CN115774830A - Rapid mapping method for sparse interference array - Google Patents
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Abstract
The invention discloses a rapid mapping method for a sparse interference array, and relates to the technical field of astronomical mapping. S1: determining a visibility density degree index sigma; σ is defined as the number of visibility data per unit area; s2: defining the relation between sigma and the grid convolution function; s3: a grid convolution function of predefined sigma; calculated as
Predefining a relation between sigma and a grid convolution function and the grid convolution function; s4: carrying out self-adaptive grid convolution operation; carrying out convolution operation on the sampled visibility, selecting the size of a self-adaptive convolution kernel, then sampling by using a convolution function, and discretizing the non-uniform visibility data to regular lattice points; s5: IFFT lattice visibilityDrawing a graph; and performing IFFT on the visibility data on the grid points to obtain an astronomical graph. The grid convolution function is selected by self-adapting the density degree of the visibility data, so that the redundant calculation amount can be reduced, and the imaging quality is improved.
Description
Technical Field
The invention relates to the technical field of astronomical mapping, in particular to a rapid mapping method for a sparse interference array.
Background
The radio interference mapping process is based on the synthetic aperture mapping principle to carry out gridding, fast inverse Fourier transform, deconvolution and other operations on sampled visibility data, and finally generates an observation image of a radio source. The interferometer scans the sky resulting in a fourier component of the sky source-visibility data, which is non-uniformly distributed due to sparse array sampling. Mapping the non-uniformly distributed visibility data requires gridding to convert the non-uniformly distributed visibility data into uniformly sampled visibility data, and the specific implementation of gridding is to convolve the non-uniformly distributed visibility data with a convolution function. Gridding is the most time-consuming and important step in radio mapping, and the performance of the algorithm directly influences the speed and quality of radio mapping.
The traditional gridding is mainly a convolution resampling process, a convolution function directly influences the gridding effect, the selection of the convolution function requires that the convolution function has better concentration in both time domain and frequency domain, and the convolution function can better avoid the aliasing problem. The convolution functions commonly used in radio-interference mapping are: cylindrical surface functions, truncated sinc functions, prolate ellipsoid functions, etc. The gridding step is mainly divided into three steps: 1. convolving the convolution function with the measured visibility, placing the visibility under rectangular coordinate sampling 2 by interpolation, processing the rectangular coordinate data by oversampling technology to improve the resolution of the image 3, and removing the influence of the convolution function by using a grid correction function.
The algorithm is firstly proposed by Brouw in 1975 and applied to astronomical data processing, a Cygrid gridding framework proposed by Winkel, lenz and the like in 2016 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 algorithm has the greatest characteristic of allowing simple parallelization and is greatly improved in operation speed; the HCGrid framework recently proposed by Wang H et al is a radio astronomical framework based on convolution, is suitable for CPU/GPU heterogeneous platforms, and can efficiently resample the original astronomical visibility data to uniform cartesian grid points and save the gridding results in the FITS file.
In the prior art, radio gridding technology is realized by aiming at a convolution function with a fixed scale, namely, the convolution function with the same scale is used for all visibilities, so that the prior art has poor adaptability to different visibilities and causes large imaging errors.
The existing gridding method depends on the selection of a convolution function, the selection of the grid convolution function is of a fixed scale, and meanwhile, the gridding process is mainly realized in a convolution interpolation mode, so that the gridding complexity is high and the error is large. The prior art researches mainly accelerate the algorithm from the perspective of high-performance computation, such as pipeline acceleration by using GPU and Open GL. The method has higher complexity and higher requirement on hardware configuration. Therefore, in summary, the conventional gridding method has the problems of high complexity, difficulty in implementation and large error, so that the radio interference mapping time is long and the mapping quality is poor. This problem is still severe in sparse array measurements.
In practical situations, the density degrees of the visibility data are different, and the visibility mapping researches with different density degrees have 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 quick mapping method for a sparse array based on self-adaptive scale. The grid convolution function is selected by self-adapting the density degree of the visibility data, so that the redundant calculation amount can be reduced, and the imaging quality is improved. The method can be used for a quick mapping method of a sparse array, and can also be widely applied to the non-uniform sampling of the radio astronomy.
Disclosure of Invention
The invention aims to provide a quick mapping method for a sparse interference array, and provides a grid convolution algorithm based on self-adaptive scale for sparse array sampling aiming at different dependence of visibility data with different densities on grid convolution functions with different scales in radio astronomical mapping. Namely, large-scale grid convolution is used for dense 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 with different sparsity degrees in radio astronomy mapping can be solved, mapping quality is improved, meanwhile, redundant calculation amount in gridding calculation can be greatly reduced, and mapping speed is improved.
The technical purpose of the invention is realized by the following technical scheme: a fast mapping method for sparse interferometric arrays, comprising the steps of:
s1: determining a visibility density degree index sigma; σ is defined as the number of visibility data per unit area, the visibility is denser the larger σ, and the visibility is sparser the smaller σ;
s2: defining the relation between sigma and the grid convolution function; when sigma is known, a grid convolution function with a specified scale size can be determined;
s3: a grid convolution function of predefined sigma; in the process of gridding algorithm, the calculated amount is
M is the number of the visibility data, and C is the size of a support set of a convolution kernel function; predefining a relation between sigma and a grid convolution function and the grid convolution function;
s4: carrying out self-adaptive grid convolution operation; performing convolution operation on the sampled visibility, selecting the size of a self-adaptive convolution kernel, then sampling by using a convolution function, and discretizing non-uniform visibility data to regular lattice points;
s5: the IFFT maps the grid point visibility; and performing IFFT on the visibility data on the grid points to obtain an astronomical graph.
In conclusion, the invention has the following beneficial effects: by utilizing the dependency of the size of a grid convolution kernel on the density degree of the visibility data, a grid convolution algorithm with the size of an adaptive scale is provided, and the condition that a large-scale convolution function is used for the visibility of dense positions and a small-scale convolution function is used for the visibility of sparse positions is pointed out 。 The grid convolution function is selected by self-adapting the density degree of the visibility data, so that the redundant calculation amount can be reduced, and the image forming quality can be improved. Can be used for quick mapping of sparse array and can also be widely applied to the non-uniform acquisition of radio astronomyIn the sample.
Drawings
FIG. 1 is a graph process based on convolution gridding in an embodiment of the present invention;
FIG. 2 is a flowchart of an adaptive scale-size grid convolution operation in an embodiment of the present invention;
FIG. 3 is a convolution interpolation process according to an embodiment of the present invention.
Detailed Description
The present invention is described in further detail below with reference to FIGS. 1-3.
Radioastronomy is a process of forming a dirty map using measured non-uniform visibility data. The concrete implementation formula is as follows:
wherein I D (l, m) denotes a dirty map, s (u, V) denotes a sampling function, and V' (u, V) denotes actually observed non-uniform visibility data. From equation (1), it can be seen that the radio interferogram involves a large number of fourier transforms because the visibility data is a pair of fourier-related pairs with the sky plot. When the amount of visibility data is large, this requires the use of fast fourier transform, but FFT requires the data to be distributed over uniform grid points, so we need to gridde the visibility data before the astronomical image is obtained using fast inverse fourier transform, i.e.:
V G (u,v)＝V'(u,v)*GCF (2)
wherein V G (u, v) represents regular visibility data and GCF represents a grid convolution function. The actual process of rasterizing is not a simple interpolation procedure as it combines smoothing with interpolation. The specific process is shown in FIG. 1.
In practice, the choice of the lattice convolution function requires the GCF to be within a small bounded area A c The outer is equal to zero and requires that the lattice convolution function be selected to avoid source aliasing as much as possible. The traditional gridding realization mainly comprises a convolution resampling process, which is a very key link in astronomical data processing, specifically speaking, the gridding realization can be realizedAnd performing convolution operation on the visibility data and the grid convolution function matrix, accumulating each visibility and convolution function coefficient matrix into a pre-defined grid, wherein each visibility influences one grid, and the size of the convolution coefficient matrix is determined by factors such as an oversampling coefficient, the grid scale and the length of a baseline in practice. The method mainly comprises three steps:
1. the convolution function is convolved with the measured non-uniform visibility, and the visibility is placed under rectangular coordinate sampling by means of interpolation
2. Processing the Cartesian coordinate data to the Cartesian coordinate data using an oversampling technique to increase the resolution of the image
3. The convolution effect is removed by a grid correction function, which to some extent is not a precise correction, except under a large number of well-distributed visibility measurement limits.
It can be known from formula (2) that the core calculation of the gridding algorithm is accumulation of single-precision floating-point complex product, operation of each visibility data needs to be performed with two times of memory reading and one time of memory writing, when a uv covers a large data point, the calculation efficiency has a large dependence on calculation hardware, and in the traditional research, the calculation is mainly decomposed into a multithread program, and the GPU is used for realizing program acceleration.
In the existing mesh implementation algorithm, the choice of the convolution function is fixed, that is, the same convolution function is required to be used for both dense visibility and sparse visibility. For example, for a convolution function with a convolution size of 5 × 5, since the kernel calculation implemented by the mesh is the accumulation of the visibility products, and the weights of the convolution functions are assigned to the corresponding mesh points, in the conventional method, if there are M visibility data, a convolution interpolation operation with a size of 5 × 5 is performed on the M visibility data, which is more computationally intensive to some extent, and the method has redundant calculation due to different requirements on the convolution kernel size for different sparseness and denseness degrees.
The embodiment is as follows: a fast mapping method for sparse interferometric arrays, as shown in fig. 1-3, comprising the steps of:
s1: determining a visibility density degree index sigma; σ is defined as the number of visibility data per unit area, and a larger σ represents denser visibility, and a larger-scale grid convolution function should be selected; the smaller the sigma, the more sparse the representation, the smaller the scale of the lattice convolution function should be selected;
s2: defining the relation between sigma and the grid convolution function; when sigma is known, a grid convolution function with a specified scale size can be determined; the method is key to the convolution function of the self-adaptive scale grid.
S3: a lattice convolution function of a predefined sigma; in the process of gridding algorithm, the calculated amount is
M is the number of visibility data, C is the support set size of the convolution kernel, e.g., 3 × 3; predefining a relation between sigma and a grid convolution function and the grid convolution function;
s4: carrying out self-adaptive grid convolution operation; performing convolution operation on the sampled visibility, selecting the size of a self-adaptive convolution kernel, then sampling by using a convolution function, and discretizing non-uniform visibility data to regular lattice points; fig. 3 is an implementation of convolution interpolation.
S5: the IFFT maps the grid point visibility; and performing IFFT on the visibility data on the grid points to obtain an astronomical graph.
Based on the mesh convolution implementation of the adaptive scale size, the dependence of the convolution function on the visibility density degree 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 explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
Claims (1)
1. A fast mapping method for sparse interferometric arrays, comprising: the method comprises the following steps:
s1: determining a visibility density degree index sigma; σ is defined as the number of visibility data per unit area, the visibility is denser the larger σ, and the visibility is sparser the smaller σ;
s2: defining the relation between sigma and the grid convolution function; when sigma is known, a grid convolution function with a specified scale size can be determined;
s3: a grid convolution function of predefined sigma; in the process of gridding algorithm, the calculated amount is
M is the number of the visibility data, and C is the size of a support set of a convolution kernel function; predefining a relation between sigma and a grid convolution function and the grid convolution function;
s4: carrying out self-adaptive grid convolution operation; carrying out convolution operation on the sampled visibility, selecting the size of a self-adaptive convolution kernel, then sampling by using a convolution function, and discretizing the non-uniform visibility data to regular lattice points;
s5: the IFFT maps the grid point visibility; and performing IFFT on the visibility data on the grid points to obtain an astronomical graph.
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