Iterative denoising method for infrared astronomical image based on linearization of collaborative filtering operator

Abstract

This invention discloses an iterative denoising method for infrared astronomical images based on linearization of a collaborative filtering operator. The method includes: acquiring the original observation image from a ground-based infrared telescope; evaluating the background noise level and performing a variance-stabilized transform to obtain a transform domain image; performing coarse hard thresholding filtering on the transform domain image to generate a guide map; performing global block matching on the guide map to obtain a locked index table; constructing a linear collaborative filtering operator based on the locked index table; in each iteration, first performing signal enhancement and amplitude modulation to obtain an enhanced input signal; then calling the linear collaborative filtering operator to perform a single linear filtering operation and calculating the filtered output; next, updating the estimated value based on the residual; finally, after K iterations, obtaining a converged image; and using an optimal algebraic inverse transform to correct the converged image and output the restored image. This invention effectively solves the problem of erroneously deleting faint star points in traditional algorithms and improves the limiting magnitude detection capability of observation systems.

Description

Technical Field

[0001] This invention belongs to the field of astronomical image processing technology, and in particular relates to an iterative denoising method for infrared astronomical images based on linearization of collaborative filtering operators. Background Technology

[0002] Infrared astronomical observation is a crucial tool for exploring cutting-edge scientific questions such as the early universe, brown dwarfs, and the formation of exoplanets. However, compared to the optical band, the imaging quality in the infrared band is subject to more severe physical limitations. The main challenge stems from the thermal glow of OH radicals and water molecules in Earth's atmosphere, where the background photon flux often exceeds that of the target object's signal by several orders of magnitude. This extreme observational environment results in raw image data exhibiting significant Poisson-Gaussian mixed noise characteristics: the photon counting process of the signal follows a Poisson distribution, while the detector's readout circuitry introduces additive Gaussian white noise.

[0003] For the restoration of such degraded images, classical linear filtering methods (such as Gaussian filtering and Wiener filtering), while computationally simple, inevitably smooth high-frequency details due to their frequency domain low-pass truncation principle. This results in dense globular clusters becoming indistinguishable and distorts the photometric profiles of stars, affecting subsequent photometric accuracy. Image denoising algorithms based on sparse representation and nonlocal self-similarity have become a research hotspot. Among them, the 3D block matching collaborative filtering algorithm (BM3D) is widely recognized as one of the best denoising algorithms currently available. BM3D finds similar blocks in the image and stacks them into a 3D array, utilizing the sparsity of the 3D transform domain for collaborative filtering, effectively preserving the edge structure of the image.

[0004] However, when applying the standard BM3D algorithm directly to astronomical image restoration, there are two key technical bottlenecks that have not yet been resolved:

[0005] First, there is the instability of iterative convergence. Deep-space images often have extremely low signal-to-noise ratios (SNRs), and a single BM3D filter often cannot completely separate noise from weak signals. To improve performance, the academic community has attempted to use iterative denoising or plug-and-play prior frameworks. However, the BM3D operator is essentially a highly nonlinear adaptive filter. Its core "block matching grouping" process is extremely dependent on the content of the input image. At low SNRs, even small noise perturbations in the input image can cause drastic jumps in the search results for similar blocks. The Jacobian matrix of this nonlinear operator is unstable, leading to the inability to satisfy the convergence condition of Banach's fixed-point theorem during iteration, easily resulting in oscillations, divergence, or the introduction of new structural artifacts.

[0006] Second, the "star-eating" phenomenon of faint targets. BM3D and its variant algorithms primarily rely on hard or soft thresholding to remove noise figures. Typically, the threshold is set to about 2.7 times the noise standard deviation. In deep-sky imaging, the signal strength of many extremely faint galaxies or stars is often submerged in a noise floor. Mathematically, these sparse, weak signals are judged as noise by the thresholding operator and directly set to zero. This results in processed images with clean backgrounds but the loss of a large number of scientifically valuable extreme magnitude targets, severely limiting the telescope's survey depth and scientific output.

[0007] In summary, existing image processing techniques struggle to effectively recover weak celestial signals buried under a noisy substrate while ensuring algorithm convergence stability. Therefore, developing an iterative enhancement method based on a rigorous mathematical model, capable of locking the filter manifold and adaptively enhancing weak signals, is of significant scientific and practical value. Summary of the Invention

[0008] This invention provides an iterative denoising method for infrared astronomical images based on linearization of the collaborative filtering operator, which achieves high noise removal and weak target enhancement of infrared astronomical observation data, effectively solves the problem of erroneous deletion of faint star points by traditional algorithms, and improves the ultimate detection magnitude of the observation system.

[0009] An iterative denoising method for infrared astronomical images based on linearization of collaborative filtering operators includes the following steps:

[0010] (1) Acquire raw observation images from the ground-based infrared telescope and assess the background noise level. Then, a variance-stabilized transform is performed to obtain the transform domain image. ;

[0011] (2) For transform domain images Perform coarse hard thresholding to generate a guide graph. ; For the guide diagram A global block match is performed to obtain a locked index table. Lock-based index table Constructing linear collaborative filtering operators ;

[0012] (3) In each iteration, signal enhancement and amplitude modulation are performed first to obtain the enhanced input signal. Then call the linear collaborative filtering operator. Perform a single linear filtering operation and calculate the filtered output. Next, calculate the filtered output. The residual between the expected reinforcement input and the expected value, and adjusted by the relaxation factor. Update the estimated values; finally, after K iterations, the converged image is obtained. ;

[0013] (4) Apply the optimal inverse algebraic transform to the converged image Perform corrections and output the restored image.

[0014] Furthermore, in step (1), the noise distribution of the original observed image is asymptotically converged to a standard normal distribution through variance stabilization transformation. And assume that the noise is additive white Gaussian noise with a constant variance of 1.

[0015] In step (2), the guide diagram is... A global block match is performed to obtain a locked index table. The specific process is as follows:

[0016] For guide map For each reference block in the image, the distance between the reference block and any candidate block within the search window is calculated, and the corresponding similar block is selected based on a set matching threshold. After traversing the entire image, the coordinate sets of all reference blocks and their corresponding similar blocks are mapped to a static three-dimensional tensor index table, denoted as . .

[0017] In step (2), the linear collaborative filtering operator Used for performing a single linear filtering operation, which is defined as the input image vector. With linear operators The product of.

[0018] In step (3), the enhanced input signal is obtained. The formula is:

[0019] ;

[0020] in, Indicates the first iteration As a reinforcing factor, This is the estimated value from the previous iteration.

[0021] Enhancement factor The range of values ​​for is: .

[0022] In step (3), the relaxation factor The constraints are satisfied: .

[0023] The specific process of step (4) is as follows:

[0024] Correction is performed using the optimal inverse algebraic transform for the converged image. For each pixel value in the dataset, calculate the final output value. ;

[0025] For the calculated final output value Non-negativity constraints are applied to correct the tiny negative values ​​caused by numerical calculation errors, and the restored image is finally output.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] This invention addresses the challenges of weak star point loss and iterative divergence under low signal-to-noise ratio (SNR) conditions through operator linearization and SNR enhancement mechanisms. By constructing a globally locked linearized cooperative operator, the filtering process is transformed into linear projection, eliminating manifold jumps and artifact oscillations. Through a generalized "enhancement-operation-subtraction" iterative framework, signal amplitude modulation and residual feedback compensation are utilized to improve the effective SNR of weak targets and overcome threshold limitations. Ultimately, this invention can achieve a significant improvement in the ultimate detection magnitude. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of an iterative denoising method for infrared astronomical images based on linearization of collaborative filtering operators, according to an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram illustrating the signal enhancement principles of existing methods and the method of the present invention in embodiments of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] It should be noted that, unless otherwise specified, the features in the following embodiments and implementation methods can be combined with each other.

[0033] To address the issues of nonlocal similarity block matching failure and loss of faint star points caused by extremely low signal-to-noise ratios in astronomical imaging, this invention constructs an iterative denoising method for infrared astronomical images based on the linearization of a cooperative filtering operator. First, a globally locked three-dimensional block matching mapping relationship is constructed using the preprocessing results of the nonlocal cooperative filtering operator, degenerating the nonlinear filtering operator into an approximately linear operator. Then, a signal enhancement factor is introduced, and the local signal-to-noise ratio at the input is improved through a superposition feedback mechanism. Based on the steepest descent method, an iterative update formula is derived, and residual backfilling is used to gradually restore the smoothed high-frequency star point information. Theoretical analysis shows that this method, by adjusting the relaxation factor, can ensure that the operator spectral radius meets the contraction condition, thereby achieving stable convergence without artifacts and effectively improving the ultimate detection magnitude.

[0034] This invention provides an iterative denoising method for infrared astronomical images based on the linearization of a cooperative filtering operator, belonging to the field of astronomical image processing technology. Addressing the problems of nonlocal similarity block matching failure and loss of faint star points caused by extremely low signal-to-noise ratios in astronomical imaging, this invention constructs an enhancement-operation-subtraction iterative optimization framework. This method first utilizes the preprocessing results of a nonlocal cooperative filtering operator to construct a globally locked three-dimensional block matching mapping relationship, degenerating the nonlinear filtering operator into an approximately linear operator. Then, a signal enhancement factor is introduced, and the local signal-to-noise ratio at the input is improved through a superposition feedback mechanism. Based on the steepest descent method, an iterative update formula is derived, and residual backfilling is used to gradually restore the smoothed high-frequency star point information. Theoretical analysis shows that this method, by adjusting the relaxation factor, can ensure that the operator spectral radius meets the contraction condition, thereby achieving stable convergence without artifacts and effectively improving the ultimate detection magnitude.

[0035] like Figure 1 As shown, the present invention mainly includes the following steps:

[0036] S1. Establishment of observation model and preprocessing for variance stabilization.

[0037] First, acquire the raw observation data from the ground-based infrared telescope. Assess background noise levels Then, a variance-stabilized transform is performed on the image, and the transform domain image is output. :

[0038] ;

[0039] The noise in infrared astronomical images essentially follows a Poisson-Gaussian mixture distribution, i.e.

[0040] ;

[0041] This heteroscedasticity causes block matching based on Euclidean distance in traditional denoising algorithms to fail. Through the above transformation, the image noise distribution asymptotically converges to a standard normal distribution. It is reasonable to assume that the noise is additive white Gaussian noise with a constant variance of 1, which is crucial for the subsequent construction of linear operators. The prerequisite.

[0042] S2. The constructed linearized collaborative filtering operator.

[0043] The core objective of this step is to eliminate the highly nonlinear and computationally time-consuming "adaptive grouping" process in traditional nonlocal block matching algorithms (such as BM3D, weighted nuclear norm minimization, etc.) and construct a fixed linear projection structure for the current observed sky region.

[0044] To avoid high-noise original image Directly performing block matching results in a "noise matching noise" error; a cleaner guide map needs to be generated first. That is, for Perform a coarse hard thresholding filter:

[0045] ;

[0046] Among them, the preprocessing threshold Set as This ensures that only significant star-shaped structures are retained in the guide graph, filtering out most of the background noise. The guide graph constructs stable reference anchors within the iterative optimization framework, and all similar block searches in subsequent steps are based on this guide graph. This ensures that the block matching algorithm captures the inherent structural similarity between pixels, avoiding mismatches caused by random noise interference in low signal-to-noise ratio environments.

[0047] Set the spatial size of the reference block to The size of the non-local search window is For the image domain Each in the coordinates Centered reference block Strictly based on the guide graph Perform a similarity search instead of based on the noisy original image.

[0048] Normalized Euclidean distance is used as the metric for inter-block similarity. Reference blocks in the guidance graph are calculated. With any candidate block in the search window Distance between :

[0049] ;

[0050] in, This indicates a block extraction operation. Set the matching threshold. ,like Then the decision block For similar blocks, their coordinates are included in the group set.

[0051] After traversing the entire graph, all reference blocks are... and its corresponding set of similar block coordinates This is mapped to a static three-dimensional tensor index table, denoted as... :

[0052] ;

[0053] Index Table Once generated, it is immediately fixed. Recalculating or modifying this index table is strictly prohibited in all subsequent iterations. This means that in later steps, regardless of how pixel values ​​are updated, the index table is directly called... Once the coordinate index is obtained, no further block matching search calculations are performed; that is, the combination of blocks is forcibly fixed.

[0054] High-dimensional image data is often distributed on low-dimensional manifolds. Traditional iterative denoising methods are prone to block matching position shifts during the iteration process due to residual noise, a phenomenon known as "manifold drift." In astronomical images, this manifests as faint star points being misidentified as noise and smoothed out. This invention addresses this by locking... Mathematically, this is equivalent to freezing the topological structure of the image in the manifold space. This strategy ensures that even when dealing with regions with extremely low signal-to-noise ratios, the algorithm can still "remember" the geometric positions of faint stars and update only the pixel intensity for denoising, thus physically avoiding the problem of star loss.

[0055] Lock-based Constructing a linear collaborative filtering operator For any input image vector The processing flow of this operator is strictly defined as the product of a series of linear matrices:

[0056] ;

[0057] in, This is the output of a single linear filtering operation. For based on Block extraction and stacking matrix (sparse matrix). It is a 3D orthogonal transformation matrix that maps spatial signals to a sparse transform domain. It is a hard-threshold diagonal matrix, which is a diagonal matrix whose diagonal elements are only 0 or 1. This is a 3D inverse transformation matrix that maps the processed coefficients back to the spatial domain. For the weighted aggregation matrix, a weighted average operation is performed to project the overlapping 3D blocks back to their corresponding positions on the 2D image plane, and the normalization of the overlapping regions is processed.

[0058] The cascade of the above five steps perfectly conforms to the definition of a linear system. Let... Then the entire complex denoising process is reduced to a single matrix multiplication:

[0059] ;

[0060] Through this explicit mathematical construction, the originally non-differentiable "black box" denoiser is transformed into one with explicit spectral properties (eigenvalues). Linear operators This eliminates discontinuity and is the mathematical basis for ensuring that subsequent iterative algorithms are artifact-free and converge stably.

[0061] S3. "Enhancement-Operation-Subtraction" Iteration and Weak Target Recovery under Spectral Constraints

[0062] This step is based on the "enhancement-operation-subtraction" framework and performs K iterations. Essentially, this process is a closed-loop feedback control system that gradually strips away noise and recovers the weak star point signal from the background through multiple small "prediction-correction" updates, under the constraint of the spectral radius.

[0063] In each iteration, the algorithm first performs signal enhancement and amplitude modulation. It then uses the estimates from the previous round. Reconstruct the current input and compute the reinforcement input. :

[0064] ;

[0065] In the formula, This is noisy observation data. It is a reinforcing factor. The larger the value, the stronger the ability to extract weak targets, but the more stringent the requirements for convergence stability; the typical value range is from 0.5 to 2.0. In the first iteration, Typically initialized to At this stage, reinforcement is primarily based on noisy data. As iterations proceed, The noise gradually decreases, and the star-like structure becomes clearer.

[0066] like Figure 2 As shown in (a), existing methods typically employ hard threshold filtering. Since the amplitude of the original weak star point signal is lower than the preset hard threshold, it is regarded as noise and forcibly set to zero when passing the threshold judgment, resulting in the loss of effective targets, i.e., the "star-eating" phenomenon. Figure 2 Figure (b) illustrates the processing effect of an embodiment of the present invention, by using feedback signals Superimposed onto the input, this artificially increases the signal-to-noise ratio of the star targets, and achieves an equivalent threshold reduction effect through the superposition factor. The weak star signals, originally submerged in noise and with amplitudes below the hard threshold, are amplified, allowing them to exceed the filter's cutoff threshold after weighting and thus be effectively captured by the algorithm, solving the "star-eating" problem in traditional methods. Subsequently, the enhanced signal... To perform a globally locked linear collaborative filter, the static tensor index table generated in step S2 is called directly. and preset operators Calculate the projection output :

[0067] ;

[0068] Because the block matching relationship determined by the guide graph is strictly reused here, the filtering process completely avoids structural drift and artifact oscillation caused by iterative updates, ensuring the locking and protection of the geometric position of weak targets.

[0069] Finally, based on the steepest descent principle, residual backfilling and state update are performed, and the filtered output is calculated. The residual between the expected reinforcement input and the expected value, and adjusted by the relaxation factor. Updated estimates:

[0070] ;

[0071] in, The term within parentheses represents the relaxation factor. This is the residual term. The physical essence of this step is an energy accumulation and noise cancellation process. As iterations proceed, the energy of the star target monotonically accumulates in the residual term, while the random noise residual at the background fluctuates randomly, canceling each other out in multiple superpositions. Simultaneously, the parameters... The spectral radius constraint must be strictly met:

[0072] ;

[0073] This condition ensures that the eigenvalues ​​of the entire iterative system always lie within the unit circle, guaranteeing the numerical stability and global convergence of the algorithm when recovering the ultimate magnitude target.

[0074] S4. Precise inverse mapping of variance-stable transform and image output.

[0075] Because step S1 employs a variance-stabilized transform, its direct algebraic inverse transform is statistically biased. For high-precision astronomical photometry requirements, direct inversion can lead to a systematic underestimation of the background mean. This method uses the optimal algebraic inverse transform for correction. For the converged image... Each pixel value in Calculate the final output value :

[0076] ;

[0077] This higher-order inverse transform formula effectively compensates for the statistical bias introduced by the nonlinear transform. Compared to a simple inverse square transform, this method ensures that the background skylight values ​​after denoising remain consistent with the original image, which is crucial for subsequent astrophotometry and flux calibration.

[0078] Finally, for the calculated Apply nonnegativity constraints to correct for small negative values ​​caused by numerical calculation errors:

[0079] ;

[0080] In the formula, This refers to a high signal-to-noise ratio astronomical image that preserves the faint star structure and removes the Poisson-Gaussian mixed noise.

[0081] Based on the above method, denoising of low signal-to-noise ratio images in infrared astronomical imaging can be achieved, and the magnitude of extreme detection stars can be effectively improved.

[0082] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An iterative denoising method for infrared astronomical images based on linearization of collaborative filtering operators, characterized in that, Includes the following steps: (1) Acquire raw observation images from the ground-based infrared telescope and assess the background noise level. Then, a variance-stabilized transform is performed to obtain the transform domain image. ; (2) For transform domain images Perform coarse hard thresholding to generate a guide graph. ; For the guide diagram A global block match is performed to obtain a locked index table. Lock-based index table Constructing linear collaborative filtering operators ; (3) In each iteration, signal enhancement and amplitude modulation are performed first to obtain the enhanced input signal. ; Then call the linear collaborative filtering operator Perform a single linear filtering operation and calculate the filtered output. Next, calculate the filtered output. The residual between the expected reinforcement input and the expected value, and adjusted by the relaxation factor. Update the estimated values; finally, after K iterations, the converged image is obtained. ; (4) Apply the optimal inverse algebraic transform to the converged image Perform corrections and output the restored image.

2. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 1, characterized in that, In step (1), the noise distribution of the original observed image is asymptotically converged to the standard normal distribution through variance stabilization transformation. And assume that the noise is additive white Gaussian noise with a constant variance of 1.

3. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 1, characterized in that, In step (2), the guide diagram is... A global block match is performed to obtain a locked index table. The specific process is as follows: For guide map For each reference block in the image, the distance between the reference block and any candidate block within the search window is calculated, and the corresponding similar block is selected based on a set matching threshold. After traversing the entire image, the coordinate sets of all reference blocks and their corresponding similar blocks are mapped to a static three-dimensional tensor index table, denoted as . .

4. The iterative denoising method for infrared astronomical images based on linearization of the collaborative filtering operator according to claim 1, characterized in that, In step (2), the linear collaborative filtering operator Used for performing a single linear filtering operation, which is defined as the input image vector. With linear operators The product of.

5. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 1, characterized in that, In step (3), the enhanced input signal is obtained. The formula is: ； in, Indicates the first iteration As a reinforcing factor, This is the estimated value from the previous iteration.

6. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 5, characterized in that, Enhancement factor The range of values ​​for is: .

7. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 6, characterized in that, In step (3), the relaxation factor The constraints are satisfied: .

8. The infrared astronomical image iterative denoising method based on linearization of the collaborative filtering operator according to claim 1, characterized in that, The specific process of step (4) is as follows: Correction is performed using the optimal inverse algebraic transform for the converged image. For each pixel value in the dataset, calculate the final output value. ; For the calculated final output value Non-negativity constraints are applied to correct the tiny negative values ​​caused by numerical calculation errors, and the restored image is finally output.

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