System and method for filtering noise from a medical image
View Patent ↗A system and method for filtering noise from a medical image are provided. A method for filtering noise from an image comprises: generating a weighted graph representing the image; selecting a plurality of nodes from the image to retain grayscale values of the plurality of nodes; and determining filtered grayscale values of the plurality of nodes.
1. A method for filtering noise from a medical image, comprising:
a memory device storing a program;
a processor in communication with the memory device, the processor operative with the program to:
generate a weighted graph representing the medical image;
selecting a subset of nodes from a plurality of nodes in the weighted graph, wherein each node in the subset of nodes is designated to retain its original grayscale values;
viewing the subset of nodes as a set of Dirichlet boundary points;
solving a combinatorial, anisotropic Dirichlet boundary value problem for each node of the plurality of nodes using the set of Dirichlet boundary points, except for the subset of nodes, to provide an interpolated grayscale value thereof; and
forming a filtered version of the medical image by replacing an original grayscale value of each of the plurality of nodes with its corresponding interpolated grayscale value, and keeping the original grayscale value of each node in the subset of nodes.
2. The method of claim 1 , wherein the weighted graph is generated with weights given by:
ω ij =e −β(p i −p j ) 2
where p i is an intensity at a first node of the plurality of nodes, p j is an intensity at a second node of the plurality of nodes and β is an anisotropy parameter.
3. The method of claim 1 , wherein the subset of nodes is selected manually or automatically.
4. The method of claim 1 , wherein the subset of nodes represents pixels or voxels in the medical image.
5. The method of claim 1 , wherein the medical image is acquired using one of a magnetic resonance (MR), computed tomography (CT), positron emission tomography (PET), a two-dimensional (2D) or three-dimensional (3D) fluoroscopic, a 2D, 3D, or four-dimensional (4D) ultrasound, or x-ray imaging technique.
6. A system for filtering noise from a medical image comprising:
a memory device storing a program;
a processor in communication with the memory device, the processor operative with the program to:
generate a weighted graph representing the medical image;
select a subset of nodes from a plurality of nodes in the weighted graph, wherein each node in the subset of nodes is designated to retain its original grayscale values;
view the subset of nodes as a set of Dirichlet boundary points;
solve a combinatorial, anisotropic Dirichlet boundary value problem for each node of the plurality of nodes using the set of Dirichlet boundary points, except for the subset of nodes, to provide an interpolated grayscale value thereof: and
form a filtered version of the medical image by replacing an original grayscale value of each of the plurality of nodes with its corresponding interpolated grayscale value, and keeping the original grayscale value of each node in the subset of nodes.
7. The system of claim 6 , wherein the weighted graph is generated with weights given by:
ω ij =e −β(p i −p j ) 2
where p i is an intensity at a first node of the plurality of nodes, p j is an intensity at a second node of the plurality of nodes and β is an anisotropy parameter.
8. The system of claim 6 , wherein the selection of the subset of nodes is performed automatically or in response to a manual input.
9. The system of claim 6 , wherein the subset of nodes represents pixels or voxels in the medical image.
10. The system of claim 6 , wherein the medical image is acquired using one of a magnetic resonance (MR), computed tomography (CT), positron emission tomography (PET), a two-dimensional (2D) or three-dimensional (3D) fluoroscopic, a 2D, 3D, or four-dimensional (4D) ultrasound, or x-ray imaging device.
11. The method of claim 1 , wherein the subset of nodes is selected by choosing samples from uniform areas of the medical image in accordance with the following equation:
h=|A T ||Ap|,
where A represents an incidence matrix, |A T | represents an absolute value of A, |Ap| represents an absolute value of a gradient, p is a vectorized version of the medical image and h is a sum of edge gradients incident on each node in the uniform area;
viewing a normalized h as a probability of sampling each node in the uniform area; and
randomly generating a fixed number of samples and selecting these as the Dirichlet boundary points.