Z-index parameterization for volumetric CT image reconstruction via 3-D dictionary learning

Despite the rapid developments of X-ray cone-beam CT (CBCT), image noise still remains a major issue for the low dose CBCT. To suppress the noise effectively while retain the structures well for low dose CBCT image, in this paper, a sparse constraint based on the 3-D dictionary is incorporated into a regularized iterative reconstruction framework, defining the 3-D dictionary learning (3-DDL) method. In addition, by analyzing the sparsity level curve associated with different regularization parameters, a new adaptive parameter selection strategy is proposed to facilitate our 3-DDL method. To justify the proposed method, we first analyze the distributions of the representation coefficients associated with the 3-D dictionary and the conventional 2-D dictionary to compare their efficiencies in representing volumetric images. Then, multiple real data experiments are conducted for performance validation. Based on these results, we found: 1) the 3-D dictionary-based sparse coefficients have three orders narrower Laplacian distribution compared with the 2-D dictionary, suggesting the higher representation efficiencies of the 3-D dictionary; 2) the sparsity level curve demonstrates a clear Z-shape, and hence referred to as Z-curve, in this paper; 3) the parameter associatedwith themaximum curvature point of the Z-curve suggests a nice parameter choice,which could be adaptively locatedwith the proposed Z-index parameterization (ZIP) method; 4) the proposed 3-DDL algorithm equippedwith the ZIPmethod could deliver reconstructions with the lowest root mean squared errors and the highest structural similarity index compared with the competing methods; 5) similar noise performance as the regular dose FDK reconstruction regarding the standard deviation metric could be achieved with the proposed method using (1/2)/(1/4)/(1/8) dose level projections. The contrast-noise ratio is improved by ∼2.5/3.5 times with respect to two different cases under the (1/8) dose level compared with the low dose FDK reconstruction. The proposed method is expected to reduce the radiation dose by a factor of 8 for CBCT, considering the voted strongly discriminated low contrast tissues.