  Respiration-correlated CBCT, commonly called 4DCBCT, provide respiratory
phase-resolved CBCT images. In many clinical applications, it is more
preferable to reconstruct true 4DCBCT with the 4th dimension being time, i.e.,
each CBCT image is reconstructed based on the corresponding instantaneous
projection. We propose in this work a novel algorithm for the reconstruction of
this truly time-resolved CBCT, called cine-CBCT, by effectively utilizing the
underlying temporal coherence, such as periodicity or repetition, in those
cine-CBCT images. Assuming each column of the matrix $\bm{U}$ represents a CBCT
image to be reconstructed and the total number of columns is the same as the
number of projections, the central idea of our algorithm is that the rank of
$\bm{U}$ is much smaller than the number of projections and we can use a matrix
factorization form $\bm{U}=\bm{L}\bm{R}$ for $\bm{U}$. The number of columns
for the matrix $\bm{L}$ constraints the rank of $\bm{U}$ and hence implicitly
imposing a temporal coherence condition among all the images in cine-CBCT. The
desired image properties in $\bm{L}$ and the periodicity of the breathing
pattern are achieved by penalizing the sparsity of the tight wavelet frame
transform of $\bm{L}$ and that of the Fourier transform of $\bm{R}$,
respectively. A split Bregman method is used to solve the problem. In this
paper we focus on presenting this new algorithm and showing the proof of
principle using simulation studies on an NCAT phantom.

Medical Physics