SYSTEM AND METHOD FOR SKIN LESION EXAMINATION USING MULTI- SPECTRAL, MULTI-SOURCE TRANSILLUMINATION
FIELD OF THE INVENTION This invention relates in general to an apparatus and method for identifying and characterizing skin specimens, such as nevi and lesions, and in particular, to a portable nevoscope which provides improved transillim ination of an area of the skin, as well as sharply focused, simultaneous viewing of the entire circumference of the area.
BACKGROUND OF THE INVENTION
A nevoscope is a device used to examine the skin in situ for lesions, nevi and the like. The nevoscope, among other tilings, provides a noninvasive means for measuring nevi thickness.
The nevoscope of the prior art is designed to be used in conjunction with a stereomicroscope, such as the Model M8 manufactured by Wild Corporation. The nevoscope in that instance comprises a vertically disposed plastic cylinder mounted around the objective lens of a stereomicroscope. The nevoscope is described in the article, "Nevoscopy: Three-Dimensional Computed Tomography of Nevi and Melanomas In Situ by Transillumination,'1 IEEE Transactions on Medical Imaging, Vol. MI-3, No. 2, Jun. 1984 by Atam P. Dhawan, Richard Gordon, and Rangaraj M. Rangayyan.
The conventional nevoscope is focused by loosening a nylon screw on a plastic cylinder and moving the plastic cylinder axially along the tube of the objective lens of a stereomicroscope. When proper focus is obtained, the nylon screw is then tightened to hold the plastic cylinder firmly in position on the stereomicroscope. This method of focusing, however, is clumsy and ill-suited to fine focusing adjustments.
A laterally disposed plastic plate with a central slot screws into the bottom of the plastic cylinder of the conventional nevoscope. The center slot is rectangular in the plane of the plastic plate and trapezoidal in its cross-sectional shape. One side of the trapezoid forms an angle of 22.5 degrees with the vertical axis of the cylinder; the other side forms an angle of 45 degrees. Two front surface mirrors are glued onto the
slated inner sides or walls of the central slot and thereby are at angles of 45 degrees and 22.5 degrees from the vertical. Unfortunately, the optical versatility of this mirror arrangement is limited in that the angle of the mirrors cannot be adjusted, and the mirrors cannot be rotated to provide a 360 degree viewing range of the skin area of interest.
The conventional nevoscope is illuminated by two fiber optic bundles which are inserted in holes drilled at 45 degree angles in opposite sides of the plastic cylinder and plate. This lighting arrangement unfortunately provides IransiUumination of poor quality due to the nonumformity of the light distribution in the region of the skin lesion.
It has been found that the clarity and focus of the image provided by a nevoscope is affected by the mechanical coupling of the bottom surface of the nevoscope with the skin area of interest. Ideally, the bottom surface of the nevoscope should be flush with the skin throughout its 360 degrees of contact. As a practical matter, this ideal arrangement has been frequently unattainable due to skin surface topography in many areas of diagnostic interest.
The prior art nevoscope is large and nonportable, making it impossible to use in practical clinical applications. The various body locations where skin lesions are present necessitate the need for a nevoscope in clinical applications that is much smaller than the nevoscope of the prior art.
Images obtained from the prior art nevoscope have been digitized and analyzed to determine lesion thickness. This analysis has included obtaining two-dimensional vertical sections and three-dimensional reconstruction of skin lesions using reconstruction methods well known in the art, such as algebraic reconstruction techniques and geometric deconvolution. These algebraic reconstruction techniques are discussed in publications such as "A Tutorial on ART (Algebraic Reconstruction Techniques)", IEEE Transactions, Nucl. Science NS-21, pp. 78-95, 1974, by Gordon and "Image Reconstruction by Wiener Deconvolution in Limited- View Computed Tomography", Applied Optics, Vol. 24, No. 23, pp. 4013-4019, Dec. 1985, by Dhawan, Rangayyan and Gordon. The thickness of the skin lesions has been obtained
from the reconstruction of the two-dimensional vertical sections. Methods employed to calculate lesion thickness are discussed in, "Nevoscopy: Three-Dimensional Computed Tomography of Nevi and Melanomas In Situ by Transillumination supra, and in "Computed Tomography By Transillumination to Detect Early Melanoma," IEEE Frontiers of Engineering and Computing in Health Car (1984) pp. 518-522, by Atam P. Dhawan, Richard Gordon, and Rangaraj M. Rangayyan.
U.S. Patent 5, 146,923 to Dhawan discloses a portable nevoscope that can view and store multiple images of the skin lesion in situ from several angles through transillumination by visible light. The multiple views are digitized and used to obtain a 3-D computer reconstruction of the skin lesion in order to measure the thickness and size of the skin lesion. The nevoscope uses a single cone-beam based on a visible light source for transillumination. Because of the use of the entire visible light spectrum, the images yielded by the prior art nevoscope suffer from multiple scattering at different wavelengths, thereby limiting the resolution of the visual, as well as the reconstructed images of the skin-leson. Thus, there is a need to reduce the effect of multiple scattering to improve the imaging, characterization and 3-D computer reconstruction of the skin lesion.
SUMMARY OF THE INVENTION This invention relates to a system for skin lesion examination using multi- spectral, multi-source transillumination. The system comprises an illuminator for providing a source of electromagnetic energy at different wavelengths, a nevoscope optically coupled to the illuminator for ttansilluminating the skin lesion, a storage device coupled to the nevoscope for recording multiple images of the rransilluminated skin lesion, and a processor coupled to the storage device for generating a three- dimensional reconstruction of the transilluminated skin lesion from the stored images. The nevoscope includes an illuminator ring having a plurality of concentric waveguide rings. Each waveguide ring transilluminates the skin lesion by directing the different wavelengths from the illuminator into an area surrounding the skin lesion.
In another aspect of the invention, a nevoscope for multi-spectral, multi-source tiansulumination of a skin abnormality comprises a lens housing, a mirror housing coupled to the lens housing; and an illuminator ring coupled to the mirror housing. The illuminator ring has a plurality of concentric waveguide rings. Each waveguide ring transilluminates the skin abnormality by directing a different wavelength from a source of electromagnetic energy into an area surrounding the skin abnormality.
In a preferred method of the invention for analyzing a skin lesion, the method comprises the steps of: a) transilluminating the skin of the patient surrounding the skin lesion using a nevoscope including an illuminator ring having a plurality of concentric waveguide rings, each waveguide ring capable of transilluminating the skin lesion by directing a different wavelength from a source of electromagnetic energy into an area surrounding the skin lesion; b) obtaining multiple images of the transilluminated skin lesion; c) digitizing each of the multiple images of the skin lesion; and d) computing an image reconstruction of the digitized images. Various objects and advantages of this invention will become apparent to those skilled in the art from the following detailed description of the preferred embodiment, when read in light of the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a block diagram view of a system for skin lesion examination using multi-spectral, multi-source transillumination according to a preferred embodiment of the invention.
Fig. 2 is an exploded side perspective view of the nevoscope of the invention. Fig. 3 is a bottom view of the illuminator ring according to a first preferred embodiment of the invention.
Fig. 4 is a cross sectional view taken along line 4-4 of the illuminator ring shown in Fig. 3.
Fig. 5 is a partial cutaway view of the illuminator ring shown in Fig. 3.
Fig. 6 is a bottom view of the illuminator ring with a filter plate attached to the bottom of the illuminator ring.
Fig. 7 is a cross sectional view taken along line 7-7 of the illuminator ring shown in Fig. 6. Fig. 8 is a illustration of a simplified model derived from diffusion theory for approximating the voxel sensitivities for a homogeneous medium.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to the drawings, there is illustrated in Fig. 1 a block diagram of a multi-spectral (MST) imaging system, shown generally at 10, used to detect, analyze and diagnose a skin lesion according to a preferred embodiment of the invention.
The system 10 includes a nevoscope 12 for providing the multi-spectral transillumination of the skin lesion. Referring now to Fig. 2, the nevoscope 12 is shown in more detail. The nevoscope 12 includes a portable lens housing 14, an eyepiece 16 that is slidably inserted into the top center section of the lens housing 14, and a mirror housing 18. A camera 20 (Fig. 1), for example, a CCD digital camera, and the like, can be positioned to record images viewed through the eyepiece 16.
The lower section of lens housing 14 contains female threads which receive male threads on the upper portion of the mirror housing 18. These threads provide a means for coupling the mirror housing 18 and the lens housing 14, as well as a means to adjust the lenses of the eyepiece 16 with respect to the skin lesion. Other methods of mechanical coupling well known in the mechanical arts are suitable to couple the lens housing 14 and the mirror housing 18. The lens housing, 14, the eyepiece 16, and the mirror housing 18 are described in U.S. Patent No. 5,146,923 to Dhawan, issued September 15, 1992, and is hereby incorporated by reference.
An illuminator ring 24 surrounds the lower section of the rnirror housing 18. Preferably, the illuminator ring 24 is fastened to the mirror housing 18 by press fitting the illuminator ring 24 onto the mirror housing 18. Alternatively, the illuminator ring 24 can be fastened to the mirror housing 18 using any conventional means in the art, such as a thumbscrew, and the like.
Referring now to Figs. 3-5, the illuminator ring 24 is shown according to a first preferred embodiment of the invention. The illuminator ring 24 includes an inner wall 26 and an outer wall 28 which converge radially inward in a conical configuration at an angle matching that of the lower portion of mirror housing 18. An opening is formed in the bottom of the inner wall 26 to form a lesion housing 30. A bundle cable 32 carrying a plurality of fiber cables, for example, five separate cables of fiber optic filaments 34, 36, 38, 40 and 42 are positioned in the illuminator ring 26 such that their tight is directed downward at an angle, for example, approximately forty-five degrees through the bottom of the illuminator ring 26, through one or more of a plurality of concentric optical waveguide rings 44, 46, 48, 50 and 52, and onto the area of skin surrounding the skin lesion to deliver uniform transillumination of the skin lesion. The light which penetrates the skin is backscattered through the skin lesion that is centrally positioned inside the lesion housing 30 to provide the transillumination. It should be realized that the downward angle of the fiber optic filaments 34, 36, 38, 40 and 42 can be any desired angle to produce the desired penetration into the skin. Each cable of fiber optic filaments 34, 36, 38, 40 and 42 directs the light uniformly into the skin of the patient around the lesion. The light from each concentric waveguide ring 44, 46, 48, 50 and 52 is directed into the skin so as to create in the skin around the lesion a conical converging ring of light, indicated by the dashed lines in Fig. 4. Each cable of fiber optic filaments 34, 36, 38, 40 and 42 focuses the light at a specific point, which may be up to 5 mm below the center of the concentric waveguide rings 44, 46, 48, 50 and 52. This converging conical ring of light from each waveguide ring 44, 46, 48, 50 and 52 creates a point of light below the lesion where the ring of light converges to a point. Achieving this point of light provides uniform illumination of the lesion by tiansillumination from witliin the skin of the patient. As a result of this uniform transillumination, accurate images of the lesion are obtained. For multi-spectral (MST) transillumination, a single waveguide ring 44, 46, 48, 50 and 52 or any quadrant of each waveguide ring 44, 46, 48, 50 and 52 may be selected at a time in a specific pattern to provide a moving-source geometry for transillumination of the skin lesion.
According to the first preferred embodiment of the invention, each concentric waveguide ring 44, 46, 48, 50 and 52 transmits electromagnetic energy, preferably in the form of visible light at a different wavelength. Since the absorption coefficient of shorter wavelengths in upper layers of skin is larger than longer wavelengths, the innermost waveguide ring 44 is preferably used for tiansillumination at the shortest wavelength with respect to the other waveguide rings 46, 48, 50 and 52. Preferably, the next innermost waveguide 46 is used for transillumination at the next shortest wavelength, and so on, such that the outermost waveguide ring 52 is preferably used for transillumination at the longest wavelength with respect to the other waveguide rings 44, 46, 48 and 50. For example, the innermost waveguide ring 44 may be used for transillumination at a wavelength in the ultra-violet (UV) frequency range; the waveguide ring 46 may be used for transillumination at a wavelength of approximately 520 nm; the waveguide ring 48 may be used for tjansillumination at a wavelength of approximately 580 nm; the waveguide ring 50 may be used for transillumination at a wavelength of approximately 610 nm; and the outermost waveguide ring 52 may be used for transillumination at a wavelength in the white light frequency range of approximately 400-700 nm. It should be realized that the invention is not limited by the number of concentric waveguide rings and the wavelength of each waveguide ring for transillumination, and that the invention can be practiced with any number of waveguide rings (concentric and/or non-concentric) than may be used for transillumination of electromagnetic energy at any desired wavelength.
Referring now to Fig. 1, the cable bundle 32 of the nevoscope 12 carries N cables of fiber optic filaments that are optically coupled to N concentric waveguide rings (where N>1) with M (where M is greater than or equal to 1) discrete sources per waveguide ring providing a total of N x M number sources of light for ttansillumination, as described above. In the illustrated example, the cable bundle 32 includes five cables of fiber optic filaments and four discrete sources per waveguide (one for each quadrant) to provide twenty sources of light for transillumination. Through the imaging system 10, transillumination through the one or more entire waveguide rings and/or through one or more waveguide ring quadrants at specific
wavelengths at different distances from the skin lesion can be obtained to acquire multi-spectral (MST) images of the transilluminated skin lesion.
The partial or full illumination of each waveguide ring 44, 46, 48, 50 and 52 can be accomplished by an electronic switching mechanism 54 for controlling the light source paths in the corresponding cable of optic fiber filaments 34, 36, 38, 40 and 42. The switching mechanism 54 can be operated by a personal computer 56 with a storage device for recording and storing multiple images of the transilluminated skin lesion. The personal computer 56 can then execute a computer program by using an appropriate central processing unit (CPU) to generate a three-dimensional reconstruction of the skin lesion from the stored images. The CPU can be of a well- known type, such as a Motorola HC/MC681 1, Intel Pentium II, and the like. The computer program can be written in a higher-level programming language of a type well-known in the art, such as assembly, BASIC, FORTRAN, C++, and the like.
The imaging system 10 preferably includes a single source of electromagnetic energy, such as an illuminator 58 containing a mercury or halogen light bulb, in conjunction with a filter assembly 60 to provide the different wavelengths through the plurality of waveguide rings 44, 46, 48, 50 and 52. In the embodiment shown in Fig. 1, the filter assembly 60 is positioned between the illuminator 58 and the bundle cable 32. In an alternative embodiment of the invention shown in Figs. 6 and 7, the filter assembly 60 positioned between the illuminator 58 and the nevoscope 12 can be replaced by a filter plate 62 attached to the bottom of the illuminator ring 24 of the nevoscope 12. The filter plate 62 preferably includes a plurality of concentric ring of filters 64, 66, 68, 70, and 72 that correspond to the waveguide rings 44, 46, 48, 50 and 52 of the illuminator ring 24. Preferably, the plurality of concentric ring of filters 64, 66, 68, 70 and 72 are precisely aligned with the waveguide rings 44, 46, 48, 50 and 52 of the illuminator ring 24 to transilluminate the skin lesion with the desired wavelength of electromagnetic energy. This can be accomplished by using means of a type well-known in the art, such as clips 74, to attach the filter plate 62 to the outer surface 26 of the illuminator ring 24. One advantage of this embodiment is that the
wavelength of electromagnetic energy to transilluminate the skin lession can be easily modified by attaching the appropriate filter plate 62 to the bottom of the nevoscope 12.
Using the filter arrangements given above, the multi-spectral imaging system 10 of the invention can be operated in several modes. One mode of operation is called the epi-illumination mode. In this mode, a specific waveguide ring 44, 46, 48, 50 and 52 (or one or more quadrants of the waveguide ring) with a corresponding wavelength of electromagnetic energy is used for transillumination of the skin lesion. In addition, an additional white-light based point source is used at one or more selected outlets from the inner wall of the nevoscope cylinder for providing directional or uniform surface illumination.
Another mode of operation is called the tiansillumination mode. In a manner similar to the epi-illumination mode, a specific waveguide ring 44, 46, 48, 50 and 52 (or one or more quadrants of the waveguide ring) with a corresponding wavelength of electromagnetic energy is used for transillumination of the skin lesion. However, no surface light source is used for surface illumination.
Yet another mode of operation is called the fluorescence transillumination mode. In this mode, the innermost waveguide ring 44 of ultraviolet (UV) light wavelength (for example, 350-400 nm) is used for transillumination. The images are then collected through specific narrow-band pass filters in the visible light range, preferably in the 400-550 nm range.
The method of image reconstruction using multi-spectral (MST) techniques will now be described. In general, the propagation of light in turbid media is most accurately described by analytic theories based on Maxwell's equations and electromagnetic wave theory. However, due to their theoretical complexity, nonavailability of solutions for arbitrary geometry and the lack of information regarding the media being probed, this approach is not pursued in tissue optics. The transport equation, which is a radiant energy balance equation, describes the extinction of a beam of radiant energy due to scattering and absorption. Individual photons that
traverse along random paths witirin a medium experience elastic scattering and absorption events at discrete sites.
The fundamental quantity for light characterization in transport theory is the angular radiant intensity L(r,Ω), often called the radiance. The radiant energy fluence rate is the integral of the radiant intensity over all directions. The magnitude and direction of the net power flow are represented by a flux vector. Witriin the context of transport theory, the optical properties of a medium are described by essentially three wavelength-dependent parameters: the absorption coefficient μa (mm"1), the scattering
coefficient μs (mm" ), and the scattering phase function p(CΪ ->Ω) . The coefficients μa and μs are macroscopic constants that represent the rates of radiance loss per unit length due to absorption and scattering respectively. Usually, the absorption and scattering parameters are lumped together and are represented by a single parameter,
μh the total linear attenuation coefficient. The phase function, p(Ω! ->Ω) , describes the scattering angular distribution at a single scattering event, where a photon is
deflected from an initial direction Ω' to a new direction Ω . A common assumption is
that p(Ω! ->Ω) is a function of only the angular separation between the incident and
emerging directions, i.e. p(Ω! -» Ω) = p(μ) , where μ = (Ω'- Ω) is the cosine of the scatter angle. The exact form oip(μ) is often unknown but it is concisely represented by a single parameter, g, the anisotropy factor, which is equal to the average cosine of the scatter angle. The value of g varies from -1 to 1, with g = -1 for purely backward directed scattering, g = 0 for isotropic scattering, and g = 1 for purely forward directed scattering.
The defining equation of transport theory is the transport equation. Let S(r,Ω) be the intensity of an isotropic source at r. The steady state, single wavelength transport equation is given by
Ω • V/r r, Ω) = -μtIr (r, Ω) + (/, (r, Ϊ)p(Ω' → ϊ)dCl' + S(r, Ω) (1)
The transport equation can be solved by several numerical methods including Monte Carlo methods based on random sampling of appropriate probability distribution functions. Monte Carlo simulation of photon transport in random media like tissues has been extensively investigated for estimation of tissue parameters and for comparison with diffusion theory. The Monte Carlo particle simulation, though simple in concept, is computationally expensive. However, a diffusion theory based approach has been analytically shown to be close to the Monte Carlo particle simulation techniques. Diffusion Approximation
The diffusion approximation may be derived from the functional expansion method of solving the transport equation. The angular intensity I(r,Ω) and the phase function are expanded in terms of a finite series of orthogonal functions in the angular variable Ω. This leads to the PN approximation to the transport equation. Limiting N to 1 leads to the Pt approximation, and the resulting equation is the Diffusion equation. Letting ψ(r) represent the fluence and 3 represent the flux, the intensity can be expressed as:
The source function can be expressed as
S(Ω,r) = s°(r) + 3 ~s ι(r) - n After decoupling the fluence and flux vectors, algebraic manipulation of the equations leads to the diffusion equation in terms of the fluence as
-V • D(r) V ψ(r) + μ
*(r)ψ(r) = s
*(r) - 3 V • D(r)
→s ,(r) where D(r) is the spatially dependent photon diffusion coefficient given by
D r) = l - [μa(r) + μλr){l - gj\ The basic premise of diffusion theory is that the intensity Ir has weak angular dependence, i.e. it is essentially isotropic. For a purely isotropic source, ^and 3 are related by Fick's law, which states that the flux vector is proportional to the negative gradient of the flux density. Under the assumptions of a homogeneous medium and an
isotropic source term, the diffusion equation further simplifies to the scalar Helmholtz equation.
- DV2ψ(r) + μaψ(r) = s0(r) Photon Diffusion Theory Based Model
Referring now to Fig. 8, a simplified model has been derived from diffusion theory for computing the voxel sensitivities for a homogeneous medium. This model is deterrninistic and incorporates the salient features of the more rigorous perturbation Monte-Carlo model at much lower computational costs. A detector's sensitivity to local changes in the absorption coefficient, under the perturbation assumption, is computed as the product of the forward and adjoint fluence rates. In this model, the forward and adjoint fluence rates are computed using Farrell's dipole diffusion solution. A photon introduced into the medium experiences its first collision at a distance equal to the mean free path (MFP) along the axis of the source. After the first collision, further scattering is isotropic. The fluence due to this isotropic point source is given by
where r
t is the distance from the embedded source and r
2 is the distance from the negative image source. By the reciprocity principle, the adjoint fluence is computed by applying the same method of images to a point collimated source positioned one transport mean free path along the detector axis. Thus, three points are considered in deteπnining detector sensitivities, the two locations of first and final scatter, and the point for which the detector sensitivity is being computed. The method uses the actual fluence distribution to estimate the photon distribution paths, but does not normalize it with respect to the source intensity or geometry. The Hybrid Three-Point Diffusion Model
The three-point diffusion model is based on the approximation to the transport equation resulting in the diffusion equation. For distances close to the source or the detector, the quantities calculated by this model are not in good agreement with analytical Monte Carlo simulation results. The three-point diffusion model provides
more precise information for optical distances greater than one mean free path. Skin is a layered tissue and each layer is optically and structurally different. The outer skin layer absorbs more light, while the dermis is less absorbing with higher scattering. A new hybrid model is necessary to compute the reconstruction weights in the volume of interest for all depths of interest. For distances less than one mean free path, the weights are computed by the straight-line model. For distances greater than one mean free path, the weights are deteirnined by the diffusion model alone. Let r be the distance of the voxel from either the source or the detector, depending on the computed quantity (source filter function or detector filter function). Then, for any voxel V(x,y,z) belonging to the volume, the weights are computed as j S(μa r) iϊ r(x,y,z) ≤ MFP
X' y, Z [S(μeff,r) - D(μeff,r) otherwise
For those photons that interact at distances less than one mean free path from the point of injection to the first scatter site, the weights are provided by Beer's law to account for a photon's loss of energy as it penetrates into the tissue. At all other interactions the weights are provided by the Green's function solution to the Diffusion
Equation, accounting for both absorption and scattering.
Inverse Process - Image Reconstruction Algorithm
The ring light source is modeled as simultaneously illuminated point light sources along the circumference of an annular ring. Let a point on the ring light source be denoted by (x,y) and let d(x,y) be a distribution function for the formation of the cone-beam emerging from the ring-light, then the source function, Sp at this point is given by a simple convolution as
Sp (x,y) = S * d(x,y) fl .O if ((x - dx)2 + (y - dy)2) ≤ (r - dr)2 [0.0 otherwise where S represents the ring light source.
For the purposes of development of the algorithm, the medium is assumed to be homogeneous and isotropic. Let the medium be denoted by a region 91 which is discretized into f by Y by Z voxels. The resolution of the voxel depends on the reconstruction dimensions. Even though the medium to be reconstructed is an
irregular semi-iiifinite geometry, the detector volume limits the reconstruction area to the volume of source-detector paths that can be estimated. This volume is modeled by a regular cubic volume of dimensions X, Y, Z voxels. Let the volume be denoted by V(x,y,z). A photon detected either by the CCD directly or through the mirror at any angle must have traveled along a ray path between the detector point and the detected volume along the direction cosines of the ray. Let the optical properties of the medium described by the voxel be μ{x,y,z). Let D(xd,yd) be the intensity of light detected by the detector at any (x,y,z) belonging to the detector field of view along a plane defined by the detector. Let S x,y,z) be a measure of contribution of a voxel at (x,y,z) for the photon distribution paths, between the source at (xs,ys) to the entire detected volume. Then, by the principle of Reciprocity, we can estimate the detected field of view for any detector placed at D(xdlyd). Let Dj(x,y,z) be a measure of contribution of a voxel for the detected field of view. Thus, the overall "weight" of a voxel for a contribution for detected intensity can be defined as W(x,y,z) = Sf(x,y,z)- Df(x,y,z) where S(x,y,z) and Dj(x,y,z) are both functions of μ{x,y,z).
Assuming a linear perturbation model, for any point source illuminating the medium, the detected intensity at D(xd,yd) can be written to model the forward process as D(xd,yd)= ∑W(x,y,z) - V(x,y,z)
ΪR
Image Reconstruction
Considering the non-linearity of the problem, and the availability of limited and truncated projections, a 3-D reconstruction approach based on algebraic reconstruction technique (ART) is proposed. Let dV(x,y,z) be the perturbation that is being estimated in the i'h iteration. Then, following an iterative ART method,
∑ W{x,y, z) ■ (p xd , yd ) - E"* (xd , yd )) V' (x,y,z) = V- x,y,z) +-2 -—
∑W(x,y,z)
∑fy(x,y,z) - V" (x,y, z)) where £'-1 (xd, yd) = — ^ is the estimated projection at (x,y).
∑ W(x,y.z)
This iterative process is repeated for n iterations.
The weights as provided by the hybrid model (forward process) are used in the iterative reconstruction procedure. The weight matrix is computed using the hybrid model described above. The first estimate of the unknown volume, V°(x,y,z), is obtained from the divergent-beam based ART reconstruction method as outlined above. These weights are calculated based on the geometrical considerations. The estimate of V°(x,y,z) is used in the hybrid diffusion model based ART reconstruction algorithm where the weight matrix is computed from the hybrid diffusion model based forward process.
In this algorithm, the reconstructed volume, V1(x,y,z) is then computed in the first iteration. Vl(x,y,z) is then backprojected using the same weight matrix to compute the estimated projections, Ff(x ,y ). The estimated projections are then compared with the measured projections (D(xd,yd) as computed from the Nevoscope images) to compute error that is used to update the initial volume reconstruction. The updated volume reconstruction is backprojected again to obtain a new estimate of the projections, as the iterations continue. The process continues until convergence when for a given weight matrix, the reconstructed volume provides minimum error between the estimated and measured projections. In accordance with the provisions of the patent statutes, the principle and mode of operation of this invention have been explained and illustrated in its preferred embodiment. However, it must be understood that this invention may be practiced otherwise than as specifically explained and illustrated without departing from its spirit or scope.