Shift-variant Point Spread Function Research Articles

Fast deconvolved beamforming For arbitrary arrays based on beam-domain sparse Bayesian learning

Aiming at the problem that the conventional deconvolved beamforming methods cannot be directly applied to the specific array with a shift-variant point spread function and also have considerable computational workload, a deconvolved beamforming method for arbitrary arrays based on beam-domain sparse Bayesian learning(SBL) is proposed. First, generalized convolution model for arbitrary arrays in beam-domain is derived. Conventional beamforming is used to obtain several complex output beams. Then, to improve the accuracy of direction of arrival(DOA) estimation, the off-grid SBL method which adopts a coarse grid and takes the sampled positions in the coarse grid as the adjustable parameters is applied to achieve deconvolution of complex output beams. Controlling the number of output beams from the conventional beamforming can accelerate the off-grid SBL method while maintaining reasonable accuracy. The simulation results show that the proposed method provides enhanced recovery performance and higher DOA estimation accuracy comparable to the traditional SBL beamforming method in element domain at the same grid interval. Especially for short and dense arrays, it can achieve a decrease in computational complexity by one to two orders of magnitude with the same accuracy.

Shift-variant deconvolution beamforming using Implicit Neural Representation for near-field acoustic image measurement

The conventional beamforming (CBF) output can be expressed as a convolution of the source distribution and the array dependent point spread function (PSF), which is defined as the response of the beamformer to a point source. The resolution and accuracy of sound source localization can be improved by deconvolution of CBF. The shift-invariant PSF assumption is only a good approximation when the source region is small compared to the distance between the array and the source. However, the PSF of the near-field underwater acoustic map measurement is shift-variant, whose mismatch with the beam could lead to performance degradation. In this paper, we proposed an optimized deconvolution method by using the neural network called implicit neural representation (INR) to solve the beam mismatch problem, due to its strong performance in learning and reconstructing spatial scenes. Rather than recompute the PSF for each pixel in the scene, INR predicts the complex-valued weight matrix in two-dimensional space that encapsulates both the spatially varying properties of the PSF and the scatter distribution of the scene. Numerical simulations and experimental results verify the effectiveness of our method. And this work can be broadly applied to arrays with shift-variant PSFs.

Fast non-line-of-sight imaging based on product-convolution expansions.

Non-line-of-sight (NLoS) imaging reveals a hidden scene using indirect diffuse reflections. A common choice for analyzing the time-of-flight (ToF) data from a non-confocal system is an ellipsoid model whose operator is high-dimensional, leading to a computationally arduous task. In this Letter, the product-convolution expansions method is utilized to formulate the operator and its adjoint based on the observation of a shift-variant point spread function (PSF) in the ToF data. The operator and its adjoint are locally approximated as a convolution, which allows the forward and backward procedure to be computed efficiently through fast Fourier transform (FFT). Moreover, the low-rank approximation of the operator is obtained by matrix decompositions, further improving the computational efficiency. The proposed method is validated using publicly accessible datasets.

Efficient computation of backprojection arrays for 3D light field deconvolution.

Light field deconvolution allows three-dimensional investigations from a single snapshot recording of a plenoptic camera. It is based on a linear image formation model, and iterative volume reconstruction requires to define the backprojection of individual image pixels into object space. This is effectively a reversal of the point spread function (PSF), and backprojection arrays H' can be derived from the shift-variant PSFs H of the optical system, which is a very time consuming step for high resolution cameras. This paper illustrates the common structure of backprojection arrays and the significance of their efficient computation. A new algorithm is presented to determine H' from H, which is based on the distinct relation of the elements' positions within the two multi-dimensional arrays. It permits a pure array rearrangement, and while results are identical to those from published codes, computation times are drastically reduced. This is shown by benchmarking the new method using various sample PSF arrays against existing algorithms. The paper is complemented by practical hints for the experimental acquisition of light field PSFs in a photographic setup.

The deconvolved conventional beamforming for conformal array

As the conformal array has the advantages over the large array aperture, superior aeroacoustic dynamics, and wide angle cover range, it is widely used in radar and sonar system. The deconvolved conventional beamforming (dCv) can yield not only the improved direction of arrival (DOA) estimation accuracy in terms of a narrower beamwidth and suppressed side lobes but also the higher directivity index than the CBF. This paper uses an extended R-L deconvolution algorithm and applies the dCv in conformal array. Simulation and experiment results show that the extended R-L can be applied to an arbitrary conformal array with a shift-variant point spread function (PSF). Beyond the high-resolution and high array gain performance advantages, the extended R-L algorithm is shown to be suitable for coherent signals. The results also show that it is better to use the actual PSF than the theoretical PSF when there exit position errors.

PSF reconstruction for Compton-based prompt gamma imaging

Compton-based prompt gamma (PG) imaging has been proposed for in vivo range verification in proton therapy. However, several factors degrade the image quality of PG images, some of which are due to inherent properties of a Compton camera such as spatial resolution and energy resolution. Moreover, Compton-based PG imaging has a spatially variant resolution loss. In this study, we investigate the performance of the list-mode ordered subset expectation maximization algorithm with a shift-variant point spread function (LM-OSEM-SV-PSF) model. We also evaluate how well the PG images reconstructed using an SV-PSF model reproduce the distal falloff of the proton beam. The SV-PSF parameters were estimated from simulation data of point sources at various positions. Simulated PGs were produced in a water phantom irradiated with a proton beam. Compared to the LM-OSEM algorithm, the LM-OSEM-SV-PSF algorithm improved the quality of the reconstructed PG images and the estimation of PG falloff positions. In addition, the 4.44 and 5.25 MeV PG emissions can be accurately reconstructed using the LM-OSEM-SV-PSF algorithm. However, for the 2.31 and 6.13 MeV PG emissions, the LM-OSEM-SV-PSF reconstruction provides limited improvement. We also found that the LM-OSEM algorithm followed by a shift-variant Richardson–Lucy deconvolution could reconstruct images with quality visually similar to the LM-OSEM-SV-PSF-reconstructed images, while requiring shorter computation time.

Resolution recovery reconstruction for a Compton camera

The spatial resolution from Compton cameras suffers from measurement uncertainties in interaction positions and energies. The degree of degradation in spatial resolution is shift-variant (SV) over the field-of-view (FOV) because the imaging principle is based on the conical surface integration. In our study, the shift-variant point spread function (SV-PSF) is derived from point source measurements at various positions in the FOV and is incorporated into the system matrix of a fully three-dimensional, accelerated reconstruction, i.e. the listmode ordered subset expectation maximization (LMOSEM) algorithm, for resolution recovery. Simulation data from point sources were used to estimate SV and asymmetric parameters for Gaussian, Cauchy, and general parametric PSFs. Although little difference in the fitness accuracy between Gaussian and general parametric PSFs was observed, the general parametric model showed greater flexibility over the FOV in shaping the curve between that for Gaussian and Cauchy functions. The estimated asymmetric SV-PSFs were incorporated into the LMOSEM for resolution recovery. For simulation data from a single point source at the origin, all LMOSEM-SV-PSFs improved the spatial resolution by 2.6 times over the standard LMOSEM. For two point-source simulations, reconstructions also gave a two-fold improvement in spatial resolution and resulted in a greater recovered activity ratio at different positions in the FOV.

Cone-beam reconstruction by backprojection and filtering.

A new analytical method for tomographic image reconstruction from cone-beam projections acquired on the source orbits lying on a cylinder is presented. By application of a weighted cone-beam backprojection, the reconstruction problem is reduced to an image-restoration problem characterized by a shift-variant point-spread function that is given analytically. Assuming that the source is relatively far from the imaged object, a formula for an approximate shift-invariant inverse filter is derived; the filter is presented in the Fourier domain. Results of numerical experiments with circular and helical orbits are considered.

A filtering approach to image reconstruction in 3D SPECT

We present a new approach to three-dimensional (3D) image reconstruction usinganalytical inversion of the exponential divergent beam transform, which canserve as a mathematical model for cone-beam 3D SPECT imaging. We apply acircular cone-beam scan and assume constant attenuation inside a convex areawith a known boundary, which is satisfactory in brain imaging. Thereconstruction problem is reduced to an image restoration problemcharacterized by a shift-variant point spread function which is givenanalytically. The method requires two computation steps: backprojection andfiltering. The modulation transfer function (MTF) of the filter is derived bymeans of an original methodology using the 2D Laplace transform. The filter isimplemented in the frequency domain and requires 2D Fourier transform oftransverse slices. In order to obtain a shift-invariant cone-beamprojection-backprojection operator we resort to an approximation, assumingthat the collimator has a relatively large focal length. Nevertheless,numerical experiments demonstrate surprisingly good results for detectors withrelatively short focal lengths. The use of a wavelet-based filtering algorithmgreatly improves the stability to Poisson noise.

MRF model-based identification of shift-variant point spread function for a class of imaging systems

Identification of pointwise space-variant blur is an important area of research in image processing and computer vision. In this paper, we propose an MAP-MRF based scheme for identifying a class of shift-variant imaging systems whose point spread function can be parameterized by a single blur parameter. The space-variant (SV) blur parameter is modeled as an MRF and the MAP estimate of the SV blur parameter is obtained using simulated annealing. The scheme is amenable to the incorporation of smoothness constraints on the spatial variations of the blur parameter and simultaneously allows for inclusion of line fields to preserve discontinuities in the shift-variant blur. The performance of the proposed scheme is tested on synthetic as well as real data and the estimates of the SV blur are found to be better than that of the window-based blur identification technique.

Analysis of photometric properties of occluding edges by the reversed projection blurring model

This paper analyzes photometric properties of occluding edges and proves that an object surface behind a nearer object is partially observable beyond the occluding edges. We first discuss a limitation of the image blurring model using the convolution, and then present an optical flux based blurring model named the reversed projection blurring (RPB) model. Unlike the multicomponent blurring model proposed by Nguyen et al., the RPB model enables us to explore the optical phenomena caused by a shift-variant point spread function that appears at a depth discontinuity. Using the RPB model, theoretical analysis of occluding edge properties are given and two characteristic phenomena are shown: (1) a blurred occluding edge produces the same brightness profiles as would be predicted for a surface edge on the occluding object when the occluded surface radiance is uniform and (2) a nonmonotonic brightness transition would be observed in blurred occluding edge profiles when the occluded object has a surface edge. Experimental results using real images have demonstrated the validity of the RPB model as well as the observability of the characteristic phenomena of blurred occluding edges.