A method of CT imaging a region of interest of an object under examination, comprising: acquiring CT projection data of the region of interest; acquiring CT projection data of a region B, wherein at least a part of the region B falls outside the support of the object, and wherein the region B is selected to enable the selection of a group of PI line segments covering the region of interest, and each PI line segment passing through the region of interest passes through the region B; and reconstructing the CT image of the region of interest in accordance with the CT projection data of the region of interest and the region B; wherein a 2D image along a PI line is defined as function f ( r) ∈ L 2, and the reconstructing processing is to seek for the intersection function fulfilling all the five constraints: C 1 = f ∈ L 2 P | Hf x = g x, x ∈ a b ∪ c d C 2 = f ∈ L 2 P | f x = f 0 x, x ∈ a b C 3 = f ∈ L 2 P | ∫ − 1 + 1 dxf x = πC f C 4 = f ∈ L 2 P | f x ≥ 0, x ∈ − 1,1 C 5 = f ∈ L 2 P | f x ≤ f max, x ∈ − 1,1 where C f = 1 π ∫ − 1 + 1 dxf x is obtained by directly calculating the CT projection data, x ∈ [-1,1] represents a normalized one dimensional PI line segment, x ∈ ( a,b) is the part of the PI line segment within the region B falling outside the support of the object under examination, and ( c, d) is the part of the PI line segment within the ROI, f 0 ( x) is an object image in the part of PI line segment within the region B, f max represents the possible maximum value in the reconstructed image, g ( x) is a one dimensional Hilbert transform value in the PI line segment, condition C 1 is implemented by POCS (Projection onto Convex Set) iterative calculation, the formula for calculating the constraint condition C 3 is: f k x = { f 0 x, x ∈ a b f k − 1 x + πC f − ∫ a b dx ′ f 0 x ′ 2 + a − b − ∫ − 1 a + ∫ b 1 dx ′ f k − 1 x ′ 2 + a − b, x ∈ − 1, a ∪ b 1. acquiring CT projection data of the region of interest; acquiring CT projection data of a region B, wherein at least a part of the region B falls outside the support of the object, and wherein the region B is selected to enable the selection of a group of PI line segments covering the region of interest, and each PI line segment passing through the region of interest passes through the region B; and reconstructing the CT image of the region of interest in accordance with the CT projection data of the region of interest and the region B; wherein a 2D image along a PI line is defined as function f ( r) ∈ L 2, and the reconstructing processing is to seek for the intersection function fulfilling all the five constraints: C 1 = f ∈ L 2 P | Hf x = g x, x ∈ a b ∪ c d C 2 = f ∈ L 2 P | f x = f 0 x, x ∈ a b C 3 = f ∈ L 2 P | ∫ − 1 + 1 dxf x = πC f C 4 = f ∈ L 2 P | f x ≥ 0, x ∈ − 1,1 C 5 = f ∈ L 2 P | f x ≤ f max, x ∈ − 1,1 where C f = 1 π ∫ − 1 + 1 dxf x is obtained by directly calculating the CT projection data, x ∈ [-1,1] represents a normalized one dimensional PI line segment, x ∈ ( a,b) is the part of the PI line segment within the region B falling outside the support of the object under examination, and ( c, d) is the part of the PI line segment within the ROI, f 0 ( x) is an object image in the part of PI line segment within the region B, f max represents the possible maximum value in the reconstructed image, g ( x) is a one dimensional Hilbert transform value in the PI line segment, condition C 1 is implemented by POCS (Projection onto Convex Set) iterative calculation, the formula for calculating the constraint condition C 3 is: f k x = { f 0 x, x ∈ a b f k − 1 x + πC f − ∫ a b dx ′ f 0 x ′ 2 + a − b − ∫ − 1 a + ∫ b 1 dx ′ f k − 1 x ′ 2 + a − b, x ∈ − 1, a ∪ b 1.