By Luis L. Bonilla
ISBN-10: 3540785450
ISBN-13: 9783540785453
These days we face a variety of and demanding imaging difficulties: nondestructive trying out of fabrics, tracking of business methods, enhancement of oil construction through effective reservoir characterization, rising advancements in noninvasive imaging suggestions for scientific reasons - automatic tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, and so on. within the CIME summer season college on Imaging (Martina Franca, Italy 2002), major specialists in mathematical recommendations and functions offered huge and important introductions for non-experts and practitioners alike to many elements of this intriguing box. the quantity comprises a part of the above lectures accomplished and up to date via extra contributions on different comparable themes.
Read or Download Inverse Problems and Imaging: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 15-21, 2002 PDF
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Extra info for Inverse Problems and Imaging: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 15-21, 2002
Sample text
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.
48(3): 493–501. 19. , and Boesiger, P. (2001). Advances in sensitivity encoding with arbitrary k-space trajectories. Magn. Reson. Med. 46(4): 638–651. 55 This chapter provides a tutorial overview of advanced image reconstruction methods used in MRI. The term “advanced” is used loosely to refer to the class of nonFourier reconstruction methods developed for handling the inverse problem with limited Fourier samples. We will consider two specific cases: (a) the superresolution reconstruction problem (associated with limited Fourier samples collected at the Nyquist rate) and (b) the parallel imaging problem (arising when Fourier samples are collected at sub-Nyquist rates, using multiple nonuniform receiver channels).
Is related to the shape and the duration of the pulse; if we consider a Gaussian-shaped pulse, ∆ω = 2π/∆t, where ∆ω is the full width at half maximum (FWHM) of the pulse’s frequency spectrum, and ∆t is the relevant FWHM of the pulse envelope in seconds. , by making the pulse longer in time) or by increasing the strength of the slice selection gradient Gz. The slice profile is determined by the spectral contents of the selective pulse, and it is approximately given by the Fourier transform of the RF pulse envelope.