Image noise reduction reconstruction method based on EMD and VMD

Abstract

The invention discloses an image noise reduction reconstruction method based on EMD and VMD, and the method employs EMD and VMD to carry out the decomposition and reconstruction of an image, achieves the reconstruction of a high-quality original image from limited, incomplete or noise-interfered observation data, and provides a new thought and a new approach for the faster image reconstruction.

Description

Technical Field

[0001] The invention belongs to the technical field of pattern recognition and machine learning, and in particular relates to an image denoising and reconstruction method based on EMD and VMD. Background Art

[0002] Image reconstruction technology is the basis for realizing many advanced applications. With the rapid development of autonomous driving technology, vehicles need to rely on cameras to obtain image information of the surrounding environment. However, due to factors such as light changes, weather conditions, and motion blur, the collected images often have quality problems. Through image reconstruction algorithms, these low-quality images can be processed to restore clear scene information, providing reliable data support for tasks such as target recognition and path planning of autonomous driving systems. Taking the face recognition system as an example, under complex lighting and low-resolution conditions, image reconstruction technology can enhance the details of face images and improve recognition accuracy, so that it can be widely used in security monitoring, access control systems and other scenarios to ensure public safety and personal privacy. Therefore, how to reconstruct high-quality original images from limited, incomplete or noise-interfered observation data is of great significance. Summary of the invention

[0003] In view of this, the present invention provides an image denoising and reconstruction method based on EMD and VMD, which realizes the reconstruction of a high-quality original image from limited, incomplete or noise-interfered observation data.

[0004] The present invention provides an image denoising and reconstruction method based on EMD and VMD, comprising the following steps:

[0005] Step 1: Represent the image to be processed as an image matrix C m×n , C m×n Convert to a vector R with one row (m×n) and one column 1 ×(m×n) :

[0006] R 1×(m×n) =[c 1×1 … c 1×j … c 1×(m×n) ]

[0007] Among them, c 1×j Represents vector R 1×(m×n) The element in the jth column of 1×(m×n) Represents vector R 1×(m×n) The elements in the (m×n)th column of ;

[0008] Step 2: Use the EMD algorithm to calculate the vector R 1×(m×n) Perform adaptive decomposition to obtain q vectors A with one row and (m×n) columns 1×(m×n) , A1×(m×n) Accumulate to obtain a vector B with one row (m×n) and one column 1×(m×n) :

[0009]

[0010] Step 3: Construct the residual vector E 1×(m×n) :

[0011] E 1×(m×n) =R 1×(m×n) -B 1×(m×n)

[0012] Step 4: Use VMD algorithm to calculate the residual vector E 1×(m×n) Perform adaptive decomposition to obtain p vectors D with one row and (m×n) columns 1×(m×n) , D 1×(m×n) Accumulate to obtain a vector F with one row (m×n) and one column 1×(m×n) :

[0013]

[0014] Step 5: B 1×(m×n) and F 1×(m×n) Add to get vector G 1×(m×n) :

[0015] G 1×(m×n) =B 1×(m×n) +F 1×(m×n)

[0016] Step 6: Vector G 1×(m×n) Transformed into image reconstruction matrix H m×n :

[0017]

[0018] Among them, H m×n The matrix of m rows and n columns represents the restored original image, h k×i Denotes the matrix H m×n The element in the kth row and ith column of the matrix H m×n All elements in are real numbers, and the image is restored.

[0019] Furthermore, the image matrix C m×n for:

[0020]

[0021] Among them, C m×n is a matrix containing m rows and n columns representing the image to be processed, c k×i is the matrix C m×n The elements in the kth row and ith column in the matrix C represent the pixels in the image. m×nAll elements in are real numbers in the range [0,255].

[0022] Beneficial effects:

[0023] The present invention utilizes EMD and VMD to decompose and reconstruct an image, thereby reconstructing a high-quality original image from limited, incomplete or noise-interfered observation data, and provides a new idea and new approach for faster image reconstruction. DETAILED DESCRIPTION

[0024] The present invention is described in detail with reference to the following embodiments.

[0025] In the present invention, the image is represented by the image matrix C m×n Indicates that each element in the matrix corresponds to each pixel in the image, the value of the element corresponds to the color value of the pixel, and the value range of the element is [0,255], specifically:

[0026]

[0027] Among them, C m×n is a matrix containing m rows and n columns, c k×i is the matrix C m×n The elements in the kth row and ith column in the matrix C represent the pixels in the image. m×n All elements in are real numbers in the range [0,255].

[0028] The present invention provides an image denoising and reconstruction method based on EMD and VMD, which specifically comprises the following steps:

[0029] Step 1: transform the image matrix C m×n Convert to a vector R with one row (m×n) and one column 1×(m×n) It can be expressed as:

[0030] R 1×(m×n) =[c 1× 1 … c 1×j … c 1×(m×n) ] (1)

[0031] where c 1×j Represents vector R 1×(m×n) The element in the jth column of 1×(m×n) Represents vector R 1×(m×n) The elements in the (m×n)th column of .

[0032] Step 2: Use the EMD algorithm to calculate the vector R 1×(m×n) Perform adaptive decomposition to obtain q vectors A with one row and (m×n) columns 1×(m×n) , and transform q vectors A with one row and (m×n) columns into1×(m×n) Accumulate to obtain a vector B with one row (m×n) and one column 1×(m×n) It can be expressed as:

[0033]

[0034] Step 3: Construct the residual vector E 1×(m×n) It is expressed as:

[0035] E 1×(m×n) =R 1×(m×n) -B 1×(m×n) (3).

[0036] Step 4: Use VMD algorithm to calculate the residual vector E 1×(m×n) Perform adaptive decomposition to obtain p vectors D with one row and (m×n) columns 1×(m×n) , p vectors D with one row (m×n) and one column 1×(m×n) Accumulate and obtain a vector F with one row (m×n) and one column 1 ×(m×n) It can be expressed as:

[0037]

[0038] Step 5: Vector B 1×(m×n) and vector F 1×(m×n) Add to get vector G 1×(m×n) It is expressed as:

[0039] G 1×(m×n) =B 1×(m×n) +F 1×(m×n) (6).

[0040] Step 6: Vector G 1×(m×n) Transformed into image reconstruction matrix H m×n It is expressed as:

[0041]

[0042] Among them, H m×n is a matrix with m rows and n columns, h k×i Denotes the matrix H m×n The element in the kth row and ith column of the matrix H m×n All elements in are real numbers. m×n This is the restored original image.

[0043] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An image denoising and reconstruction method based on EMD and VMD, characterized in that: The following steps are involved: Step 1: Represent the image to be processed as an image matrix C m×n , C m×n Convert to a vector R with one row (m×n) and one column 1×(m×n) : R 1×(m×n) =[c 1×1 … c 1×j … c 1×(m×n) ] Among them, c 1×j Represents vector R 1×(m×n) The element in the jth column of 1×(m×n) Represents vector R 1×(m×n) The elements in the (m×n)th column of ; Step 2: Use the EMD algorithm to calculate the vector R 1×(m×n) Perform adaptive decomposition to obtain q vectors A with one row and (m×n) columns 1 ×(m×n) , A 1×(m×n) Accumulate to obtain a vector B with one row (m×n) and one column 1×(m×n) : Step 3: Construct the residual vector E 1×(m×n) : E 1×(m×n) =R 1×(m×n) -B 1×(m×n) Step 4: Use VMD algorithm to calculate the residual vector E 1×(m×n) Perform adaptive decomposition to obtain p vectors D with one row and (m×n) columns 1×(m×n) , D 1×(m×n) Accumulate to obtain a vector F with one row (m×n) and one column 1×(m×n) : Step 5: B 1×(m×n) and F 1×(m×n) Add to get vector G 1×(m×n) : G 1×(m×n) =B 1×(m×n) +F 1×(m×n) Step 6: Vector G 1×(m×n) Transformed into image reconstruction matrix H m×n : Among them, H m×n The matrix of m rows and n columns represents the restored original image, h k×i Denotes the matrix H m×n The element in the kth row and ith column of the matrix H m×n All elements in are real numbers, and the image is restored.

2. The image denoising and reconstruction method according to claim 1, characterized in that: The image matrix C m×n for: Among them, C m×n is a matrix containing m rows and n columns representing the image to be processed, c k×i is the matrix C m×n The elements in the kth row and ith column in the matrix C represent the pixels in the image. m×n All elements in are real numbers in the range [0,255].

Images