Advanced Image Processing in Magnetic Resonance Imaging by Luigi Landini, Vincenzo Positano, Maria Santarelli

By Luigi Landini, Vincenzo Positano, Maria Santarelli

The recognition of magnetic resonance (MR) imaging in medication is not any secret: it truly is non-invasive, it produces prime quality structural and sensible photo facts, and it's very flexible and versatile. examine into MR know-how is advancing at a blistering velocity, and sleek engineers needs to stay alongside of the newest advancements. this can be in simple terms attainable with an organization grounding within the simple rules of MR, and complicated picture Processing in Magnetic Resonance Imaging solidly integrates this foundational wisdom with the most recent advances within the field.

Beginning with the fundamentals of sign and picture new release and reconstruction, the booklet covers intimately the sign processing strategies and algorithms, filtering options for MR pictures, quantitative research together with photograph registration and integration of EEG and MEG suggestions with MR, and MR spectroscopy concepts. the ultimate portion of the e-book explores useful MRI (fMRI) intimately, discussing basics and complex exploratory info research, Bayesian inference, and nonlinear research. a number of the effects provided within the e-book are derived from the individuals' personal paintings, offering hugely sensible event via experimental and numerical methods.

Contributed via foreign specialists on the vanguard of the sphere, complicated photograph Processing in Magnetic Resonance Imaging is an crucial consultant for an individual attracted to additional advancing the know-how and services of MR imaging.

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Extra resources for Advanced Image Processing in Magnetic Resonance Imaging (Signal Processing and Communications)

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2 FREQUENCY ENCODING Frequency encoding makes the oscillation frequency of an MR signal linearly dependent on its spatial origin. Let us consider an idealized one-dimensional object with spin distribution ρ(x). 13 Example of a pulse timing diagram relevant to the slice selection operation. 35) where the constant of proportionality c is dependent on the flip angle, the main field strength, and so on. 35 is said to be frequency encoded because its oscillation frequency is linearly related to the spatial location; consequently, Gx is called a frequency-encoding gradient.

1 Gibbs ringing artifacts. 3 CONSTRAINED IMAGE RECONSTRUCTION For years, the belief existed that information beyond the measurement cutoff frequency was not recoverable, thus the Rayleigh resolution limit [1]. Although the information is not apparent in the measured data, we now have learned how to look elsewhere for the additional information required to restore those frequency contents [2,3]. Constrained methods are the mathematical tools developed to accomplish this objective by using a priori information to compensate for the lack of high-frequency experimental data in the reconstruction process.

Data-consistency constraint: Ω1 = {ρ( x ) : F{ρ( x )} = D(k ), for all the measured k values}. 2. Limited-support constraint: Ω 2 = {ρ( x ) : ρ( x ) = 0, for | x | > W /2}. 3. Bounded-magnitude constraint: Ω 3 = {ρ( x ) : | ρ( x ) | ≤ B}. 4. Phase constraint: Ω 4 = {ρ( x ) : arg{ρ( x )}θ ( x )}. 5. Bounded-noise variance constraint: { } Ω 5 = {ρ( x ) : || s − F ρ( x )} ||2 ≤ σ ε2 . Although POCS has played an important role in nonparametric image reconstruction, it is not without limitations. Three of the most serious limitations are: First, it can handle only convex-type constraints, which prevents some effective but nonconvex-type constraints from being used.

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