Filtered Backprojection Reconstruction with Depth-Dependent Filtering

A direct filtered-backprojection （FBP） reconstruction algorithm is presented for circular cone-beam computed tomography （CB-CT） that allows the filter operation to be applied efficiently with shift-variant band-pass characteristics on the kernel function. Our algorithm is derived from the ramp-filter based FBP method of Feldkamp et al. and obtained by decomposing the ramp filtering into a convolution involving the Hilbert kernel （global operation） and a subsequent differentiation operation （local operation）. The differentiation is implemented as a finite difference of two （Hilbert filtered） data samples and carried out as part of the backprojection step. The spacing between the two samples, which defines the low-pass characteristics of the filter operation, can thus be selected individually for each point in the image volume. We here define the sample spacing to follow the magnification of the divergent-beam geometry and thus obtain a novel, depth-dependent filtering algorithm for circular CB-CT. We evaluate this resulting algorithm using computer-simulated CB data and demonstrate that our algorithm yields results where spatial resolution and image noise are distributed much more uniformly over the field-of-view, compared to Feldkamp＇s approach.

Reducing metal artifacts by restricting negative pixels

When the object contains metals,its x-ray computed tomography(CT)images are normally affected by streaking artifacts.These artifacts are mainly caused by the x-ray beam hardening effects,which deviate the measurements from their true values.One interesting observation of the metal artifacts is that certain regions of the metal artifacts often appear as negative pixel values.Our novel idea in this paper is to set up an objective function that restricts the negative pixel values in the image.We must point out that the naïve idea of setting the negative pixel values in the reconstructed image to zero does not give the same result.This paper proposes an iterative algorithm to optimize this objective function,and the unknowns are the metal affected projections.Once the metal affected projections are estimated,the filtered backprojection algorithm is used to reconstruct the final image.This paper applies the proposed algorithm to some airport bag CT scans.The bags all contain unknown metallic objects.The metal artifacts are effectively reduced by the proposed algorithm.

An Alternative Derivation for Bronnikov's Reconstruction Algorithm in X-ray Phase Contrast Tomography

In this article, we present an alternative derivation for Bronnikov's reconstruction algorithm in X-ray phase contrast tomography with holographic measurements. A two-step method was used in the alternative derivation. The phase shift induced by the object was obtained by Fourier transform and the real part of the complex refractive index of the object was retrieved by applying the conventional filtered backprojection method. The alternative derivation provides an easier way to understand the reconstruction formula.