Interior reconstruction

In iterative reconstruction in digital imaging, interior reconstruction (also known as limited field of view (LFV) reconstruction) is a technique to correct truncation artifacts caused by limiting image data to a small field of view. The reconstruction focuses on an area known as the region of interest (ROI). Although interior reconstruction can be applied to dental or cardiac CT images, the concept is not limited to CT. It is applied with one of several methods.

The purpose of each method is to solve for vector ${\displaystyle x}$ in the following problem:

Let ${\displaystyle X}$ be the region of interest (ROI) and ${\displaystyle Y}$ be the region outside of ${\displaystyle X}$. Assume ${\displaystyle A}$, ${\displaystyle B}$, ${\displaystyle C}$, ${\displaystyle D}$ are known matrices; ${\displaystyle x}$ and ${\displaystyle y}$ are unknown vectors of the original image, while ${\displaystyle f}$ and ${\displaystyle g}$ are vector measurements of the responses (${\displaystyle f}$ is known and ${\displaystyle g}$ is unknown). ${\displaystyle x}$ is inside region ${\displaystyle X}$, (${\displaystyle x\in X}$) and ${\displaystyle y}$, in the region ${\displaystyle Y}$, (${\displaystyle y\in Y}$), is outside region ${\displaystyle X}$. ${\displaystyle f}$ is inside a region in the measurement corresponding to ${\displaystyle X}$. This region is denoted as ${\displaystyle F}$, (${\displaystyle f\in F}$), while ${\displaystyle g}$ is outside of the region ${\displaystyle F}$. It corresponds to ${\displaystyle Y}$ and is denoted as ${\displaystyle G}$, (${\displaystyle g\in G}$).

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