Abstract: A system and three methods are provided for massively parallel Magnetic Resonance Imaging of an object. They are based on using numerous, perhaps hundreds of, radio frequency receiver coils that measure Magnetic Resonance (MR) signal. In particular, the receiver coils are arranged both on-surface, i.e. relatively close and roughly parallel to the object surface, as well as off-surface, i.e. relatively distant or at a significant angle, such as 45 or 90 degrees, with respect to the object surface. The coils are arranged in a three-dimensional volume space at different positions, orientations, and distances, possibly in multiple layers. Each receiver coil is associated with a sensitivity map and provides partially under-sampled MR signal data with respect to frequency, phase, or k-space. The data from all coils are combined, using all the sensitivity maps in the image space or k-space, to obtain over-sampled data which is processed to reconstruct an unaliased image.

Abstract: Apparatus for measuring magnetic field intensity characteristics around a target object enclosed in a 3D volume space is disclosed. It comprises (a) a means for magnetically polarizing the target object with a known polarizing magnetic field to introduce a magnetic density distribution (MDI) f(r1), (b) a means for measuring magnetic field characteristics g(r2) around the target object at a set of points r2 in a 3D volume space that in particular extends substantially along a radial direction pointing away from the approximate center of the object, (c) a means for setting up a vector-matrix equation; and (d) a means for solving this vector-matrix equation and obtaining a solution for f(r1) that provides a 3D tomographic image of the target object. This novel apparatus is integrated with frequency and phase encoding methods of Magnetic Resonance Imaging (MRI) technique in prior art to achieve different trade-offs.

Abstract: Three-dimensional (3D) tomographic image of a target object such as soft-tissue in humans is obtained in the method and apparatus of the present invention. The target object is first magnetized by a polarizing magnetic field pulse. The magnetization of the object is specified by a 3D spatial Magnetic Density image (MDI). The magnetic field due to the magnetized Object is measured in a 3D volume space that extends in all directions Including substantially along the radial direction, not just on a surface as in prior art. This measured data includes additional information overlooked in prior art and this data is processed to obtain a more accurate 3 D image reconstruction in lesser time than in prior art. The methods and apparatuses of the present invention are combined with frequency and phase encoding techniques of Magnetic Resonance imaging (MRI) technique in prior art to achieve different trade-offs.

Abstract: Field Image Tomography (FIT) is a fundamental new theory for determining the three-dimensional (3D) spatial density distribution of field emitting sources. The field can be the intensity of any type of field including (i) Radio Frequency (RF) waves in Magnetic Resonance Imaging (MRI), (ii) Gamma radiation in SPECT/PET, and (iii) gravitational field of earth, moon, etc. FIT exploits the property that field intensity decreases with increasing radial distance from the field source and the field intensity distribution measured in an extended 3D volume space can be used to determine the 3D spatial density distribution of the emitting source elements. A method and apparatus are disclosed for MRI of target objects based on FIT. Spinning atomic nuclei of a target object in a magnetic field are excited by beaming a suitable Radio Frequency (RF) pulse. These excited nuclei emit RF radiation while returning to their normal state.

Abstract: A method of fast matrix multiplication and a method and apparatus for fast solving of a matrix equation are disclosed. They are useful in many applications including image blurring, deblurring, and 3D image reconstruction, in 3D microscopy and computer vision. The methods and apparatus are based on a new theoretical result—the Generalized Convolution Theorem (GCT). Based on GCT, matrix equations that represent certain linear integral equations are first transformed to equivalent convolution integral equations through change of variables. Then the resulting convolution integral equations are evaluated or solved using the Fast Fourier Transform (FFT). Evaluating a convolution integral corresponds to matrix multiplication and solving a convolution integral equation corresponds to solving the related matrix equation through deconvolution. Carrying-out these convolution and deconvolution operations in the Fourier domain using FFT speeds up computations significantly.

Abstract: Methods and apparatuses for 3D tomographic imaging of objects such as soft-tissues in humans are disclosed. They are similar to the Magnetic Resonance Imaging (MRI) methods and apparatuses but they are based on the new Field Paradigm founded on the principle that the field intensity distribution in a 3D volume space uniquely determines the 3D density distribution of the field emission source and vice versa. The object to be imaged is first magnetized by a polarizing magnetic field pulse. The magnetization of the object is specified by a 3D spatial Magnetic Density Image (MDI) that needs to be determined. The magnetic field due to the magnetized object is measured in a 3D volume space that extends in all directions and in particular substantially along the radial direction from the center of the object being imaged. Further, magnetic field intensity may be measured along multiple directions at each point.

Abstract: This invention discloses methods and apparatuses for 3D imaging in Magnetoencephalography (MEG), Magnetocardiography (MCG), and electrical activity in any biological tissue such as neural/muscle tissue. This invention is based on Field Paradigm founded on the principle that the field intensity distribution in a 3D volume space uniquely determines the 3D density distribution of the field emission source and vice versa. Electrical neural/muscle activity in any biological tissue results in an electrical current pattern that produces a magnetic field. This magnetic field is measured in a 3D volume space that extends in all directions including substantially along the radial direction from the center of the object being imaged. Further, magnetic field intensity is measured at each point along three mutually perpendicular directions.

Abstract: A method and apparatus are disclosed for high-sensitivity Single-Photon Emission Computed Tomography (SPECT), and Positron Emission Tomography (PET). The apparatus includes a two-dimensional (2D) gamma detector array that moves to different positions in a three-dimensional (3D) volume space near an emission source and records a data vector g. In particular, the 3D volume space in which emission data g is measured extends substantially along a radial direction r pointing away from the emission source and each photon detector element in the 2D gamma detector array is provided with a very large collimator aperture. Data g is related to the 3D spatial density distribution f of the emission source, noise vector n, and a system matrix H of the SPECT/PET apparatus through the linear system of equations g=Hf+n. This equation is solved for f by a method that reduces the effect of noise.

Abstract: Field Image Tomography (FIT) is a fundamental new theory for determining the three-dimensional (3D) spatial density distribution of field emitting sources. The field can be the intensity of any type of field including (i) Radio Frequency (RF) waves in Magnetic Resonance Imaging (MRI), (ii) Gamma radiation in SPECT/PET, and (iii) gravitational field of earth, moon, etc. FIT exploits the property that field intensity decreases with increasing radial distance from the field source and the field intensity distribution measured in an extended 3D volume space can be used to determine the 3D spatial density distribution of the emitting source elements. A method and apparatus are disclosed for MRI of target objects based on FIT. Spinning atomic nuclei of a target object in a magnetic field are excited by beaming a suitable Radio Frequency (RF) pulse. These excited nuclei emit RF radiation while returning to their normal state.

Abstract: A method and apparatus are disclosed for high-sensitivity Single-Photon Emission Computed Tomography (SPECT), and Positron Emission Tomography (PET). The apparatus includes a two-dimensional (2D) gamma detector array that, unlike a conventional SPECT machine, moves to different positions in a three-dimensional (3D) volume space near an emission source and records a data vector g which is a measure of gamma emission field. In particular, the 3D volume space in which emission data g is measured extends substantially along a radial direction r pointing away from the emission source, and unlike a conventional SPECT machine, each photon detector element in the 2D gamma detector array is provided with a very large collimator aperture. Data g is related to the 3D spatial density distribution f of the emission source, noise vector n, and a system matrix H of the SPECT/PET apparatus through the linear system of equations g=Hf+n. This equation is solved for f by a method that reduces the effect of noise.

Abstract: A method and apparatus for directly sensing both the focused image and the three-dimensional shape of a scene are disclosed. This invention is based on a novel mathematical transform named Rao Transform (RT) and its inverse (IRT). RT and IRT are used for accurately modeling the forward and reverse image formation process in a camera as a linear shift-variant integral operation. Multiple images recorded by a camera with different camera parameter settings are processed to obtain 3D scene information. This 3D scene information is used in computer vision applications and as input to a virtual digital camera which computes a digital still image. This same 3D information for a time-varying scene can be used by a virtual video camera to compute and produce digital video data.

Abstract: This invention is based on a new signal processing transform named Rao Transform (RT) which was invented recently by the author of the present invention. Forward RT provides a computationally efficient method and an associated apparatus for computing the output signal of a Linear Shift-Variant System (LSVS) from the input signal and a set of moment parameters of the linear Shift-Variant Point Spread Function (SV-PSF) that characterizes the LSVS. Inverse RT provides a computationally efficient method and an associated apparatus for computing the input signal or restored signal of an LSVS from the output signal and a set of moment parameters of the linear SV-PSF that characterizes the LSVS. This invention is useful in many applications including the restoration of defocus blurred and motion blurred images recorded by a camera with a linear SV-PSF. The apparatus include means for computing forward and inverse RT coefficients.

Abstract: A method and apparatus for directly sensing both the focused image and the three-dimensional shape of a scene are disclosed. This invention is based on a novel mathematical transform named Rao Transform (RT) and its inverse (IRT). RT and IRT are used for accurately modeling the forward and reverse image formation process in a camera as a linear shift-variant integral operation. Multiple images recorded by a camera with different camera parameter settings are processed to obtain 3D scene information. This 3D scene information is used in computer vision applications and as input to a virtual digital camera which computes a digital still image. This same 3D information for a time-varying scene can be used by a virtual video camera to compute and produce digital video data.

Abstract: This invention is based on a new class of mathematical transforms named Rao Transforms invented recently by the author of the present invention. Different types of Rao Transforms are used for solving different types of linear/non-linear, uni-variable/multi-variable integral/integro-differential equations/systems of equations. Methods and apparatus that are unified and computationally efficient are disclosed for solving such equations. These methods and apparatus are also useful in solving ordinary and partial differential equations as they can be converted to integral/integro-differential equations. The methods and apparatus of the present invention have applications in many fields including engineering, science, medicine, and economics.

Abstract: This invention is based on a new signal processing transform named Rao Transform (RT) which was invented recently by the author of the present invention. Forward RT provides a computationally efficient method and an associated apparatus for computing the output signal of a Linear Shift-Variant System (LSVS) from the input signal and a set of moment parameters of the linear Shift-Variant Point Spread Function (SV-PSF) that characterizes the LSVS. Inverse RT provides a computationally efficient method and an associated apparatus for computing the input signal or restored signal of an LSVS from the output signal and a set of moment parameters of the linear SV-PSF that characterizes the LSVS. This invention is useful in many applications including the restoration of defocus blurred and motion blurred images recorded by a camera with a linear SV-PSF. The apparatus include means for computing forward and inverse RT coefficients.

Abstract: A method based on image defocus information is disclosed for determining distance (or ranging) of objects from a camera system and autofocusing of camera systems. The method uses signal processing techniques. The present invention includes a camera characterized by a set of four camera parameters: position of the image detector inside the camera, focal length of the optical system in the camera, the size of the aperture of the camera, and the characteristics of the light filter in the camera. In the method of the present invention, at least two images of the object are recorded with different values for the set of camera parameters. The two images are converted to one-dimensional signals by summing them along a particular direction whereby the effect of noise is reduced and the amount of computations are significantly reduced. Fourier coefficients of the one-dimensional signals and a log-by-rho-squared transform are used to obtain a calculated table.

Abstract: The present invention is a method and apparatus for determining the distance of a surface patch of an object from a camera system and also for focusing a surface patch of such object as well as obtaining an improved focus image of the surface patch. The present invention also includes a method of determining a set of unknown parameters of a linear shift-invariant system. The camera system of the present invention has an aperture through which light enters, an image detector, an image forming optical system having first and second principal planes and a focal length, the second principal plane arranged closer to the image detector than the first principal plane, a light filter, a camera controller, and an image processor operatively connected to the image detector and to the camera controller.

Abstract: Apparatus and methods based on signal processing techniques are disclosed for determining the distance of an object from a camera, rapid autofocusing of a camera, and obtaining focused pictures from blurred pictures produced by a camera. The apparatus of the present invention includes a camera characterized by a set of four camera parameters: position of the image detector or film inside the camera, focal length of the optical system in the camera, the size of the aperture of the camera, and the characteristics of the light filter in the camera. In the method of the present invention, at least two images of the object are recorded with different values for the set of camera parameters. The two images are converted to a standard format to obtain two normalized images. The values of the camera parameters and the normalized images are substituted into an equation obtained by equating two expressions for the focused image of the object.

Abstract: The present invention concerns a method of determining the distance between a surface patch of a 3-D spatial scene and a camera system. The distance of the surface patch is determined on the basis of at least a pair of images, each image formed using a camera system with either a finite or infinitesimal change in the value of at least one camera parameter. A first and second image of the 3-D scene are formed using the camera system which is characterized by a first and second set of camera parameters, and a point spread function, respectively, where the first and second set of camera parameters have at least one dissimilar camera parameter value. A first and second subimage is selected from the first and second images so formed, where the subimages correspond to the surface patch of the 3-D scene, the distance from which to the camera system, is to be determined.