How Long to Read Questions of Uniqueness and Resolution in Reconstruction from Projections

How Long Does it Take to Read Questions of Uniqueness and Resolution in Reconstruction from Projections?

It takes the average reader 3 hours and 14 minutes to read Questions of Uniqueness and Resolution in Reconstruction from Projections by M. B. Katz

Assuming a reading speed of 250 words per minute. Learn more

Description

Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.

How long is Questions of Uniqueness and Resolution in Reconstruction from Projections?

Questions of Uniqueness and Resolution in Reconstruction from Projections by M. B. Katz is 188 pages long, and a total of 48,504 words.

This makes it 63% the length of the average book. It also has 59% more words than the average book.

How Long Does it Take to Read Questions of Uniqueness and Resolution in Reconstruction from Projections Aloud?

The average oral reading speed is 183 words per minute. This means it takes 4 hours and 25 minutes to read Questions of Uniqueness and Resolution in Reconstruction from Projections aloud.

What Reading Level is Questions of Uniqueness and Resolution in Reconstruction from Projections?

Questions of Uniqueness and Resolution in Reconstruction from Projections is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

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