Signal Processing for Magnetic Resonance Imaging and - download pdf or read online

By Hong Yan

This reference/text comprises the newest sign processing ideas in magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) for extra effective medical diagnoses-providing ready-to-use algorithms for photo segmentation and research, reconstruction and visualization, and removing of distortions and artifacts for elevated detection of illness. Detailing low-cost methods for stronger photograph and spectrum caliber, sign Processing for Magnetic Resonance Imaging and Spectroscopy discusses the evaluate of particular shapes and geometric positive aspects in MR photographs; smooth options for MR facts processing; the characterization and research of cerebral, muscular, and cardiac tissues; wavelet rework and projection on convex units (POCS), tools for photo reconstruction, recovery, and enhancement; and powerful tools for the relief of ghost artifacts.

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H Stark, JW Woods, I Paul, R Hingorani. Direct Fourier reconstruction in computer tomography. IEEE Trans Acoust Speech Signal Process ASSP-29: 237–245, 1981. H Stark, JW Woods, I Paul, R Hingorani. An investigation of computerized tomography by direct Fourier inversion and optimum interpolation. IEEE Trans Biomed Eng BME-29:496–505, 1981. SR Deans. The Radon Transform and Some of Its Applications. John Wiley, New York, 1983. GT Herman. Image Reconstruction from Projection: The Fundamentals of Computerized Tomography.

Theorem 3 (Inverse Radon Transform) Let P(s, ␾) be the Radon transform of I(x, y) defined in Eq. (46). Then I(x, y) can be reconstructed from P(s, ␾) by 1 I(x, y) = 2␲ 2 Proof ͵͵ ␲ 0 ϱ Ϫϱ ѨP(s, ␾) Ѩs ds d␾ x cos ␾ ϩ y sin ␾ Ϫ s (48) We first invoke the two-dimensional inverse Fourier transform I(x, y) = ͵͵ ϱ ϱ Ϫϱ Ϫϱ S(kx , ky)ei2␲ (kxxϩkyy) dkx dky (49) Converting it to the polar coordinate system (using kx = k cos ␾, ky = k sin ␾) yields ͵͵ 2␲ I(x, y) = ϱ 0 Sp (k, ␾)ei2␲k(x cos ␾ϩy sin ␾)k dk d␾ (50) 0 where Sp (k, ␾) = S(k cos ␾, k sin ␾).

Some examples of reconstruction demonstrating the effect of these factors are shown in Fig. 6. A special result regarding the filter function is summarized in the following remark. Remark 5 When H(k) is an all-pass filter, Pˆ (s, ␾) = P(s, ␾), and the resulting reconstruction algorithm is known as the back-projection algorithm. Let Iˆ(x, y) be the back-projection image, namely, ͵ ␲ ˆI(x, y) = Ꮾ{P(s, ␾)} = P(x cos ␾ ϩ y sin ␾, ␾) d␾ (67) 0 Then Iˆ(x, y) is related to I(x, y) by ˆI(x, y) = I(x, y) ** 2 1 2 x ϩy where ** denotes two-dimensional convolution.

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