Long-object problem and short-object problem both deal with reconstruction problems with truncated conebeam CT projections acquired with a helical path. They have significantly less practical limitations than original exact cone-beam CT reconstruction algorithms which the cone-beam must cover the whole object. The short-object problem can be defined as reconstruction of the whole object having a finite support in the axial direction with helical scan extends a little bit above and below the object's support. However the longobject problem is to reconstruct the central region of interest (ROI) of a long object having an infinite support in the axial direction with helical scan extends a little a bit above and below the ROI. Although the short-object problem is more difficult to solve than the conventional exact reconstruction with non-truncated projections, the long-object problem presents greater challenge to researchers. Recently, with the great development of panel detector technology and computer technology, more and more researchers have been inspired to work on it. Because of great practical value of long-object algorithms, this paper focuses on the review and discussion of recent developments in long-object algorithms. All Long-object algorithms are classified as exact and approximate algorithms. After going briefly over the history of cone-beam algorithms, some novel cone-beam long-object algorithms are introduced, such as: Tam's algorithm, PImethod, PHI-method, etc. Then, the methods described are being compared and discussed.
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