Patent ID: 7697658

Claim:
The method for limited-angle interior tomography, comprising the steps of: a) identify a region of interest (ROI) in an object; b) measure truncated differences of Hilbert transform data through the ROI where the data are defined by the equation ∫ s 1 s 2 ⁢ ⁢ ⅆ ⅆ h ⁢ D f ⁡ ( s , P - y ⁡ ( s ) + hy ′ ⁡ ( s ) ) ⁢ | h = 0 ⁢ ⅆ s + ⁢ ⁢ D f ⁡ ( s 2 , P - y ⁡ ( s 2 ) ) - D f ⁡ ( s 1 , P - y ⁡ ( s 1 ) ) = z ⁢ 1 π ⁢ PV ⁢ ∫ ⁢ f ⁡ ( P - t ⁢ ⁢ θ 2 ) t ⁢ ⁢ ⅆ t - 1 π ⁢ PV ⁢ ∫ ⁢ f ⁡ ( P - t ⁢ ⁢ θ 1 ) t ⁢ ⁢ ⅆ t . ( 5.1 ) where ƒ is the object function representing the linear attenuation coefficient, D ƒ is the measured projection data, PV represents the principal value, y(s), s 1 ≦s≦s 2 , is a scanning curve, P is a point in the ROI, and θ j is a unit vector from y(s j ) to P; c) determine or acquire a linear attenuation coefficient distribution of a subregion in the ROI; d) reconstruct the ROI according to measured truncated differences of Hilbert transform data and said linear attenuation coefficient property for said subregion.