Super-resolution based on blind deconvolution using similarity of power spectra

This study addresses the blind image deconvolution which uses only blurred image and less point spread function (PSF) information to restore the original image. To identify the blind image it is a very important step for restoring the image. Therefore, the first step is to look for PSF model. In this paper, particle swarm optimization (PSO) is utilized to seek the unknown PSF. The objective function is based on the wavelet transform. It can identify the parameters of PSF exactly. Finally, the feasibility and validity of proposed algorithm are demonstrated by several simulations.

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.

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.

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.

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 μm and 1.625 μm) 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.

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.

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.

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.

A camera shake of the relative motion between cameras and original scenes often occurs during a shoot, resulting in blurred images. This paper presents a method of restoring blurred images based on patch-based PSF (Point Spread Function) estimation and channel-dependent image deblurring. Initially, a pair of noisy and blurred images is acquired by consecutive shooting under short and long exposures to more accurately estimate the 2D trajectory formed by the camera shake, which is also known as PSF. From the noisy image, one patch with strong edges is extracted using gradient operators and the corresponding blurry patch is found within the blurry image. The boundaries of both patches are padded in a specified tile pattern to prevent the appearance of vertical or horizontal lines due to boundary discontinuity. Tikhonov regularization is then iteratively conducted on Gaussian pyramid images with adaptive noise thresholding to get the optimized PSF. Finally, the color conversion of the blurred image into a luminance and two chrominance images is done to apply the channel dependent image deblurring where the spatial resolution of the chrominance images is reduced based on the natural gradient distribution to abandon the valueless data regardless of the restoration quality. Moreover, another artificially blurred image made by the convolution of the known Gaussian PSF and the noisy image is used to reduce undesirable ringing-artifacts and increase the sharpness. The experimental results show that the proposed method can provide more improved PSFs and restored images accompanied by the reduction of computing time and ring artifacts.

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.

At present time methods of optical encryption are actively developed. The majority of existing methods of optical encryption use not only light intensity distribution, easily registered with photosensors, but also its phase distribution which require application of complex holographic schemes in conjunction with spatially coherent monochromatic illumination. This leads to complex optical schemes and low decryption quality. To eliminate these disadvantages it is possible to implement optical encryption using spatially incoherent monochromatic illumination which requires registration of light intensity distribution only. Encryption is accomplished by means of optical convolution of image of scene to be encrypted and encryption diffractive optical element (DOE) point spread function (PSF) which serves as encryption key. Encryption process is described as follows. Scene is illuminated with spatially-incoherent monochromatic light. In the absence of encryption DOE lens forms image of scene in photosensor plane. DOE serves as encryption element, its PSF - encryption key. Light passing through DOE forms convolution of object image and DOE PSF. Registered by photosensor convolution is encrypted image. Decryption was conducted numerically on computer by means of inverse filtration with regularization. Kinoforms were used as encryption DOE because they have single diffraction order. Two liquid crystal (LC) spatial light modulators (SLM) were used to implement dynamic digital information input and dynamic encryption key change. As input scene amplitude LC SLM HoloEye LC2002 with 800×600 pixels 32×32 μm² and 256 gray levels was used. To image synthesized encryption kinoforms phase LC SLM HoloEye PLUTO VIS with 1920×1080 pixels 8×8 μm² and 256 phase levels was used. Set of test images was successfully optically encrypted and then numerically decrypted. Encrypted images contents are hidden. Decrypted images despite quite high noise levels are positively recognizable. Results of optical encryption and numerical decryption are presented.

Context. Fitting photometry algorithms can be very effective provided that an accurate model of the instrumental point spread function (PSF) is available. When high-precision time-resolved photometry is required, however, the use of point-source star images as empirical PSF models can be unsatisfactory, due to the limits in their spatial resolution. Theoretically-derived models, on the other hand, are limited by the unavoidable assumption of simplifying hypothesis, while the use of analytical approximations is restricted to regularly-shaped PSFs. Aims. This work investigates an innovative technique for space-based fitting photometry, based on the reconstruction of an empirical but properly-resolved PSF. The aim is the exploitation of arbitrary star images, including those produced under intentional defocus. The cases of both MOST and COROT, the first space telescopes dedicated to time-resolved stellar photometry, are considered in the evaluation of the effectiveness and performances of the proposed methodology. Methods. PSF reconstruction is based on a set of star images, periodically acquired and presenting relative subpixel displacements due to motion of the acquisition system, in this case the jitter of the satellite attitude. Higher resolution is achieved through the solution of the inverse problem. The approach can be regarded as a special application of super-resolution techniques, though a specialised procedure is proposed to better meet the PSF determination problem specificities. The application of such a model to fitting photometry is illustrated by numerical simulations for COROT and on a complete set of observations from MOST. Results. We verify that, in both scenarios, significantly better resolved PSFs can be estimated, leading to corresponding improvements in photometric results. For COROT, indeed, subpixel reconstruction enabled the successful use of fitting algorithms despite its rather complex PSF profile, which could hardly be modeled otherwise. For MOST, whose direct-imaging PSF is closer to the ordinary, comparison to other models or photometry techniques were carried out and confirmed the potential of PSF reconstruction in real observational conditions.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

Blind spikes deconvolution, or blind super-resolution, deals with the problem of estimating the delays and amplitudes of spikes from its convolution with an unknown low-pass point spread function. By constraining the point spread function in a known low-dimensional subspace, a convex optimization algorithm called AtomicLift has been proposed to exactly recover the spikes up to an unavoidable scaling ambiguity in the noiseless setting. This paper analyzes the performance of AtomicLift in the presence of bounded noise, and shows that the spikes are localized in a stable manner where the localization inaccuracy is proportional to the noise level. Moreover, we show AtomicLift is also capable to handle sparse outliers in the frequency domain.

The point spread function (PSF) of a gamma camera describes the photon count density distribution at the detector surface when a point source is imaged. Knowledge of the PSF is important for computer simulation and accurate image reconstruction of single photon emission computed tomography (SPECT) images. To reduce the number of measurements required for PSF characterization and the amount of computer memory to store PSF tables, and to enable generalization of the PSF to different collimator-to-source distances, the PSF may be modeled as the two-dimensional (2D) convolution of the depth-dependent component which is free of detector blurring (PSF(ideal)) and the distance-dependent detector response. Owing to limitations imposed by the radioactive strength of point sources, extended sources have to be used for measurements. Therefore, if PSF(ideal) is estimated from measured responses, corrections have to be made for both the detector blurring and for the extent of the source. In this paper, an approach based on maximum likelihood expectation-maximization (ML-EM) is used to estimate PSF(ideal). In addition, a practical measurement procedure which avoids problems associated with commonly used line-source measurements is proposed. To decrease noise and to prevent nonphysical solutions, shape constraints are applied during the estimation of PSF(ideal). The estimates are generalized to depths other than those which have been measured and are incorporated in a SPECT simulator. The method is validated for Tc-99m and T1-201 by means of measurements on physical phantoms. The corrected responses have the desired shapes and simulated responses closely resemble measured responses. The proposed methodology may, consequently, serve as a basis for accurate three-dimensional (3D) SPECT reconstruction.