Frequency domain based image super-resolution reconstruction method and device

Abstract

The application discloses a kind of based on frequency domain's image super-resolution reconstruction method and equipment, method includes: the focal spot of ray source is discretized into multiple virtual sub-focal points;Control the ray source each projection angle under the emission ray to measured object, obtain the angle projection data corresponding to each projection angle;Based on the system parameters of each virtual sub-focal point and each discrete frequency point, determine the frequency domain system matrix for angle projection data frequency domain conversion;Based on the angle projection data corresponding to each projection angle, determine the angle projection frequency domain vector of the angle projection data corresponding to each projection angle, based on frequency domain system matrix, to frequency domain vector conversion, obtain the central projection frequency domain vector corresponding to each projection angle corresponding to each projection angle;To the central projection frequency domain vector corresponding to each projection angle corresponding to each projection angle, obtain the central enhanced projection data corresponding to each projection angle;Based on the central enhanced projection data corresponding to each projection angle, obtain the reconstruction image of measured object.

Description

Technical Field

[0001] This invention relates to the field of computer tomography, and in particular to a frequency domain-based image super-resolution reconstruction method and computing device. Background Technology

[0002] In X-ray CT imaging, the finite size of the X-ray focal spot is one of the main factors leading to blurred projection data and reduced image spatial resolution. In actual CT systems, the focal spot typically has a certain geometric size (e.g., on the order of millimeters). Therefore, rays emitted from different positions at the focal spot pass through the object along adjacent paths and are projected onto different positions on the detector, resulting in the attenuation information of multiple paths being superimposed in the projection data. This superposition effect forms a penumbra blurring area at the object's edge, thereby reducing the system's geometric resolution. This blurring effect manifests as blurred edges and loss of detail in the reconstructed image, limiting the application of CT in fields such as fine structure detection and material characterization.

[0003] To address this problem, existing solutions mainly fall into two categories: hardware improvements and software algorithms. Hardware improvements, such as micro-focal source design, can reduce penumbra blur, but they are costly and difficult to widely implement. In terms of software algorithms, traditional deconvolution methods are sensitive to the a priori value of the point spread function, easily amplifying noise and producing artifacts. Existing methods mostly operate in the spatial domain, failing to fully utilize the low-pass filtering characteristics of focus blur in the frequency domain, thus resulting in poor image reconstruction quality. Summary of the Invention

[0004] To address the existing technical problems, this invention provides a frequency domain-based image super-resolution reconstruction method, computer program product, and computing device, which can improve the spatial resolution and edge sharpness of CT images, achieving stable, efficient, and high-quality imaging.

[0005] Firstly, a frequency domain-based image super-resolution reconstruction method is provided, comprising: discretizing the focal spot of an X-ray source into multiple virtual sub-foci and determining the system parameters of each virtual sub-foci; controlling the X-ray source to emit X-rays at various projection angles onto the object under test, and acquiring projection data at each projection angle through a detector to obtain angular projection data corresponding to each projection angle; acquiring each discrete frequency point for performing frequency domain transformation on the angular projection data; determining the frequency domain system matrix for performing frequency domain transformation on the angular projection data based on the system parameters of each virtual sub-foci and each discrete frequency point; determining the angular projection frequency domain vector of the angular projection data corresponding to each projection angle based on the angular projection data corresponding to each projection angle, and transforming the frequency domain vector based on the frequency domain system matrix to obtain the central projection frequency domain vector corresponding to each projection angle at the central virtual sub-foci; enhancing the central projection frequency domain vector corresponding to each projection angle to obtain the central enhanced projection data corresponding to each projection angle; and executing an image reconstruction algorithm based on the central enhanced projection data corresponding to each projection angle to obtain a reconstructed image of the object under test.

[0006] In a second aspect, a computer program product is provided, comprising a computer program, characterized in that, when executed by a processor, the computer program implements the frequency domain-based image super-resolution reconstruction method of the first aspect of this application.

[0007] Thirdly, a computing device is provided, characterized in that it includes a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the frequency domain-based image super-resolution reconstruction method of the first aspect of this application.

[0008] This application discretizes the focal spot of the X-ray source into virtual sub-foci and constructs a frequency domain system matrix, which can accurately correct the geometric blur of the focal spot from the physical model and obtain a high-resolution center projection frequency domain vector of an approximately ideal point source. Combined with regularized inversion and smoothing high-frequency enhancement filtering, it can effectively suppress noise and ringing artifacts while restoring details. The entire process processes each projection angle independently and can be computed in parallel. The frequency domain system matrix can be pre-constructed. Finally, the enhanced projection is input into the standard reconstruction algorithm, which can significantly improve the spatial resolution and edge sharpness of CT images and achieve stable, efficient, and high-quality imaging. Attached Figure Description

[0009] Figure 1 This is an application environment diagram of a frequency domain-based image super-resolution reconstruction method in one embodiment; Figure 2 This is a flowchart of a frequency domain-based image super-resolution reconstruction method in one embodiment; Figure 3 This is a schematic diagram illustrating how the focal spot of an X-ray source is discretized into multiple virtual sub-foci in one embodiment. Figure 4 This is a schematic diagram of a frequency domain-based image super-resolution reconstruction device in one embodiment; Figure 5 This is a schematic diagram of a computing device in one embodiment. Detailed Implementation

[0010] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0011] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0012] In the following description, the expression “some embodiments” refers to a subset of all possible embodiments. However, it should be understood that “some embodiments” can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0013] See Figure 1 This diagram illustrates the application environment of a frequency-domain-based image super-resolution reconstruction method in one embodiment. The frequency-domain-based image super-resolution reconstruction method is applied in a computing device 10, which can acquire angular projection data at various projection angles. This angular projection data can be obtained through a detection device. A radiation source in the detection device rotates around the object under test, acquiring angular projection data of the object from different angles. This projection data is then used to reconstruct a cross-sectional image of the scanned area. The acquisition of angular projection data involves the attenuation of the radiation source; tissues of different densities absorb radiation to varying degrees, and this difference is used to distinguish different tissue structures. The computing device 10 can reconstruct the angular projection data based on the frequency-domain-based image super-resolution reconstruction method to obtain a super-resolution image corresponding to the object under test.

[0014] Please see Figure 2 This is a flowchart of a frequency-domain-based image super-resolution reconstruction method provided in an embodiment of this application. The frequency-domain-based image super-resolution reconstruction method is applied in a computing device and includes the following steps: S11. Discretize the focal spot of the X-ray source into multiple virtual sub-foci and determine the system parameters of each virtual sub-foci.

[0015] In this embodiment, discretizing the focal spot of the X-ray source into multiple virtual sub-foci refers to approximating the actual X-ray source focal spot with a certain spatial size—that is, the region where the electron beam bombards the anode target to generate X-rays—as a set of several independent and spatially separated ideal point sources in the physical modeling of X-ray or CT imaging systems. Each point source is called a virtual sub-foci, and its intensity distribution corresponds to the intensity distribution of the original focal spot. Through this discretization, the blurred projection effect produced by the originally continuous and extended focal spot can be decomposed into a weighted superposition of the sharp projections produced by multiple ideal point sources, thereby establishing an accurate mathematical model of the influence of a finite-sized focal spot on image quality in the frequency or spatial domain. This method is an important technique for studying the geometry and intensity distribution of the focal spot and its influence on the spatial resolution and artifacts (such as geometric blur) of CT images, and is often used in processes such as system matrix construction, iterative reconstruction, projection simulation, or resolution correction. Figure 3 As shown, Figure 3 This is a schematic diagram of discretizing the focal spot of an X-ray source into multiple virtual sub-foci in one embodiment, with the focal spot discretized into multiple virtual sub-foci along the discretization direction.

[0016] The system parameters of each virtual subfocus are used to describe the intensity, geometric offset, and resulting frequency domain scaling and translation effects of each subfocus relative to the central virtual subfocus.

[0017] S12. Control the X-ray source to emit X-rays to the object under test at each projection angle, and obtain the projection data at each projection angle through the detector to obtain the angle projection data at each projection angle.

[0018] The object to be tested is fixed on the rotating stage of the CT scanning system, and its position is adjusted to be centered in the scanning field of view. Appropriate X-ray tube voltage and current are set according to the material and size of the object. Scanning geometry parameters are set according to actual scanning requirements. The scan employs continuous rotation, acquiring projection data at certain angular intervals within a 360° range. At each projection angle, the detector records the attenuation intensity value of the X-rays after passing through the object, and after logarithmic transformation, the angular projection data for each projection angle is obtained. The angular projection data for each projection angle is a row of data from a two-dimensional detector. The angular projection data for all projection angles constitute a two-dimensional matrix, thus obtaining the complete projection data. The row index of the blurred projection image corresponds to the detector unit, and the column index corresponds to the projection angle. This blurred projection image is the original projection data including the focal blur effect. The CT scanning system includes a radiation source, a turntable, and a detector. The object to be tested is placed on the turntable, with the rotation center of the turntable aligned with the reconstruction origin. The radiation source and detector are fixed on both sides, with the central ray passing through the rotation center. For each projection angle, the radiation source emits X-rays, which pass through the object and are projected onto the detector. The turntable rotates to the next angle, and the data acquisition is repeated until a 180-degree or 360-degree range is covered. Using the projection data from all angles, algorithms such as filtered backprojection and iterative reconstruction are used to calculate the reconstructed image of the object's internal attenuation coefficient.

[0019] S13. Obtain the discrete frequency points of the angle projection data to perform frequency domain transformation.

[0020] In this embodiment, obtaining the discrete frequency points for performing frequency domain transformation on the angle projection data means converting the projection data collected at a projection angle to the frequency domain through Fourier transform, thereby obtaining a set of discrete frequency points and complex values ​​at each frequency point. These discrete frequency points are the basis for subsequent frequency domain filtering, system matrix construction, regularization solution, and other operations.

[0021] S14. Based on the system parameters of each virtual subfoci and each discrete frequency point, determine the frequency domain system matrix for frequency domain transformation of the angle projection data.

[0022] In this embodiment, the frequency domain system matrix is ​​constructed by performing frequency scaling, phase shifting, and cubic Lagrange interpolation on each virtual subfoci, followed by weighted summation. The frequency domain system matrix establishes a linear relationship between the central projected frequency domain vector corresponding to the central virtual subfoci and the angular projected data, and is the core of subsequent frequency domain correction.

[0023] S15. Based on the angle projection data corresponding to each projection angle, determine the angle projection frequency domain vector of the angle projection data corresponding to each projection angle. Based on the frequency domain system matrix, transform the frequency domain vector to obtain the center projection frequency domain vector corresponding to each projection angle at the center virtual sub-foci.

[0024] In this embodiment, the central virtual subfocus refers to the virtual subfocus located at the center among multiple discretized virtual subfocuses. The central projection frequency vector represents the frequency domain vector of the projection data corresponding to the central virtual subfocus.

[0025] For each projection angle, a Discrete Fourier Transform (DFT) is performed on the projection sequence for each angle (using an algorithm such as Fast Fourier Transform), followed by a frequency shift operation. This transformation converts the original angle projection data into a set of complex frequency domain values, each corresponding to a specific spatial frequency. Simultaneously, the specific frequency value of each discrete frequency point can be determined by the detector's sampling interval and the number of sampling points. Arranging these complex values ​​at discrete frequency points in sequence yields the angle projection frequency domain vector for that projection angle. This process is repeated for all projection angles, generating a corresponding frequency domain vector for each angle, which can then be used for subsequent frequency domain correction or reconstruction.

[0026] After obtaining the angular projection data for each projection angle, the angular projection data is converted into the frequency domain representation corresponding to the ideal central virtual subfoci. The core of this conversion is the frequency domain system matrix, which has been pre-constructed using the geometric parameters, intensity weights, and frequency interpolation coefficients of the virtual subfoci, establishing a linear relationship between the spectrum of the angular projection data and the spectrum of the projection data corresponding to the central virtual subfoci. The central projection frequency domain vector is a set of frequency domain representations: each projection angle corresponds to a central projection frequency domain vector, and the elements in each vector represent complex amplitudes at different spatial frequencies. These data can then be transformed back to the spatial domain using inverse Fourier transform and combined with inverse frequency shifting to obtain clear projection images without focal spot blur at each projection angle, providing high-quality input for subsequent filtered backprojection reconstruction.

[0027] S16. Perform image enhancement on the center projection frequency domain vector corresponding to each projection angle to obtain the center enhanced projection data corresponding to each projection angle.

[0028] In this embodiment, the center-enhanced projection data is the projection image obtained by applying a high-frequency enhancement filter to the center projection frequency domain vector at each projection angle and then returning it to the spatial domain through inverse Fourier transform.

[0029] S17. Based on the center-enhanced projection data corresponding to each projection angle, execute the image reconstruction algorithm to obtain the reconstructed image of the object under test.

[0030] By discretizing the focal spot into multiple virtual sub-foci and accurately measuring the intensity, position, frequency scaling, and translation parameters of each sub-foci, a frequency domain system matrix can be constructed to represent the projection from an ideal point source to the actual blurred projection. This frequency domain system matrix is ​​then used to inversely transform the frequency domain vector of the measured projection, recovering the projection spectrum of the central virtual sub-foci. This process physically corrects the blurring caused by the focal spot size, resulting in a reconstructed image with resolution approaching that of an ideal point source, which is particularly beneficial for detecting minute structures or high-contrast edges.

[0031] After obtaining the center projection frequency domain vector, further image enhancement can compensate for high-frequency attenuation caused by detector pixels and reconstruction algorithms, resulting in sharper edges. Simultaneously, since the entire transformation is based on a regularized least squares framework, implicitly included in the solution of the frequency domain system matrix, it can enhance high frequencies while reducing amplified noise and ringing artifacts. Compared to directly performing spatial deconvolution on the projection, the frequency domain matrix transformation and enhancement strategy is more stable, recovering true high-frequency information while controlling noise levels.

[0032] In the above embodiments, by discretizing the focal spot of the X-ray source into virtual sub-foci and constructing a frequency domain system matrix, the geometric blur of the focal spot can be accurately corrected from the physical model, and a high-resolution center projection frequency domain vector of an approximately ideal point source can be obtained. Combined with regularized inversion and smoothing high-frequency enhancement filtering, noise and ringing artifacts are effectively suppressed while restoring details. The entire process processes each projection angle independently and can be computed in parallel. The frequency domain system matrix can be pre-constructed. Finally, the enhanced projection is input into the standard reconstruction algorithm, which can significantly improve the spatial resolution and edge sharpness of CT images, and achieve stable, efficient, and high-quality imaging.

[0033] In some embodiments, determining the system parameters for each virtual subfocus includes: Obtain the intensity weight of each virtual sub-focus; Obtain the scaling factor for each virtual sub-focus; In the detector's coordinate system, obtain the first offset of each virtual subfocus relative to the central virtual subfocus.

[0034] In this embodiment, the focal size of the X-ray source focal spot is expressed as... mm, discretizing the focal spot at equal intervals into A virtual sub-focus. Because at the projection angle... At that time, the detector coordinates The corresponding projection data is It can be modeled as each virtual sub-foci at a projection angle of At that time, the detector coordinates The weighted sum of the corresponding projections yields the projection model based on virtual sub-foci, i.e. in Indicates the first The intensity weight of each virtual subfocus. This indicates that at the projection angle is At that time, the detector coordinates At that time, the first Projection data corresponding to each virtual subfocus Here, the intensity distribution map of the X-ray source can be measured using the pinhole imaging method, thereby obtaining... . , Indicates the first The incident intensity of the X-ray source at each virtual subfocus is determined. To recover the projection of the central virtual subfocus from the blurred projection, it is necessary to accurately characterize the mathematical relationship between the projections of each virtual subfocus and the projection of the central virtual subfocus, thereby obtaining the mathematical relationship between the blurred projection and the projection of the central virtual subfocus. This application establishes an analytical model of this relationship in the frequency domain based on equidistant fan-beam CT imaging geometry.

[0035] Consider the simplified relationship in the parallel beam case. The projection of each virtual subfocus can be regarded as a translation of the projection of the central virtual subfocus along a direction perpendicular to the projection direction. In parallel beam geometry, the translation of the source point is equivalent to the translation of the projection onto the detector. Therefore, this translation relationship can be used to simplify the above projection model based on virtual subfocuses, resulting in the following: In an equidistant sector, the... The first mapping relationship between the projections of each virtual subfoci and the projection of the central virtual subfoci, after performing a Fourier transform and Taylor expansion on this first mapping relationship, yields a second mapping relationship on the frequency spectrum, namely: at the projection angle Next, the A virtual subfoci at discrete frequency points Projection on This can be represented as the central virtual subfoci at discrete frequency points. Upward projection The formula for the second mapping relationship, based on the translation and weighting, is as follows: .

[0036] in, Indicates the first The scaling factor of the virtual sub-focus, the first The scaling factor of the virtual subfocus represents the first virtual subfocus. The scaling of the projected spectrum of each virtual subfocus relative to the projected spectrum of the central virtual subfocus on the frequency axis. Indicates the first The offset of the projection of the first virtual subfocus relative to the projection of the central virtual subfocus in the detector coordinate system, i.e., the offset of the projection of the first virtual subfocus relative to the projection of the central virtual subfocus in the detector coordinate system. The first offset corresponding to each virtual sub-focus. The second mapping relationship gives the first... The approximate relationship between the projected frequency domain vectors of each virtual subfocus and the projected frequency domain vector of the central virtual subfocus after frequency scaling.

[0037] Optionally, the scaling factors for obtaining each virtual sub-focus include: Obtain the second offset of each virtual sub-foci relative to the central virtual sub-foci in the discretization direction; Determine the first distance from the central virtual subfoci to the center of rotation; Based on the first distance and the second offset corresponding to each virtual sub-foci, determine the scaling factor corresponding to each virtual sub-foci.

[0038] Optionally, obtaining the first offset of each virtual sub-focus relative to the central virtual sub-focus includes: Determine the second distance from the central virtual subfocal point to the plane of the detector; The first offset of each virtual sub-foci is determined based on the first distance, the second distance, and the second offset corresponding to each virtual sub-foci.

[0039] In this embodiment, , ,in, Indicates the first The second offset corresponding to each virtual sub-focus This represents the first distance from the central virtual subfocus to the center of rotation. Indicates the second distance.

[0040] In some embodiments, determining the frequency domain system matrix for frequency domain transformation of the angle projection data based on the system parameters of each virtual subfoci and each discrete frequency point includes: For the matrix elements in the frequency domain system matrix ,in In the frequency domain system matrix, the first... The row frequency index and the first The value at the position of the column frequency index, The calculation process includes: For the The virtual subfocus is determined. The virtual subfocus is at the first The discrete frequency point corresponding to each row frequency index Frequency scaling factor at that location; Based on the frequency scaling factor, the frequency interval in which the frequency scaling factor lies at each discrete frequency point is determined, and the left boundary index of the frequency interval is determined. Based on the left boundary index, multiple target frequency points adjacent to the frequency scaling factor are determined. Based on these multiple target frequency points and the column frequency index... Determine the first Interpolation coefficients corresponding to each virtual subfoci; Based on the The first offset corresponding to the first virtual subfocus is used to determine the first... Phase factors corresponding to each virtual subfoci; The first The intensity weight, scaling factor, phase factor, and interpolation coefficient corresponding to each virtual subfoci are multiplied together to determine the first virtual subfoci. Virtual subfocus pairs of matrix elements The contribution value is determined by iterating through all virtual subfoci and identifying the matrix elements of each virtual subfoci. The contribution value of each virtual subfocus pair matrix element The contribution values ​​are accumulated to obtain the matrix elements. The value; By sequentially traversing the column frequency indices and row frequency indices in the frequency domain system matrix, the value of each matrix element in the frequency domain system matrix is ​​determined.

[0041] In this embodiment, in actual CT imaging, since the X-ray focus has a finite size, the projection data acquired by the detector at the projection angle is a weighted superposition of multiple virtual sub-focus projections, such as the first mapping relationship. A Fourier transform is performed on the first mapping relationship. Combining the first mapping relationship after the Fourier transform with the second mapping relationship, an expression for the angle projection data and the projection of the central virtual sub-focus, scaled by a frequency scale in the frequency domain, is obtained, i.e., the third mapping relationship. in, This represents frequency domain data under a projection angle. This represents the center frequency domain data corresponding to the projection angle at the center virtual subfocus. The above equation describes the ambiguity effect caused by finite focal points as a scaling, translation, and weighted combination of the spectrum of the center virtual subfocus, laying the theoretical foundation for subsequently recovering the projection of the center virtual subfocus by solving a linear system. To recover the projection of the center virtual subfocus from the ambiguity projection, the mapping relationship in the third equation must be transformed into a relationship expression between the frequency domain vector corresponding to the ambiguity projection and the frequency domain vector corresponding to the projection of the center virtual subfocus.

[0042] First, the frequency domain relationship represented by the third mapping relationship is discretized to achieve numerical calculation. This is based on the total number of detector elements. Multiple discrete frequency points were obtained. Indicates the first discrete frequency points, among which The maximum value is For each discrete frequency point , need to This can be represented as a weighted sum of the projections of the central virtual subfoci onto different frequency points. Because... It is generally not equal to any predefined discrete frequency point, so cubic Lagrange interpolation is used, using four adjacent grid points. To approximate Finally, we can obtain the angle projection frequency domain vector of the angle projection data corresponding to a projection angle and the center projection frequency domain vector corresponding to the projection angle at the center virtual subfoci.

[0043] in It is the left boundary index, which makes index, interpolation coefficient Calculated using the Lagrange basis function. The above describes the value of the central virtual subfocus projection after frequency scaling in the frequency domain. This can be represented as a weighted sum of the projections of the central virtual subfoci onto different frequency points. Wherein... Indicates the first Individual row frequency index. Indicates the first A virtual subfoci at discrete frequency points The corresponding phase factor, Indicates the first The virtual subfocus is at the first The discrete frequency point corresponding to each row frequency index Frequency scaling factor at that location. Indicates the first A virtual subfoci at discrete frequency points The interpolation coefficients at that location. Represents the frequency domain vector of angular projection in The value at that location, The center projection frequency domain vector represents the first... discrete frequency points The value at that location. Indicates the first A virtual subfoci at discrete frequency points The corresponding left boundary index.

[0044] The above can be written in matrix form as follows: , The frequency domain vector representing the angle projection data corresponding to the projection angle. The central projection frequency domain vector corresponding to the projection angle at the central virtual subfoci. This is the frequency domain system matrix. Therefore, the matrix elements in the frequency domain system matrix... Due to discrete frequency points Only with a finite number of discrete frequency points Relevant, therefore It is a sparse matrix, suitable for efficient storage and computation. Traverse sequentially. and Determine the value of each matrix element in the frequency domain system matrix.

[0045] In the above embodiments, the actual finite-size focal spot is decomposed into multiple virtual sub-foci, and intensity weights, frequency scaling factors, and phase shifts are introduced respectively. This accurately describes the modulation effect of focal spot geometry, intensity distribution, and offset on the projected spectrum, improving the forward simulation accuracy of fuzzy projection from a physical mechanism perspective. The entire mapping process is completed in the Fourier domain, utilizing the linearity of the frequency domain and can be implemented through Fast Fourier Transform. Cubic Lagrange interpolation is used to map the scaled non-grid frequency points to a discrete frequency grid, avoiding the step error introduced by simple nearest neighbor interpolation. At the same time, the smoothness and continuity of spectrum resampling are ensured through four adjacent nodes, reducing discretization artifacts.

[0046] In some embodiments, based on the frequency domain system matrix, the frequency domain vector is transformed to obtain the central projection frequency domain vector corresponding to each projection angle at the central virtual subfoci, including: Perform the conjugate transpose on the frequency domain system matrix to determine the conjugate matrix of the frequency domain system matrix; Determine the diagonal elements of the matrix obtained by multiplying the frequency domain system matrix and the conjugate matrix, and generate a diagonal preprocessing matrix based on the diagonal elements; For a given projection angle, an objective function is constructed based on the frequency domain system matrix, the diagonal preprocessing matrix, and the angle projection frequency domain vector. Based on the objective function, the least squares iterative calculation is performed to determine the center projection frequency domain vector.

[0047] In this embodiment, due to It is an ill-conditioned equation, so a regularization term needs to be introduced. Based on the regularization term, a preprocessing LSQR algorithm is used to construct a diagonal preprocessing matrix. Then the objective function ,in , The LSQR method is applied iteratively to solve the problem. The center projection frequency domain vector is . It is the conjugate matrix of the frequency domain system matrix.

[0048] By constructing a diagonal preprocessing matrix and transforming the frequency domain system matrix, the condition number of the objective function can be significantly improved, thereby accelerating the convergence speed of the least squares iteration. Simultaneously, the sparsity of the frequency domain system matrix is ​​fully utilized; based on the diagonal preprocessing matrix, it only relies on the diagonal elements of the frequency domain system matrix, resulting in simple computation and extremely low storage overhead. Combined with the LSQR algorithm and regularization parameters, noise amplification can be effectively suppressed, balancing resolution and stability. Therefore, this method significantly improves computational efficiency and robustness against ill-conditioned problems while ensuring reconstruction accuracy.

[0049] In some embodiments, enhancing the center projection frequency domain vector corresponding to each projection angle to obtain center-enhanced projection data corresponding to each projection angle includes: For a projection angle, obtain the target frequency domain projection data corresponding to the frequency points in the center projection frequency domain vector that are within the preset frequency range, and apply gain to the target frequency domain projection data to obtain frequency domain enhanced projection data. For the frequency domain enhanced projection data, perform inverse frequency shift and inverse Fourier transform in sequence, and use the real part after the inverse Fourier transform as the center enhanced projection data.

[0050] Gaining the target frequency domain projection data to obtain frequency domain enhanced projection data includes: By using the filter transfer function to gain the target frequency domain projection data, a frequency domain projection enhanced image is obtained. The expression for the filter transfer function is as follows: in Represents discrete frequency points. Indicates frequency response, Indicates the intensity factor. Indicates the cutoff frequency.

[0051] By solving ill-conditioned linear systems While the recovered center projection frequency domain vector theoretically reduces focus blur, its high-frequency components are inevitably suppressed to some extent due to the introduction of regularization parameters. To compensate for this high-frequency loss without excessively amplifying noise, a frequency domain high-frequency enhancement filter is used to filter the center projection frequency domain vector. This filter selectively enhances the energy in the mid-to-high frequency range while preserving low-frequency information.

[0052] Due to the sampling interval of the detector The highest resolvable frequency of the system, i.e., the Nyquist frequency, is determined. Any frequency component outside this range cannot be effectively resolved by the system, and its enhancement will inevitably amplify aliasing noise. Therefore, the boost range of the filter must be strictly limited within the finite bandwidth of the system. To facilitate frequency normalization and symmetrical design, a cutoff frequency is set. And the effective enhancement range of the filter is limited to This ensures that the enhanced frequency band does not exceed the Nyquist frequency. High-frequency components exhibit a gradual attenuation characteristic with increasing frequency under the imaging system and regularization constraints. To correct for high-frequency spectral components that still exist but whose amplitude is suppressed, a gain function that increases linearly with frequency is employed. This makes the enhancement proportional to the frequency, thus alleviating the high-frequency amplitude attenuation problem without introducing additional frequency components. However, a simple linear boost can cause abrupt changes at the frequency band boundaries, leading to spatial domain ringing artifacts. Therefore, a cosine term is introduced. Modulation is performed. Among them... To enhance the intensity factor, used to control the compensation amplitude. The cutoff frequency is [frequency value]. This function operates at zero frequency. and- The gain is 1 at the beginning, with a smooth rise in the mid-frequency band, and the maximum gain is at... nearby.

[0053] For each projection angle, the recovered center projection frequency domain vector is multiplied point-by-point by the filter gain to obtain the enhanced spectrum, i.e., the frequency domain enhanced projection data. Finally, after inverse frequency shifting and inverse Fourier transform, and taking the real part, the enhanced projection, i.e., the center enhanced projection data, is obtained. The above operation is repeated for all projection angles to form a high-resolution projection matrix.

[0054] Based on the center-enhanced projection data corresponding to each projection angle, an image reconstruction algorithm is executed to obtain the reconstructed image of the object under test, including: For a projection angle, perform a fast Fourier transform on the center-enhanced projection data to obtain frequency projection data; Perform a filtering operation on the frequency projection data to obtain the filtered spectrum; Perform an inverse Fourier transform on the filtered spectrum to obtain the filtered projection data; Perform geometric projection coordinate transformation on each pixel to obtain the detector coordinates of each pixel; Based on the filtered projection data and the detector coordinates of each pixel, a weighted back projection is performed to determine the back projection contribution matrix corresponding to the projection angle. The reconstructed image is obtained by summing the backprojection contribution matrices corresponding to each projection angle.

[0055] In this embodiment, after obtaining the center-enhanced projection data for each projection angle, a filtered back-projection reconstruction algorithm is executed. First, a Fast Fourier Transform (FFT) is performed on the enhanced projection sequence for each projection angle to convert the center-enhanced projection data for each projection angle to the frequency domain, obtaining the frequency projection data for each projection angle. Then, a ramp filter is applied in the frequency domain to compensate for the inherent low-frequency bias in the projection data and enhance the high-frequency components, thereby obtaining the filtered spectrum for each projection angle. After completing the frequency domain filtering, an Inverse Fourier Transform (IFT) is used to restore the data to the spatial domain, obtaining the filtered projection data for each projection angle.

[0056] Next, for each pixel in the reconstructed image, its projected coordinates on the detector are calculated based on the current projection angle and system geometric parameters. Using these coordinates, the projection value corresponding to each pixel is obtained from the filtered projection data through interpolation, and multiplied by the fan-beam geometric weighting factor to compensate for ray divergence effects. The resulting value is the backprojection contribution of that pixel at the projection angle.

[0057] Repeating the weighted backprojection operation for all pixels generates a backprojection contribution matrix corresponding to the projection angle, with the same size as the reconstructed image. Then, the backprojection contribution matrices calculated for each projection angle are summed and multiplied by a normalization coefficient to obtain the reconstructed image of the object under test. This entire process fully utilizes the efficiency of frequency domain filtering and the intuitiveness of spatial domain backprojection, achieving the conversion from high-quality enhanced projection to high-resolution tomographic images.

[0058] In another aspect, this application provides a computer program product, including a computer program that, when executed by a processor, implements the frequency domain-based image super-resolution reconstruction method of any embodiment of this application.

[0059] Among them, in the computer program product, the optional implementation form of the program module architecture of the computer program that implements each step of the target recognition method can be a frequency domain-based image super-resolution reconstruction device.

[0060] Please see Figure 4One embodiment of this application provides a frequency domain-based image super-resolution reconstruction apparatus, comprising: a determining module 41, configured to discretize the focal spot of an X-ray source into multiple virtual sub-foci and determine the system parameters of each virtual sub-foci; an acquiring module 42, configured to control the X-ray source to emit X-rays to the object under test at various projection angles, and acquire projection data at each projection angle through a detector to obtain angular projection data corresponding to each projection angle; the determining module 41 is further configured to acquire each discrete frequency point for performing frequency domain transformation on the angular projection data; the determining module 41 is further configured to determine the angular projection data based on the system parameters of each virtual sub-foci and each discrete frequency point. The frequency domain system matrix is ​​used for frequency domain transformation; the determination module 41 is also used to determine the angle projection frequency domain vector of the angle projection data corresponding to each projection angle based on the angle projection data corresponding to each projection angle, and transform the frequency domain vector based on the frequency domain system matrix to obtain the center projection frequency domain vector corresponding to each projection angle at the center virtual sub-foci; the enhancement module 43 is used to enhance the center projection frequency domain vector corresponding to each projection angle to obtain the center enhanced projection data corresponding to each projection angle; the reconstruction module 44 is used to execute the image reconstruction algorithm based on the center enhanced projection data corresponding to each projection angle to obtain the reconstructed image of the object under test.

[0061] Please see Figure 5 In another aspect of this application, a computing device 10 is also provided, including a memory 3011 and a processor 3012. The memory 3011 stores a computer program, and when the computer program is executed by the processor, the processor 3012 performs the steps of the frequency domain-based image super-resolution reconstruction method provided in any of the above embodiments of this application. The computing device 10 can be (e.g., a desktop computer, laptop computer, tablet computer, handheld computer, smart speaker, server, etc.), a mobile phone (e.g., a smartphone, cordless phone, etc.), a wearable device (e.g., a pair of smart glasses or a smartwatch), or a similar device.

[0062] The processor 3012 is the control center, connecting various parts of the computer device via various interfaces and lines. It executes software programs and / or modules stored in the memory 3011, and calls data stored in the memory 3011 to perform various functions and process data. Optionally, the processor 3012 may include one or more processing cores; preferably, the processor 3012 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user page, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may not be integrated into the processor 3012.

[0063] The memory 3011 can be used to store software programs and modules. The processor 3012 executes various functional applications and data processing by running the software programs and modules stored in the memory 3011. The memory 3011 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for at least one function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the computer device, etc. In addition, the memory 3011 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device. Accordingly, the memory 3011 may also include a memory controller to provide the processor 3012 with access to the memory 3011.

[0064] In another aspect, this application also provides a storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the frequency domain-based image super-resolution reconstruction method provided in any of the above embodiments of this application.

[0065] Those skilled in the art will understand that all or part of the processes in the methods provided in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0066] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A frequency domain-based image super-resolution reconstruction method, characterized in that, include: The focal spot of the X-ray source is discretized into multiple virtual sub-foci, and the system parameters of each virtual sub-foci are determined, including: obtaining the intensity weight of each virtual sub-foci; obtaining the scaling factor of each virtual sub-foci; and obtaining the first offset of each virtual sub-foci relative to the central virtual sub-foci in the coordinate system of the detector. The X-ray source is controlled to emit X-rays to the object under test at various projection angles, and the projection data at each projection angle is obtained by the detector to obtain the angle projection data corresponding to each projection angle. Obtain the discrete frequency points from which the frequency domain transformation is performed on the angle projection data; Based on the system parameters of each virtual subfoci and each discrete frequency point, determine the frequency domain system matrix for frequency domain transformation of the angle projection data, including: for the matrix elements in the frequency domain system matrix ,in Represents the first in the frequency domain system matrix The row frequency index and the first The value at the position of the column frequency index, The calculation process includes: for the first... The virtual subfocus is determined. The virtual subfocus is at the first The discrete frequency point corresponding to each row frequency index The frequency scaling factor is determined at each discrete frequency point; based on the frequency scaling factor, the frequency interval in which the frequency scaling factor is located is determined, and the left boundary index of the frequency interval is determined. According to the left boundary index, multiple target frequency points adjacent to the frequency scaling factor are determined, and based on the multiple target frequency points and the column frequency index... Determine the first A virtual subfoci at discrete frequency points The interpolation coefficients at the corresponding position; based on the first The first offset corresponding to the first virtual sub-focus is used to determine the first... A virtual subfoci at discrete frequency points The corresponding phase factor at the position; the first The intensity weight, scaling factor, phase factor, and interpolation coefficient corresponding to each virtual subfocus are multiplied together to determine the first virtual subfocus. A virtual subfocus pair of the matrix elements The contribution value is determined by iterating through all virtual sub-foci and determining the relationship between each virtual sub-foci and the matrix elements. The contribution value of each virtual sub-focus is used to determine the matrix elements. The contribution values ​​are summed to obtain the matrix elements. The value of each element in the frequency domain system matrix is ​​determined by sequentially traversing the row frequency index and the column frequency index. Based on the angle projection data corresponding to each projection angle, the angle projection frequency domain vector of the angle projection data corresponding to each projection angle is determined. Based on the frequency domain system matrix, the frequency domain vector is transformed to obtain the center projection frequency domain vector corresponding to each projection angle at the center virtual sub-foci. The center projection frequency domain vector corresponding to each projection angle is enhanced to obtain the center enhanced projection data corresponding to each projection angle. Based on the center-enhanced projection data corresponding to each projection angle, an image reconstruction algorithm is executed to obtain the reconstructed image of the object under test.

2. The image super-resolution reconstruction method based on the frequency domain as described in claim 1, characterized in that, The scaling factor for obtaining each of the virtual sub-focuses includes: Obtain the second offset of each of the virtual sub-foci relative to the central virtual sub-foci in the discretization direction; Determine the first distance from the central virtual sub-foci to the center of rotation; Based on the first distance and the second offset corresponding to each of the virtual sub-foci, the scaling factor corresponding to each of the virtual sub-foci is determined.

3. The image super-resolution reconstruction method based on the frequency domain as described in claim 2, characterized in that, The step of obtaining the first offset of each of the virtual sub-foci relative to the central virtual sub-foci includes: Determine a second distance from the central virtual subfocal point to the plane of the detector; The first offset of each virtual sub-focus is determined based on the first distance, the second distance, and the second offset corresponding to each virtual sub-focus.

4. The image super-resolution reconstruction method based on the frequency domain as described in claim 1, characterized in that, The transformation of the frequency domain vector based on the frequency domain system matrix to obtain the central projection frequency domain vector corresponding to each projection angle at the central virtual sub-foci includes: Perform a conjugate transpose on the frequency domain system matrix to determine the conjugate matrix of the frequency domain system matrix; Determine the diagonal elements of the matrix obtained by multiplying the frequency domain system matrix and the conjugate matrix, and generate a diagonal preprocessing matrix based on the diagonal elements; For a given projection angle, an objective function is constructed based on the frequency domain system matrix, the diagonal preprocessing matrix, and the angle projection frequency domain vector. Based on the objective function, the least squares iterative calculation is performed to determine the center projection frequency domain vector.

5. The image super-resolution reconstruction method based on the frequency domain as described in claim 1, characterized in that, The step of enhancing the center projection frequency domain vector corresponding to each projection angle to obtain the center enhanced projection data corresponding to each projection angle includes: For a given projection angle, obtain the target frequency domain projection data corresponding to the frequency point in the center projection frequency domain vector that is within a preset frequency range, and apply gain to the target frequency domain projection data to obtain frequency domain enhanced projection data. For the frequency domain enhanced projection data, inverse frequency shift and inverse Fourier transform are performed sequentially, and the real part after the inverse Fourier transform is used as the center enhanced projection data.

6. The image super-resolution reconstruction method based on the frequency domain as described in claim 5, characterized in that, The step of gaining the target frequency domain projection data to obtain frequency domain enhanced projection data includes: The target frequency domain projection data is amplified using a filter transfer function to obtain a frequency domain projection enhanced image. The expression for the filter transfer function is as follows: in Represents discrete frequency points. Indicates frequency response, Indicates the intensity factor. Indicates the cutoff frequency.

7. The image super-resolution reconstruction method based on the frequency domain as described in claim 5, characterized in that, The process of executing an image reconstruction algorithm based on the center-enhanced projection data corresponding to each projection angle to obtain a reconstructed image of the object under test includes: For one of the projection angles, perform a fast Fourier transform on the center-enhanced projection data to obtain frequency projection data; The frequency projection data is filtered to obtain the filtered spectrum. Perform an inverse Fourier transform on the filtered spectrum to obtain the filtered projection data; Perform geometric projection coordinate transformation on each pixel to obtain the projected coordinates of each pixel on the detector; Based on the filtered projection data and the projection coordinates of each pixel, a weighted back projection is performed to determine the back projection contribution matrix corresponding to the projection angle. The reconstructed image is obtained by summing the backprojection contribution matrices corresponding to each of the projection angles.

8. A computing device, characterized in that, It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the frequency domain-based image super-resolution reconstruction method as described in any one of claims 1 to 7.

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