This paper attempts to apply the actual redundancy involved in X‐ray CT projection data which have been treated as independent data for the improvement of the image quality of a reconstructed image. It is known that the projection data of an X‐ray CT contains random noise, such as photon noise, which has a negative effect on image quality. A simple smoothing filter which generally is used to reduce this effect, causes the degradation of image resolution. Therefore, it is possible to suppress only high‐frequency noise components. However, when the structure of the projection data was analyzed, it became clear that projection data contain a large redundancy in determining the lower‐frequency components of the image. By properly taking advantage of this redundancy for image reconstruction, it is possible to suppress the low‐frequency component. This paper clarifies quantitatively the noise suppression effect using redundancy by comparing the case where redundancy is not used at all with the case where redundancy is used completely.
A theory of natural observation methods was originally formulated for two complementary systems: neighboring type and equilibrium type. This paper introduces a new system, normal-type system, that is different from the forementioned two types. One characteristic feature of the normal-type natural observation method is its ability to reconstruct an original waveform from the sum of a finite number of observation values. The natural observation theory of a normal type evolves naturally under the condition that a waveform and its power component can be expressed in the sum form. These meanings are discussed by comparing a frequency response of the normal-type natural observation taansform with that of a conventional filter bank. Furthermore, a criterion for determining observation parameters in order to realize the natural observation of normal type under a given tolerance of error is described. It is believed that the proposed theory offers new insights into systematization of the natural observation theory.
Tbe natural observation method provides a procedure to analyze the time-varying characteristics of the continuous-time waveform with mathematical rigor and can resolve the fundamental problem encountered in Fourier analysis method. In this paper, for discrete-time waveforms a discrete natural observation method is proposed which has characteristics similar to those for the continuous natural observation method. Similar to the continuous natural observation theory of normal type, the discrete natural observation theory is introduced by requiring that the waveform values and the power component can be expressed in terms of sum forms. The discrete natural observation method is complete by itself as a discrete type, and not only is it similar in nature to those of the continuous type but also can be shifted naturally to the continuous type as the sampling interval vanishes.
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