CN115774830B

CN115774830B - Rapid imaging method for sparse interference array

Info

Publication number: CN115774830B
Application number: CN202211333324.8A
Authority: CN
Inventors: 张利; 覃芹
Original assignee: Guizhou University
Current assignee: Guizhou University
Priority date: 2022-10-28
Filing date: 2022-10-28
Publication date: 2023-09-29
Anticipated expiration: 2042-10-28
Also published as: CN115774830A

Abstract

The invention discloses a rapid imaging method for a sparse interference array, and relates to the technical field of astronomical imaging. S1: determining a visibility density degree index sigma; sigma is defined as the number of visibility data per unit area; s2: defining a relation between sigma and a grid convolution function; s3: predefining a grid convolution function of sigma; the calculated amount isPre-defining sigmaA relationship between the grid convolution functions and the grid convolution functions; s4: performing self-adaptive grid convolution operation; performing convolution operation on the visibility of the samples, selecting the self-adaptive convolution kernel size, sampling by using a convolution function, and discretizing the non-uniform visibility data to regular grid points; s5: the IFFT maps the visibility of the lattice points; and performing IFFT on the visible data on the grid points to obtain an astronomical chart. By selecting the grid convolution function by adapting the degree of visibility data density, the amount of redundant computation can be reduced while improving the quality of the image.

Description

Rapid imaging method for sparse interference array

Technical Field

The invention relates to the technical field of astronomical imaging, in particular to a rapid imaging method for a sparse interference array.

Background

The radiointerference mapping process is to perform operations such as gridding, fast inverse Fourier transform and deconvolution on the sampled visible data based on the synthetic aperture mapping principle, and finally generate an observation image of the radio source. The interferometer scans the sky resulting in a fourier component of the sky source, the visibility data, which is unevenly distributed due to the sparse array sampling. The patterning of non-uniformly distributed visibility data requires gridding to convert it into uniformly sampled visibility data, the specific implementation of gridding being to convolve the non-uniformly distributed visibility data with a convolution function. Gridding is the longest and most important step in radiograms, and the performance of the algorithm directly affects the speed and quality of the radiograms.

The traditional meshing is mainly a convolution resampling process, the convolution function directly influences the meshing effect, the convolution function is required to have good concentration in both time domain and frequency domain on the selection of the convolution function, and the convolution function can well avoid the aliasing problem. The convolution functions commonly used in radiointerference mapping are: cylindrical surface function, truncated sine function, oblong function, etc. The gridding step is mainly divided into three steps: 1. the convolution function convolves with the measured visibility, the visibility is placed under rectangular coordinate sampling 2 in an interpolation mode, rectangular coordinate data are processed by utilizing an oversampling technology to improve the resolution 3 of the image, and the influence of the convolution function is removed by utilizing a grid correction function.

The algorithm is firstly proposed by Brouw and applied to astronomical data processing in 1975, a Cygrid gridding framework proposed by Winkel, lenz and the like is applied to 21cm neutral hydrogen measurement, the framework allows convolution and resampling of any effective astronomical FITS file data information to a regular grid, and the biggest characteristic of the algorithm is that simple parallelization is allowed and the operation speed is greatly improved; the latest HCgrid framework proposed by Wang H et al is a radio astronomical framework based on convolution, is suitable for a CPU/GPU heterogeneous platform, and can efficiently resample original astronomical visibility data to uniform Cartesian grid points and store a gridding result in a FITS file.

In the prior art of grid shooting, the grid shooting is realized aiming at convolution functions with fixed scale, namely, convolution functions with the same scale are used for all the visibility, so that the prior art has poor adaptability to different visibility, and the imaging error is larger.

The existing gridding method depends on the selection of a convolution function, the selection of the convolution function of the grid is of a fixed scale, and meanwhile, the gridding process is mainly realized in a convolution interpolation mode, and the process leads to high gridding complexity and larger error. The prior art studies have accelerated the algorithm mainly from the point of view of high performance computation, such as pipeline acceleration with GPU and Open GL. The method has higher complexity and higher requirement on hardware configuration. Therefore, in summary, the existing meshing method has the problems of high complexity, difficulty in realization and large error, so that the radiointerference mapping time is long and the mapping quality is poor. This problem remains severe in sparse array measurements.

Aiming at the fact that the degree of the density of the visible data is different, the visibility mapping research of different degrees of the density has different requirements on the convolution function. In order to solve the problems of large calculation amount and large mapping error caused by fixed-scale grid convolution, the invention provides a rapid mapping method for a sparse array based on an adaptive scale. By selecting the grid convolution function by adapting the degree of visibility data density, the amount of redundant computation can be reduced while improving the quality of the image. The method can be used for rapid imaging of sparse arrays, and can also be widely applied to non-uniform sampling of radioastronomy.

Disclosure of Invention

The invention aims to provide a rapid mapping method for a sparse interference array, and provides a self-adaptive scale-based grid convolution algorithm for sparse array sampling aiming at the fact that visible data with different densities in radioastronomical mapping depend on grid convolution functions with different scales. That is, a large scale grid convolution is used for denser visibility data and a small scale grid convolution function is used for sparse visibility data. Through the convolution function of the self-adaptive scale, the problem of edge blurring caused by visibility of different sparseness degrees in radioastronomical imaging can be solved, the imaging quality is improved, and meanwhile, the redundant calculation amount in gridding calculation can be greatly reduced, and the imaging speed is improved.

The technical aim of the invention is realized by the following technical scheme: a rapid patterning method for a sparse interference array, comprising the steps of:

s1: determining a visibility density degree index sigma; sigma is defined as the number of visibility data per unit area, with greater sigma being more visible and less visible;

s2: defining a relation between sigma and a grid convolution function; knowing σ, a grid convolution function of a specified scale size can be determined;

s3: predefining a grid convolution function of sigma; in the processing process of the gridding algorithm, the calculated amount is as followsM is the number of visibility data, C is the support set size of the convolution kernel; the relation between sigma and the grid convolution function are predefined;

s4: performing self-adaptive grid convolution operation; performing convolution operation on the visibility of the samples, selecting the self-adaptive convolution kernel size, sampling by using a convolution function, and discretizing the non-uniform visibility data to regular grid points;

s5: the IFFT maps the visibility of the lattice points; and performing IFFT on the visible data on the grid points to obtain an astronomical chart.

In summary, the invention has the following beneficial effects: by utilizing the dependence of the size of the grid convolution kernel on the degree of density of visibility data, a grid convolution algorithm with an adaptive scale size is provided, and a large-scale convolution function is used for the visibility of a dense place, and a small-scale convolution function is used for the visibility of a sparse place _。 By selecting the grid convolution function by adapting the degree of visibility data density, the amount of redundant computation can be reduced while improving the quality of the image. The method can be used for rapid imaging of sparse arrays, and can also be widely applied to non-uniform sampling of radioastronomy.

Drawings

FIG. 1 is a diagram forming process based on convolution meshing in an embodiment of the present invention;

FIG. 2 is a flow chart of an adaptive scale size grid convolution operation in an embodiment of the present invention;

fig. 3 is a convolution interpolation process in an embodiment of the present invention.

Detailed Description

The invention is described in further detail below with reference to fig. 1-3.

Radioastronomical imaging is the process of forming a dirty map using measured non-uniform visibility data. The specific implementation formula is as follows:

wherein I is ^D (l, m) denotes a dirty map, s (u, V) denotes a sampling function, and V' (u, V) denotes actual observed non-uniform visibility data. From equation (1), it can be seen that radiometric interferometry involves a large number of fourier transforms, since the visibility data and sky plot are a pair of fourier relationship pairs. When the amount of visibility data is large, this requires the use of a fast fourier transform, but the FFT requires the data to be distributed over uniform grid points, so we need to gridding the visibility data before using the fast inverse fourier transform to get the astronomical image, i.e.:

V ^G (u,v)＝V'(u,v)*GCF (2)

wherein V is ^G (u, v) represents regular visibility data and GCF represents a grid convolution function. The process of meshing is not in fact a simple interpolation procedure, as it combines smoothing with interpolation. The specific flow is shown in figure 1.

In practice, the choice of the grid convolution function requires that the GCF be in a small bounded region A _c Is equal to zero and requires that the selected grid convolution function be as efficient as possible to avoid aliasing of the source. The traditional gridding implementation is mainly a convolution resampling process, and is a very key link in astronomical data processing, specifically, the visibility data and a grid convolution function matrix are subjected to convolution operation, each visibility and the convolution function coefficient matrix are added into a predefined grid to be removed, each visibility influences one grid, and in practice, the size of the convolution coefficient matrix is determined by factors such as an oversampling coefficient, a grid scale, the length of a base line and the like. The implementation mainly comprises three steps:

1. convoluting the convolution function with the measured non-uniform visibility, and placing the visibility under rectangular coordinate sampling by interpolation

2. Processing rectangular coordinate data by using an oversampling technology to improve resolution of an image

3. The convolution effect is removed using a grid correction function, which is not to some extent an accurate correction unless it is under the limitation of a large number of well-distributed visibility measurements.

As can be seen from the formula (2), the core calculation of the meshing algorithm is accumulation of single-precision floating point complex products, the operation of each visibility data needs to be performed with two memory reads and one memory write operation, when the data points covered by uv are larger, the dependence of the calculation efficiency on the calculation hardware is larger, and in the traditional research, the program acceleration is realized by decomposing the calculation into a multi-thread program and utilizing the GPU.

In existing mesh implementation algorithms, the choice of convolution function is fixed, i.e., the same convolution function is required for both dense and sparse visibility. For example, for a convolution function with a convolution size of 5*5, since kernel calculation implemented by the grid is accumulation of products of visibility, weights of the convolution function are assigned to corresponding grid points, in a traditional method, if M pieces of visibility data are provided, a convolution interpolation operation with a size of 5*5 is performed on the M pieces of visibility, so that calculation amount is large to a certain extent, and redundant calculation exists in the method due to different density degree requirements on the convolution kernel size.

Examples: a rapid patterning method for a sparse interference array, as shown in fig. 1-3, comprising the steps of:

s1: determining a visibility density degree index sigma; sigma is defined as the number of visibility data per unit area, with a larger sigma representing denser visibility, then a large scale grid convolution function should be selected; smaller σ represents more sparse, then a small scale grid convolution function should be chosen;

s2: defining a relation between sigma and a grid convolution function; knowing σ, a grid convolution function of a specified scale size can be determined; the key of the self-adaptive scale size grid convolution function in the method is that the self-adaptive scale size grid convolution function is used for the method.

S3: predefining a grid convolution function of sigma; in the processing process of the gridding algorithm, the calculated amount is as followsM is the number of visibility data, C is the support set size of the convolution kernel, such as 3×3; the relation between sigma and the grid convolution function are predefined;

s4: performing self-adaptive grid convolution operation; performing convolution operation on the visibility of the samples, selecting the self-adaptive convolution kernel size, sampling by using a convolution function, and discretizing the non-uniform visibility data to regular grid points; fig. 3 is an implementation of convolution interpolation.

Based on the adaptive scale-size grid convolution implementation, the dependence of the convolution function on the degree of visibility-sparseness can be replaced by using a small scale convolution function for dense visibility and a large scale convolution function for sparse visibility.

The present embodiment is only for explanation of the present invention and is not to be construed as limiting the present invention, and modifications to the present embodiment, which may not creatively contribute to the present invention as required by those skilled in the art after reading the present specification, are all protected by patent laws within the scope of claims of the present invention.

Claims

1. A rapid imaging method for a sparse interference array is characterized by comprising the following steps: the method comprises the following steps: