atmospheric turbulence or camera movement results in low-quality images. We propose a system that takes a blurred image as input and produces a deblurred image by utilizing various filtering techniques. Additionally, we utilize the Siamese Network to match local image segments. A Siamese Neural Network model is used that is trained to account for image matching in the spatial domain. The best-matched image returned by the model is then further used for Signal-to-Noise ratio and Point Spread Function estimation. The Wiener filter is then used to deblur the image. Finally, the results of the deblurring techniques with existing algorithms are compared and it is shown that the error in deblurring an image using the techniques presented in this paper is considerably lesser than other techniques.

Harmonization of in-plane resolution in CT using multiple reconstructions from single acquisitions.

To providea methodology that removes the spatial variability of in-plane resolution using different CT reconstructions. The methodology does not require any training, sinogram, or specific reconstructionmethod. The methodology is formulated as a reconstruction problem. The desired sharp image is modeled as an unobservable variable to be estimated from an arbitrary number of observations with spatially variant resolution. The methodology comprises three steps: (1) density harmonization, which removes the density variability across reconstructions; (2) point spread function (PSF) estimation, which estimates a spatially variant PSF with arbitrary shape; (3) deconvolution, which is formulated as a regularized least squares problem. The assessment was performed with CT scans of phantoms acquired with three different Siemens scanners (Definition AS, Definition AS+, Drive). Four low-dose acquisitions reconstructed with backprojection and iterative methods were used for the resolution harmonization. A sharp, high-dose (HD) reconstruction was used as a validation reference. The different factors affecting the in-plane resolution (radial, angular, and longitudinal) were studied with regression analysis of the edge decay (between 10% and 90% of the edge spread function (ESF) amplitude). Results showed that the in-plane resolution improves remarkably and the spatial variability is substantially reduced without compromising the noise characteristics. The modulated transfer function (MTF) also confirmed a pronounced increase in resolution. The resolution improvement was also tested by measuring the wall thickness of tubes simulating airways. In all scanners, the resolution harmonization obtained better performance than the HD, sharp reconstruction used as a reference (up to 50 percentage points). The methodology was also evaluated in clinical scans achieving a noise reduction and a clear improvement in thin-layered structures. The estimated ESF and MTF confirmed the resolution improvement. We propose a versatile methodology to reduce the spatial variability of in-plane resolution in CT scans by leveraging different reconstructions available in clinical studies. The methodology does not require any sinogram, training, or specific reconstruction, and it is not limited to a fixed number of input images. Therefore, it can be easily adopted in multicenter studies and clinical practice. The results obtained with our resolution harmonization methodology evidence its suitability to reduce the spatially variant in-plane resolution in clinical CT scans without compromising the reconstruction's noise characteristics. We believe that the resolution increase achieved by our methodology may contribute in more accurate and reliable measurements of small structures such as vasculature, airways, and wallthickness.

Determination of the optimal range for virtual monoenergetic images in dual-energy CT based on physical quality parameters.

Virtual monoenergetic images (VMI) obtained from Dual-Energy Computed Tomography (DECT) with iodinated contrast are used in radiotherapy of the Head and Neck to improve the delineation of target volumes and organs at-risk (OAR). The energies used to vary from 40 to 70keV, but noise at low keV and the use of Single Energy CT (SECT) at low kVp settings may shrink this interval. There is no guide about how to find out the optimal range where VMI has a significant improvement related to SECT images. Our study proposes a procedure to determine this optimal range, based on common image quality parameters, and establishes this range in a Siemens Somatom Confidence and a Head and Neck protocol. We compared the quality of the VMI series at 40-60keV versus single X-ray tube voltage computed tomography (SECT) at 80 and 120kVp . Our reference was 120kVp . DECT images were sequentially acquired using the Siemens Somatom Confidence RT Pro CT according to the head and neck protocol in our department. VMI series were constructed using the Syngo Via software Monoenergetic+ algorithm. Quality parameters were: image uniformity, high- and low-contrast resolution, noise, and sensitivity to the iodinated contrast. We used the Catphan 604 phantom for quality control, except when assessing iodine sensitivity. To evaluate high contrast resolution, we calculated the modulation transfer function (MTF) using the point spread function estimation of a point bead and the slanted edge methods. For the low-contrast resolution, we used a statistical method for assessing differences between contrast structures and local noise. To measure the absolute value of noise and compare its texture, we used the standard deviation and the noise power spectrum. We measured iodine sensitivity by dissolving the Optiray Ultraject iodinated contrast in water in concentrations of 0 to 4500mg/l and then compared the contrast to noise ratio (CNR) and analyzed the linear correlation between concentration and HU. The entire series met the minimum quality requirements. However, the one at 40keV presented uniformity at the limits of acceptability. The high- and low-contrast resolutions were similar between series. The noise of the VMI series decreased with increasing energy, while sensitivity to the contrast displayed the opposite behavior. All series showed linearity of HUs from very low iodine concentrations. Images at 60keV presented lower iodine sensitivity than SECT at 80kVp , while those at 55keV were similar to them. Our method of image comparison based on standard quality parameters in phantom gave clear results about the optimal range and can be used as a guide to characterize any other DECT imaging protocols. The optimal range for using VMI images in iodinated contrasts in the Siemens system was 45-55keV. Lower energies lacked noise and uniformity, while higher ones could be substituted by SECT images at low kilovoltage (80kVp ).

A light field measurement system through PSF estimation by a morphology-based method

Light field imaging technology can obtain three-dimensional (3D) information of a test surface in a single exposure. Traditional light field reconstruction algorithms not only take a long time to trace back to the original image, but also require the exact parameters of the light field system, such as the position and posture of a microlens array (MLA), which will cause errors in the reconstructed image if these parameters cannot be precisely obtained. This paper proposes a reconstruction algorithm for light field imaging based on the point spread function (PSF), which does not require prior knowledge of the system. The accurate PSF derivation process of a light field system is presented, and modeling and simulation were conducted to obtain the relationship between the spatial distribution characteristics and the PSF of the light field system. A morphology-based method is proposed to analyze the overlapping area of the subimages of light field images to identify the accurate spatial location of the MLA used in the system, which is thereafter used to accurately refocus light field imaging. A light field system is built to verify the algorithm’s effectiveness. Experimental results show that the measurement accuracy is increased over 41.0% compared with the traditional method by measuring a step standard. The accuracy of parameters is also improved through a microstructure measurement with a peak-to-valley value of 25.4% and root mean square value of 23.5% improvement. This further validates that the algorithm can effectively improve the refocusing efficiency and the accuracy of the light field imaging results with the superiority of refocusing light field imaging without prior knowledge of the system. The proposed method provides a new solution for fast and accurate 3D measurement based on a light field.

Point spread function estimation for wide field small aperture telescopes with deep neural networks and calibration data

ABSTRACT The point spread function (PSF) reflects states of a telescope and plays an important role in the development of data-processing methods, such as PSF-based astrometry, photometry, and image restoration. However, for wide field small aperture telescopes (WFSATs), estimating PSF in any position of the whole field of view is hard, because aberrations induced by the optical system are quite complex and the signal-to-noise ratio of star images is often too low for PSF estimation. In this paper, we further develop our deep neural network (DNN)-based PSF modelling method and show its applications in PSF estimation. During the telescope alignment and testing stage, our method collects system calibration data through modification of optical elements within engineering tolerances (tilting and decentring). Then, we use these data to train a DNN (Tel–Net). After training, the Tel–Net can estimate PSF in any field of view from several discretely sampled star images. We use both simulated and experimental data to test performance of our method. The results show that the Tel–Net can successfully reconstruct PSFs of WFSATs of any states and in any positions of the field of view (FoV). Its results are significantly more precise than results obtained by the compared classic method – inverse distance weight interpolation. Our method provides foundations for developing deep neural network-based data-processing methods for WFSATs, which require strong prior information of PSFs.

A phase model using the Huber norm for estimating point spread function under frozen flow hypothesis

In astronomical observation and space exploration, the light of an object in the outer space is inevitably distorted by the atmospheric turbulence around the Earth before it reaches the ground-based telescope aperture. The target object so observed is degraded by unknown point spread functions (PSFs). Estimating the PSFs is thus crucial for ground-based astronomy. In order to know the PSFs, we first need to estimate the phase, i.e., the wavefront aberration of incoming light at telescope aperture. In this paper, under the frozen flow hypothesis, we propose a new model for estimating the phase in the case of single- and multi-layered atmospheric turbulence. The new model, which deploys the Huber norm as the regularizer, can be cast as a saddle-point problem and solved efficiently by existing well-developed optimization algorithms. We test a spatially-varying image deblurring problem by using the estimated PSFs, which demonstrates the compelling numerical performance of the new phase model.

Learning deconvolutions for astronomical images

ABSTRACT Astronomical images allow people to explore the Universe and monitor space; however, due to the long distances involved, such images are generally collected using telescopic equipment. The equipment optical characteristics and the imaging environment cause image degradation, such as blurring, lost details, and sometimes serious losses of object structures and contours, thus limiting the applications of these images. Unfortunately, improving the equipment to acquire much sharper images is expensive. Therefore, we propose a post-processing structure learning method to restore astronomical images that is low in cost but has exciting effects. The proposed method uses single backbone neural networks or their simple combinations to solve a series of image restoration problems, including point spread function (PSF) estimation, non-blind deconvolution, and blind deconvolution. In tests on simulated and real astronomical images, the proposed method achieves dramatic improvements compared to other state-of-the-art methods. Although this work concentrates on astronomical images, the proposed framework is applicable to a wide range of fields.

Point-spread function of the BOLD response across columns and cortical depth in human extra-striate cortex.

Columns and layers are fundamental organizational units of the brain. Well known examples of cortical columns are the ocular dominance columns (ODCs) in primary visual cortex and the column-like stripe-based arrangement in the second visual area V2. The spatial scale of columns and layers is beyond the reach of conventional neuroimaging, but the advent of high field magnetic resonance imaging (MRI) scanners (UHF, 7 T and above) has opened the possibility to acquire data at this spatial scale, in-vivo and non-invasively in humans. The most prominent non-invasive technique to measure brain function is blood oxygen level dependent (BOLD) fMRI, measuring brain activity indirectly, via changes in hemodynamics. A key determinant of the ability of high-resolution BOLD fMRI to accurately resolve columns and layers is the point-spread function (PSF) of the BOLD response in relation to the spatial extent of neuronal activity. In this study we take advantage of the stripe-based arrangement present in visual area V2, coupled with sub-millimetre anatomical and gradient-echo BOLD (GE BOLD) acquisition at 7 T to obtain PSF estimates and along cortical depth in human participants. Results show that the BOLD PSF is maximal in the superficial part of the cortex (1.78 mm), and it decreases with increasing cortical depth (0.83 mm close to white matter).

Multi-CCD modelling of the point spread function

Context.Galaxy imaging surveys observe a vast number of objects, which are ultimately affected by the instrument’s point spread function (PSF). It is weak lensing missions in particular that are aimed at measuring the shape of galaxies and PSF effects represent an significant source of systematic errors that must be handled appropriately. This requires a high level of accuracy at the modelling stage as well as in the estimation of the PSF at galaxy positions.Aims.The goal of this work is to estimate a PSF at galaxy positions, which is also referred to as a non-parametric PSF estimation and which starts from a set of noisy star image observations distributed over the focal plane. To accomplish this, we need our model to precisely capture the PSF field variations over the field of view and then to recover the PSF at the chosen positions.Methods.In this paper, we propose a new method, coined Multi-CCD (MCCD) PSF modelling, which simultaneously creates a PSF field model over the entirety of the instrument’s focal plane. It allows us to capture global as well as local PSF features through the use of two complementary models that enforce different spatial constraints. Most existing non-parametric models build one model per charge-coupled device, which can lead to difficulties in capturing global ellipticity patterns.Results.We first tested our method on a realistic simulated dataset, comparing it with two state-of-the-art PSF modelling methods (PSFEx and RCA) and finding that our method outperforms both of them. Then we contrasted our approach with PSFEx based on real data from the Canada-France Imaging Survey, which uses the Canada-France-Hawaii Telescope. We show that our PSF model is less noisy and achieves a ∼22% gain on the pixel’s root mean square error with respect toPSFEx.Conclusions.We present and share the code for a new PSF modelling algorithm that models the PSF field on all the focal plane that is mature enough to handle real data.

PSF Estimation Method of Simple-Lens Camera Using Normal Sinh-Arcsinh Model Based on Noise Image Pairs

With the development of computational photography, single-lens camera combined with corresponding image deblurring algorithm is gradually becoming a new research direction, replacing complex modern optical imaging system such as single lens reflex (SLR) camera. For single-lens camera, the Point Spread Function (PSF) estimation accuracy will directly affect the image restoration effect. In this paper, we designed the simple-lens cameras with one, two and three lenses, respectively, and propose a robust and accurate PSF estimation method of simple-lens camera. The key point of estimation is to obtain the blur image and clear image pairs, which are necessary for non-blind deconvolution PSF estimation. Considering the structure characteristic of simple-lens camera, we take picture of original clear image displayed on the computer screen to get the image pairs through corner detection and color correction is made to remove color distortion. In addition, a few studies have shown that the PSF of the simple lens is close to the spatially deformed wedge, so we use a more reasonable Normal Sinh-Arcsinh (NSAS) model to fit the blur kernel and get its parameters by Powell algorithm. The experiment results have shown that the space-variant PSF estimated by the proposed method achieves better performance than the compared methods both qualitatively and quantitatively.

PSF Estimation in Crowded Astronomical Imagery as a Convolutional Dictionary Learning Problem

We present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity of astrometric and photometric measurements extracted from wide-field sky monitoring imagery. Our radically new approach utilizes convolutional sparse representations to model the continuous functions involved in the image formation. This approach avoids the need to detect and precisely localize individual point sources that is shared by existing methods. In experiments involving simulated astronomical imagery, it significantly outperforms the recent alternative method with which it is compared.

The maximum entropy on the mean method for image deblurring

Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. In this article, we adapt the principal of maximum entropy on the mean (MEM) to both deconvolution of general images and point spread function estimation (blind deblurring). This approach shifts the paradigm toward regularization at the level of the probability distribution on the space of images whose expectation is our estimate of the ground truth. We present a self-contained analysis of this method, reducing the problem to solving a differentiable, strongly convex finite-dimensional optimization problem for which there exists an abundance of black-box solvers. The strength of the MEM method lies in its simplicity, its ability to handle large blurs, and its potential for generalization and modifications. When images are embedded with symbology (a known pattern), we show how our method can be applied to approximate the unknown blur kernel with remarkable effects.

Computational estimation of point-spread-function field in axially symmetric optical systems

The Point-Spread-Function (PSF) field characterizes the geometric and diffractive properties of most optical system designs for imaging applications. The conventional method of computing the PSF field is carried out in two steps: first, geometrical computation of the wave aberration function, and then, diffraction evaluation. That method usually applies two approximations: (1) the exit and entrance pupil ray intersection coordinates are equal; and (2) the optical field amplitude distribution does not change between exit and entrance pupil planes. We propose here a variation of the conventional method that allows overcoming these two approximations in axially symmetric optical systems. To show the potentials of the method we applied it to a Cooke triplet. We analyse the influence of the number of traced rays on the measured accuracy of the method. We also evaluate the differences in the PSF estimation accuracy with respect to a method where the two aforementioned approximations were applied.

Blind Deconvolution for Poissonian Blurred Image With Total Variation and L 0-Norm Gradient Regularizations

This paper proposes a regularized blind deconvolution method for restoring Poissonian blurred image. The problem is formulated by utilizing the L0 -norm of image gradients and total variation (TV) to regularize the latent image and point spread function (PSF), respectively, and combining them with the negative logarithmic Poisson log-likelihood. To solve the problem, we propose an approach which combines the methods of variable splitting and Lagrange multiplier to convert the original problem into three sub-problems, and then design an alternating minimization algorithm which incorporates the estimation of PSF and latent image as well as the updation of Lagrange multiplier into account. We also design a non-blind deconvolution method based on TV regularization to further improve the quality of the restored image. Experimental results on both synthetic and real-world Poissonian blurred images show that the proposed method can achieve restored images of very high quality, which is competitive with or even better than some state of the art methods.