Method to process images obtained by tomography or few view tomosynthesis

A method for processing images obtained by tomography or tomosynthesis, the method comprising:

• acquiring a plurality of 2D projection images of an imaging system, the acquiring a plurality of 2D projection images of an object being defined by Rf=s, wherein s is a vector of the acquired projections, R is a projection operator which models the imaging system and f is a 3D image of the object to be reconstructed with knowledge of R and s;
• processing the acquired 2D projection images including applying an iterative algorithm defined by its iteration, generating at least one set of processed projection images, the iteration being defined so that at each iteration the 3D image of the object is a linear function of the processed 2D projection images according to the property f(n)= Rp(n), wherein R a matrix such that RRf is a 3D image, wherein at each iteration the algorithm generates sets of processed projection images as per the conjugate gradient method:
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• wherein p, q, t are such that p(0) is arbitrary, typically zero or equal to the vector of the acquired 2D projection images, and q(0)=t(0)=RR′p(0)−s.

A method for processing images obtained by tomography or tomosynthesis, the method comprising:

• acquiring of 2D projection images of an object using an imaging system, the acquiring a plurality of 2D projection images of an object being defined by Rf=s, wherein s is a vector of the acquired projections, R is a projection operator which models the imaging system and f is a 3D image of the object to be reconstructed with knowledge of R and s;
• processing the acquired 2D projection images including applying an iterative algorithm defined by its iteration, generating at least one set of processed projection images, the iteration being defined so that at each iteration the 3D image of the object is a linear function of the processed 2D projection images according to the property f(n)= Rp(n), wherein R is a matrix such that RRf is a 3D image, wherein at each iteration the algorithm generates a set of projection images with
• Vθ(n)[p]=(Iθ(n)−ρθ(n)Iθ(n)R R)p+ρθ(n)Iθ(n)s+Iφ(n)p,
• wherein θ(n) and φ(n) are respectively a first and a second sub-set of indices of acquired projective measurements, defined for each iteration, the two sub-sets being separate, their joining indexing the entirety of the vector of the acquired 2D projection images, and Iθ(n) and Iφ(n) are matrices whose coefficients are all zero except for the indices of the diagonal belonging to θ(n) and φ(n) respectively in which their value is 1, so that p=Iθ(n)p+Iφ(n)p, in which p(0)=ρθ(n)Iθ(0)s or else p(0)=0, and ρθ(n), is a fixed parameter so that ∥Iθ(n)=ρθ(n) RR∥<1 and thereby guarantees the convergence of the method.

A medical imaging system comprising:

• an acquisition system for the acquisition of a plurality of 2D projection images of an object, comprising a radiation source and a sensor;
• a storage means configured to store acquired 2D projection images;
• and
• a processing system configured to:
• acquire a plurality of 2D projection images of an object using the system, the acquiring a plurality of 2D projection images of an object being defined by Rf=s, wherein s is a vector of the acquired projections, R is a projection operator which models the imaging system and f is a 3D image of the object to be reconstructed with knowledge of R and s;
• and
• process the acquired 2D projection images including applying an iterative algorithm defined by its iteration, at each iteration n=1, . . . , N generating at least one set of processed projection images, the iteration being defined so that at each iteration the 3D image of the object is a linear function of the processed 2D projection images according to the property f(n)= Rp(n), wherein R is a matrix such that RRf is a 3D image, wherein at each iteration, the algorithm generates a set of processed projection images, the iteration being defined for any vector in space of the 2D projection images by:
• V[p]=(I−ρR R)p+ρs,
• wherein p(0)=ρs or p(0)=0, s is the set of acquired 2D projection images, ρ is a fixed parameter so that ∥I=ρ RR∥<1 and thereby guarantees convergence of the method, and I is the square unit matrix.