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Topic: Filtered back projection

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	Patent 4189775: Method and apparatus for subsection analysis using computed tomography
		projection data, are obtained from radiation beams penetrating the sectional portion of the subject in parallel therewith and in fixed directions of projection at varied angles, and then the projection data are filtered for the calculation of modified projection data.
		The filtering operation is performed in order to remove fuzziness or blurring that may be caused if the image is constructed from the data back projected as they are.
		According to the fundamental principles of the filtered-back projection method, the projection data g(X,.theta.) is transformed to the frequency domain by Fourier transformation multiplied by the filter function H(.omega.), transformation by inverse Fourier transform to calculate the modified projection data, the back-projected for reconstruction and display of an image of the sectional portion.
	www.freepatentsonline.com /4189775.html (4748 words)

	Single photon emission computed tomography - Wikipedia, the free encyclopedia
		Then a series of projection images are acquired using a gamma camera.
		The projection images are stored digitally and a sophisticated computer program is used to process them and produce the slices (this is called reconstruction).
		At the time of writing (2004), by far the most commonly used method is ' filtered back projection '.
	en.wikipedia.org /wiki/SPECT (208 words)

	Filtered Back Projection (Site not responding. Last check: 2007-11-06)
		The projections of these sources at 45 degree intervals are represented on the sides of an octagon.
		Figure 5 B illustrates the basic idea behind back projection, which is to simply run the projections back through the image (hence the name ``back projection'') to obtain a rough approximation to the original.
		The combination of back projection and ramp filtering is known as filtered back projection.
	www.owlnet.rice.edu /~elec539/Projects97/cult/node2.html (216 words)

	PC-I The First Tomographic Imaging Device and the First Computed Tomographic Imaging Device (PET): 1968-1971
		Figure 5 illustrates the concept of filtered back projection and was presented by Chesler at the Meeting on Tomographic Imaging in Nuclear Medicine September 15-16, 1972.
		This development of filtered back projection was the first reconstruction of this type to be applied to PET and CT data.
		The filtered back projection algorithm was immediately applied to data from PC-I and the subsequent computed tomographic images were dubbed PET images as an acronym for positron emission tomography.
	www.mit.edu /~glb/node4.html (627 words)

	Patent 4219876: Computed tomography using radiation
		When modified projection data are calculated by means of interpolation from the profile of recast projection data the required calculations may be considerably reduced by properly selecting the second sampling interval which is determined with respect to the pitch of the picture element arrangement and penetration direction of the radiation beam.
		The measured projection data thus discretely collected are inputted into a computer where a set of radiation beams passing substantially parallel with one another through the sectional portion in a given direction at a given interval is selected at each given angular direction.
		In place of the change of the sampling method of the modified projection data by the second sampling interval, another method is allowable in which the radiation beams are measured at sampling intervals depending on the penetration direction of the radiation beams, and the modified projection data sampled at the sampling interval are directly used.
	www.freepatentsonline.com /4219876.html (5319 words)

	Filtered Back-Projection
		In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram.
		The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation.
		We stress that the modification of the filter improve the reconstruction quality especially at low (faster) interpolation degrees ( n = 1); the difference between the methods becomes marginal for cubic or higher degrees ( n ≥ 3).
	bigwww.epfl.ch /publications/horbelt0202.html (404 words)

	[No title]
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	www.asstr.org /files/Collections/libertine/novels/wlp/Curt_Aldrich.Little_Beth%27s_Boyfriends.WLP-147.txt (23862 words)

	Introduction to PET Physics: Image reconstruction
		Reconstruction of images from projections is a problem to which much attention has been paid over the last 30 years, and many analytical and iterative reconstruction schema exist.
		FBP is straight-forward to implement but does have the property of amplifying noise in the signal (see section 4.3).
		FBP generalises to 3D directly if the projections can be obtained over all j as well as q.
	depts.washington.edu /nucmed/IRL/pet_intro/intro_src/section4.html (1098 words)

	Parallel Implementation of the Filtered Back Projection Algorithm for Tomographic Imaging
		The projection data as well as the response function were distributed to all the nodes; convolution was done in parallel by carrying out all the multiplications on different processors in parallel.
		This gives us the filtered projections in the discrete domain and correspond to Q(n), where the Q's are taken at the various angles at which the projections were taken, and "n" is the ray number at which the line projection was taken.
		Since lb and hb are references to the columns of the 2D matrix containing the filtered projections (mat), a double referencing is made, and the values corresponding to the low-bin and high-bin are stored in 3D matrices (lbmat and hbmat).
	www.sv.vt.edu /xray_ct/parallel/Parallel_CT.html (6435 words)

	SPECT Reconstruction
		The Fourier Transform (FT) is a mathematical operation that changes a projection's data from being a function of counts per pixel to a completely equivalent function of amplitude versus cycles/pixel.
		The process stops when most of the projections of the image are close to the values of the original projection data (i.e.
		The computer now goes through this entire process again by starting on the projections of the rows and then the columns until there are no (or minimal) differences between the estimated data projections and the true projection data that was collected.
	www.uab.edu /radiography/Nmt422/SPECT_Reconstruction.htm (732 words)

	[No title]
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	www.libraryofmoria.com /legolasgimli/whenyouarewithme.txt (23786 words)

	Comparing FBP and MFA
		The FBP method generates the minimum bias at the filter cutoff frequency of 0.8 pixel/cycle, the minimum variance at 0.1 pixel/cycle, and the minimum average MSE at 0.4 pixel/cycle.
		In this project, the cutoff frequency from 0.1 pixel/cycle to 1 pixel/cycle was examined.
		At low filter cutoff frequency for the FBP method or at low iteration number of the ML method, the image smoothness (indicated by the variance measure) is achieved at the expense of image sharpness (fidelity).
	www2.ncsu.edu /ncsu/CIL/med_imaging/reconeval/manuscript.doc.html (3174 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		A key parameter in the practical application of filtered back-projection (FBP), the standard clinical image reconstruction algorithm for positron emission tomography (PET), is the choice of a low-pass filter window function and its cut-off frequency.
		However, the filter windows and cut-off frequencies for clinical reconstruction are usually chosen empirically, based on a small sample of images and filters.
		The projection spectrum SNR measure did not prove to be an accurate indicator of subjective image quality or lesion detectability with variations in Poisson noise and image resolution.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=649393 (334 words)

	Modified Filtered Back Projection (Site not responding. Last check: 2007-11-06)
		Projections (logarithm of intensity ratio of incident and outcoming beam) which have abnormaly high values are truncated and linearly interpolated with values of neighbouring projections.
		That may not necessarily be achieved because it is possible that projection which passes many cells representing a bone might have higher value than a projection which passes some cells representing a metal implant but mostly passing through cells representing water or air.
		Comparison of prostate geometry (first), image reconstructed with filtered back projection (second), image reconstructed with modified filtered back projection (third) and a compound image (fourth): an implant was reconstructed with FBP and other parts were reconstructed with MFBP.
	www-rcp.ijs.si /~zdravkok/int_fbp/int_fbp.htm (192 words)

	Biomedical Imaging Group: CT Reconstruction (index)
		The approximation of this continuous 1D function in the Dual-spline space of degree DegOnSino of the projection is obtained by a further convolution with a B-spline.
		Number of angles at which the projections are performed (angle are equally spaced between 0 and pi), the degree of the spline space of the image, the degree of the spline-space on the sinogram.
		By Pressing the Button "Back Projection" the reconstruction is performed, and the difference image between reconstructed image and the original is computed.s.
	bigwww.epfl.ch /demo/ctreconstruction (308 words)

	[No title]
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	www.snowcrest.net /koontah/fanfic/Breath4.txt (16006 words)

	Seattle by Lava Lamp
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	www.ibiblio.org /michael/seattle (22633 words)

	A convolution back projection algorithm for local tomography (Site not responding. Last check: 2007-11-06)
		The present work deals with the problem of recovering a local image from localised projections using the concept of approximation identity.
		It is based on the observation that the Hilbert transform of an approximation identity taken from a certain class of compactly supported functions with sufficiently many zero moments has no significant spread of support.
		The main features of the algorithm are simplicity and similarity with standard filtered back projection (FBP) along with the economic use of data.
	www.austms.org.au /Publ/Jamsb/V46P3/2143.html (125 words)

	SPIDER: BP W2 (Back Projection - 2D, filtered weighted) (Site not responding. Last check: 2007-11-06)
		Calculates 2-dimensional weighted back projection reconstruction for single-tilt geometry using built-in Parzen filter function.
		The dimensions of projections do not have to be powers of two.
		If the radius of the reconstructed circle is too large comparing to the size of projections the warning is printed.
	www.strubi.ox.ac.uk /strubi/cryo/spider2000/man/bpw2.html (296 words)

	RR-1787 : The Gradient and laplacien filtered back projection operators
		We propose a way to pre-process the raw data that allow us to compute directly the reconstructed values of the gradient or of the laplacien at any location in the plane (defined with real coordinate- s) without reconstructing an image of the absorption coefficients.
		The reconstructed values of the gradient and of the laplacien correspond to the exact mathematical definition of the differentials of the image and do not imply the use of a band limited filter depending on a constant s, as proposed previously by other authors.
		For noisy data, we propose also an extension of existing FBP techniques, adapted to the computation of the gradient and of the laplacien.
	www.inria.fr /rrrt/rr-1787.html (325 words)

	Fourier Filtered Back Projection (FFBP) Techniques
		So, the technique of back projection displays a Doppler map of the S-wave sources, but convolved with a point spread function (PSF) in the relative intensity distribution, which depends on the wavelength (or velocity) dispersion of the observations.
		In applying the Fourier filter to the spectral data, the high-pass ramp filter needed to sharpen the PSF of the back-projection is given by:
		The Doppler image, produced by back projection, can be considered as ``painting down'' probability strips onto the velocity map (Horne 1991).
	mintaka.sdsu.edu /faculty/quyen/node25.html (1097 words)

	SPIDER: BP GW (Back Projection - weighted, arbitrary geometry)
		This is the first step of the weighted back projection with arbitrary geometry.
		The weighting function is the invers of the sum of the sinc-functions along the z-directions in the coordinate systems of each generating projection.
		Let PW be the projection to be weighted and PG the projection generating the sinc-function.
	www.wadsworth.org /spider_doc/spider/docs/man/bpgw.html (622 words)

	GEMSS: SPECT Image Reconstruction (Site not responding. Last check: 2007-11-06)
		Filtered back-projection is a common reconstruction algorithm, but it is only applicable to single slices.
		Modern fully 3D iterative reconstruction algorithms provide enhanced image reconstruction for the whole image volume, but this comes at the expense of high computational effort.
		Figure 1: Comparison of filtered back projection and 3D reconstruction.
	www.gemss.de /4.6/index.shtml (93 words)

	Arizona Math Awareness Week 1998 (Site not responding. Last check: 2007-11-06)
		What you are seeing is the reconstruction of a slice of a human brain by filtered back projection.
		A total of one hundred projections are made, back projected, and individually filtered.
		With a few projections, the object is blurry, but as more projections are added, it becomes clear that the original image is a human brain.
	math.arizona.edu /~maw1998/catscan/page6.html (99 words)

	SPIDER: BP WY (Back Projection - weighted, Y) (Site not responding. Last check: 2007-11-06)
		This is the first step of the weighted back projection for a tilt series with equal angular increment (not statistical).
		A series of projections is weighted by R in Fourier space.
		The direction (X or Y <> wx or wy) depends on the tilting and reconstruction geometry (see 'BP XY', the simple back projection used in the second step of the reconstruction.
	wolf.bms.umist.ac.uk /unix/spider/man/bpwy.html (234 words)

	Filtered back projection in TutorGig Encyclopedia
		In Mathematics of Medical imaging 'Filtered back projection ' is a reconstruction algorithm used to invert the Radon transform.
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	Gauss filtered back projection \dots (Site not responding. Last check: 2007-11-06)
		Gauss filtered back projection for the reconstruction of the Wigner function
		Optical homodyne tomography is a quantum state determination process, where measured quadrature distributions are averaged with appropriate sampling functions.
		In this way the result is an $s$-parametrised quasi probability distribution where the parameter is determined by the filter.
	quantum.ttk.pte.hu /~wigner/proceedings/papers/w45.htm (79 words)

	Help text on bckfil
		The filter applied is ABS(S)EXP(-(S/W)*2/2) where S is the frequency with the Nyquist frequency of one cycle/2 pixels as the maximum.
		The filter is applied to the entire spectrum.
		You may want to rebin before using it if you are only interested in a small region of your spectra, although it is a reasonably fast operation.
	lheawww.gsfc.nasa.gov /~still/molly/bckfil.html (216 words)

	Filter Design for Filtered Back-Projection guided by the interpolation model (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Filter Design for Filtered Back-Projection guided by the interpolation model (ResearchIndex)
		Filter Design for Filtered Back-Projection guided by the interpolation model (2002)
		Abstract: We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm.
	citeseer.ist.psu.edu /536107.html (312 words)

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