A signal blind area completion method based on fast matrix filling

Abstract

This invention discloses a signal blind zone completion method based on fast matrix filling. The steps are as follows: setting model parameters and selecting the missing signal image to be repaired and the corresponding GIS map image; constructing an optimized model according to the set model parameters; simplifying the constructed optimized model; and quickly solving the simplified model to obtain the repaired signal image. This invention can complete the blind zone signal while preserving the correct signal values. Furthermore, this method uses a bilateral affine matrix approximation, ensuring both accuracy and speed. Even when processing large signal images, this invention maintains real-time performance and has good blind zone completion results.

Description

Technical Field

[0001] This invention belongs to the field of computer image processing technology, specifically relating to a signal blind spot completion method based on fast matrix filling. Background Technology

[0002] Signal blind spot completion is an important issue in production and daily life. In practice, due to cost considerations, signal sensors are often only deployed in certain areas of a map. Signal blind spot completion involves estimating the signal data of all points on the map based on the partial signal data measured by the signal sensors.

[0003] Currently, addressing the poor signal coverage issues arising from the typical harsh environments of dense forests and high temperatures and humidity in southwestern and southern my country, the urgent technological gap in China's emergency command and rescue information technology sector lies in how to quickly fill in missing signal images as target images. To date, no relevant or complementary technical solutions exist, either domestically or internationally, to address this problem.

[0004] In terms of signal gap filling, current technology still relies on designing theoretical models and algorithms (such as parallel scalar quantizers) for simulation verification, lacking practical testing and failing to meet the many needs of modern emergency command and communication support.

[0005] In view of this, the present invention proposes a signal blind spot completion method based on fast matrix filling, which uses the approximate form of a two-sided affine matrix. At the same time, in order to estimate the correct blind spot signal value, the confidence level is set with a simple value to achieve higher and faster signal blind spot completion calculation efficiency. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, the present invention aims to provide a signal blind spot completion method based on fast matrix filling, thereby solving the problem that the theoretical model algorithms in existing signal blind spot completion technologies lack practical testing and have poor efficiency (such as parallel scalar quantizers).

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The present invention provides a signal blind zone completion method based on fast matrix filling, comprising the following steps:

[0009] 1) Set model parameters, including: luminance bandwidth σ l Color bandwidth σ uv Spatial bandwidth σ xy And the smoothing parameter λ; and select the missing signal image G to be repaired and the corresponding GIS map image P;

[0010] 2) Construct the optimization model based on the model parameters set in step 1);

[0011] 3) Simplify the optimization model constructed in step 2);

[0012] 4) Solve the simplified model in step 3) quickly to obtain the repaired and complete signal image T.

[0013] Furthermore, the objective function of the optimal model in step 2) is as follows:

[0014]

[0015] Among them, t i Let t be the value of the blind zone signal image T at pixel i; j Let C be the value of the blind zone signal image T at pixel j; i The confidence level of the signal value at pixel i is determined as follows: if the location is a blind zone, it is considered completely unreliable and its confidence level is set to 0; otherwise, it is considered completely reliable and its confidence level is set to 1. i Let be the value of the input signal image G at pixel i; λ is an adjustable smoothing parameter; j∈Ω(i) indicates that pixel j belongs to the neighborhood of pixel i; W is the bilateral affine matrix calculated according to equation (2). The affine matrix after doubly normalizing W;

[0016]

[0017] in, Indicates the spatial location of pixel i in a GIS map image P; This represents the spatial location of pixel j in a GIS map image P. These represent the values ​​of the l, u, and v channels of pixel i, respectively; Let L, U, and V represent the values ​​of the l, u, and v channels of pixel j, respectively. From the definition of a bilateral affine matrix, we know that the closer the distance between pixels i and j, the closer their colors are, and the corresponding value W of the bilateral affine matrix. i，j The larger it is;

[0018] The above optimization model is used to evaluate t. i Taking the derivative and setting it to 0, we get:

[0019]

[0020] Writing the above equation in matrix form yields:

[0021]

[0022] Furthermore, the method for simplifying the model in step 3) is as follows:

[0023] The bilateral affine matrix is ​​approximated by the following formula:

[0024] W≈S T BS (5)

[0025] Among them, S T B and S represent the Splat, Blur, and Slice processes, respectively.

[0026] Splat: Uniformly quantizes the five-dimensional coordinates of a pixel, projecting the pixel onto a corresponding five-dimensional grid. The value of each grid is the average of all pixel values ​​projected onto that grid.

[0027] Blur: The B matrix corresponds to a five-dimensional Gaussian filter with a bandwidth of 1 applied to a five-dimensional grid;

[0028] Slice: Replaces pixel values ​​with the values ​​of their corresponding grids;

[0029] The normalized bilateral affine matrix used in the objective function of the optimization model Defined by the following formula:

[0030]

[0031] Among them, D m D n S is a diagonal matrix. T S = D m ; diag(·) is a function that places a vector on the diagonal of a matrix, thus transforming the vector into a diagonal matrix; 1 represents a vector consisting entirely of 1s.

[0032] Then let:

[0033] T = S T Z (7)

[0034] Where Z is a temporary variable;

[0035] Substituting equations (6) and (7) into (3), we get:

[0036]

[0037] Furthermore, step 4) specifically includes:

[0038] Calculate the coefficient matrix in equation (8) Calculate the vector on the right side of equation (8), i.e., SCG;

[0039] Equation (8) defines a system of linear equations, which is solved using the preconditioned conjugate gradient method to obtain Z;

[0040] Since the size of Z is smaller than that of T, equation (8) can be solved quickly.

[0041] According to equation (7), a slice operation is performed on Z to obtain the repaired and complete signal image T.

[0042] The beneficial effects of this invention are:

[0043] The method of this invention can complete the blind zone signal while preserving the correct signal value. At the same time, the method uses the approximate form of a bilateral affine matrix, which ensures both accuracy and speed. Even when processing large signal images, this invention can guarantee real-time performance and has a good blind zone completion effect. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method of the present invention.

[0045] Figure 2a This is a schematic diagram of a signal image with missing signal values.

[0046] Figure 2b This is a schematic diagram of a GIS forest area map.

[0047] Figure 2c This is a schematic diagram of the result image after signal completion according to the present invention.

[0048] Figure 2d This is a schematic diagram of the result image after fusing a GIS forest area map image with a complete signal image.

[0049] Figure 3 This is a schematic diagram illustrating the approximate solution process for a two-sided affine matrix. Detailed Implementation

[0050] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0051] Reference Figure 1 As shown, the present invention provides a signal blind zone completion method based on fast matrix filling, comprising the following steps:

[0052] 1) Set model parameters, including: luminance bandwidth σ l Color bandwidth σ uv Spatial bandwidth σ xy And the smoothing parameter λ; and select the missing signal image G to be repaired and the corresponding GIS map image P;

[0053] 2) Construct the optimization model based on the model parameters set in step 1);

[0054] The objective function of the optimized model in step 2) is as follows:

[0055]

[0056] Among them, t i Let t be the value of the blind zone signal image T at pixel i; j Let C be the value of the blind zone signal image T at pixel j; i The confidence level of the signal value at pixel i is determined as follows: if the location is a blind zone, it is considered completely unreliable and its confidence level is set to 0; otherwise, it is considered completely reliable and its confidence level is set to 1. i Let be the value of the input signal image G at pixel i; λ is an adjustable smoothing parameter; j∈Ω(i) indicates that pixel j belongs to the neighborhood of pixel i; W is the bilateral affine matrix calculated according to equation (2). The affine matrix after doubly normalizing W;

[0057]

[0058] in, Indicates the spatial location of pixel i in a GIS map image P; This represents the spatial location of pixel j in a GIS map image P. These represent the values ​​of the l, u, and v channels of pixel i, respectively; Let L, U, and V represent the values ​​of the l, u, and v channels of pixel j, respectively. From the definition of a bilateral affine matrix, we know that the closer the distance between pixels i and j, the closer their colors are, and the corresponding value W of the bilateral affine matrix. i，j The larger it is;

[0059] The above optimization model is used to evaluate t. i Taking the derivative and setting it to 0, we get:

[0060]

[0061] Writing the above equation in matrix form yields:

[0062]

[0063] 3) Simplify the optimization model constructed in step 2);

[0064] The method for simplifying the model is as follows:

[0065] The bilateral affine matrix is ​​approximated by the following formula:

[0066] W≈S T BS (5)

[0067] Among them, ST B and S represent the Splat, Blur, and Slice processes, respectively. Assume there is a pixel value X to be processed. A pixel's position (x, y) and color value (l, u, v) are both determined by its position (x, y) and color value (l, u, v). Therefore, X can be considered as P = (p... x p y p l p u p v The approximate result of the two-sided affine matrix is ​​obtained by the following three steps, as follows: Figure 3 As shown;

[0068] Splat: Uniformly quantizes the five-dimensional coordinates of a pixel, projecting the pixel onto a corresponding five-dimensional grid. The value of each grid is the average of all pixel values ​​projected onto that grid.

[0069] Blur: The B matrix corresponds to a five-dimensional Gaussian filter with a bandwidth of 1 applied to a five-dimensional grid;

[0070] Slice: Replaces pixel values ​​with the values ​​of their corresponding grids;

[0071] The normalized bilateral affine matrix used in the objective function of the optimization model Defined by the following formula:

[0072]

[0073] Among them, D m D n S is a diagonal matrix. T S = D m ; diag(·) is a function that places a vector on the diagonal of a matrix, thus transforming the vector into a diagonal matrix; 1 represents a vector consisting entirely of 1s.

[0074] Then let:

[0075] T = S T Z (7)

[0076] Where Z is a temporary variable;

[0077] Substituting equations (6) and (7) into (3), we get:

[0078]

[0079] 4) Solve the simplified model from step 3) quickly to obtain the repaired signal image T; specifically including:

[0080] Calculate the coefficient matrix in equation (8) Calculate the vector on the right side of equation (8), i.e., SCG;

[0081] Equation (8) defines a system of linear equations, which is solved using the preconditioned conjugate gradient method to obtain Z;

[0082] Since the size of Z is smaller than that of T, equation (8) can be solved quickly.

[0083] According to equation (7), a slice operation is performed on Z to obtain the repaired and complete signal image T.

[0084] In the example, the method of the present invention is applied to a forest environment; Figure 2a The image shown contains missing signal values, where white represents missing pixel values ​​and non-white represents missing signal values. Figure 2a The corresponding GIS forest area map image is as follows Figure 2b As shown, for Figure 2a The signal image in the image was repaired to obtain the following result: Figure 2c To repair the complete image. Ultimately, Figure 2c The signal image shown and Figure 2b The GIS forest area map images shown were overlaid to obtain the following: Figure 2d The image shown.

[0085] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A signal blind zone completion method based on fast matrix filling, characterized in that, The steps are as follows: 1) Set model parameters, including: luminance bandwidth Color bandwidth Spatial bandwidth And the smoothing parameter λ; and select the missing signal image to be repaired. and the corresponding GIS map images ; 2) Construct the optimization model based on the model parameters set in step 1); 3) Simplify the optimization model constructed in step 2); 4) Solve the simplified model from step 3) quickly to obtain the repaired and complete signal image. ; The objective function of the optimized model in step 2) is as follows: (1)； in, Image of the blind zone signal to be predicted At pixel The value at; Image of the blind zone signal to be predicted At pixel The value at; For pixels The confidence level of the signal value at a given point is determined as follows: if the point is a blind zone, it is considered completely unreliable and its confidence level is set to 0; otherwise, it is considered completely reliable and its confidence level is set to 1. For input signal image At pixel The value at; It is an adjustable smoothing parameter; Represents pixels Belongs to pixels The neighborhood; The bilateral affine matrix is ​​calculated according to equation (2). To The affine matrix after doubly normalization; (2)； in, Represents GIS map images The spatial location of the middle pixel i; Represents GIS map images The spatial location of the middle pixel j These represent the values ​​of the l, u, and v channels of pixel i, respectively; Let these represent the values ​​of the l, u, and v channels of pixel j, respectively. From the definition of a bilateral affine matrix, we can see that the closer the distance between pixels i and j, the closer their colors are, and the corresponding values ​​of the bilateral affine matrix... The larger it is; Based on the above optimization model, Taking the derivative and setting it to 0, we get: (3)； Writing the above equation in matrix form yields: (4)。 2. The signal blind zone completion method based on fast matrix filling according to claim 1, characterized in that, The method for simplifying the model in step 3) is as follows: The bilateral affine matrix is ​​approximated by the following formula: (5)； Among them, S T B and S represent the Splat, Blur, and Slice processes, respectively. Splat: Uniformly quantizes the five-dimensional coordinates of a pixel, projecting the pixel onto a corresponding five-dimensional grid. The value of each grid is the average of all pixel values ​​projected onto that grid. Blur: The B matrix corresponds to a five-dimensional Gaussian filter with a bandwidth of 1 applied to a five-dimensional grid; Slice: Replaces pixel values ​​with the values ​​of their corresponding grids; The normalized bilateral affine matrix used in the objective function of the optimization model Defined by the following formula: (6)； in, , It is a diagonal matrix. ; , A function that places a vector on the diagonal of a matrix to transform it into a diagonal matrix. It is a vector consisting entirely of 1s; Then let: (7)； Where Z is a temporary variable; Substituting equations (6) and (7) into (3), we get: (8)。 3. The signal blind zone completion method based on fast matrix filling according to claim 2, characterized in that, Step 4) specifically includes: Calculate the coefficient matrix in equation (8) Calculate the vector on the right side of equation (8), i.e. ; Equation (8) defines a system of linear equations, which is solved using the preconditioned conjugate gradient method to obtain the following results. ; because Size ratio Since the value is small, equation (8) can be solved quickly. According to equation (7) Perform a slice operation to obtain a repaired and complete signal image. .

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