Abstract: Plasma concentration of a compound of interest is measured in two or ideally 4 or more blood samples taken from a patient over a period of time following bolus injection. The measured values are input into a computer processor programmed to execute a computer program comprising an algorithm that uses the gamma variate (GV) function to model drug plasma concentration, then uses Tikhonov regularization to perform the fit, selecting a regularization constant so that the relative error in the plasma clearance is minimized. One or more output values representative of renal function are generated.

Abstract: A method is provided for decompressing an image originally compressed using a known compression technique. An original compressed image file is defined by a plurality of locations that correspond to image data. A set of smooth test images is created by iteratively applying a plurality of different size PIXON® kernels to each location of a starting image beginning with a smallest size kernel. Each smooth test image is compressed using the known compression technique, then compared against the original compressed image at each location of the image to determine a goodness-of-fit of the compressed smooth test image to each location of the original compressed image file. For each location, the smooth test image that has the largest size kernel that passes a pre-determined goodness-of-fit criterion is selected for a given location of the decompressed image. A compression method utilizes the PIXON® method for optimization of knot points within an image.

Abstract: Plasma concentration of a compound of interest is measured in two or ideally 4 or more blood samples taken from a patient over a period of time following bolus injection. The measured values are input into a computer processor programmed to execute a computer program comprising an algorithm that uses the gamma variate (GV) function to model drug plasma concentration, then uses Tikhonov regularization to perform the fit, selecting a regularization constant so that the relative error in the plasma clearance is minimized. One or more output values representative of renal function are generated.

Abstract: A method is provided for decompressing an image originally compressed using a known compression technique. An original compressed image file is defined by a plurality of locations that correspond to image data. A set of smooth test images is created by iteratively applying a plurality of different size PIXON® kernels to each location of a starting image beginning with a smallest size kernel. Each smooth test image is compressed using the known compression technique, then compared against the original compressed image at each location of the image to determine a goodness-of-fit of the compressed smooth test image to each location of the original compressed image file. For each location, the smooth test image that has the largest size kernel that passes a pre-determined goodness-of-fit criterion is selected for a given location of the decompressed image. A compression method utilizes the PIXON® method for optimization of knot points within an image.

Abstract: A computer-based system and method are provided to determine the minimum number of factors required to account for input data by seeking an approximate minimum complexity model. In an exemplary embodiment, covariance in the daily returns of financial securities is estimated by generating a positive-definite estimate of the elements of a covariance matrix consistent with the input data. Complexity of the covariance matrix is minimized by assuming that the number of independent parameters is likely to be much smaller than the number of elements in the covariance matrix. Each variable is described as a linear combination of independent factors and a part that fluctuates independently. The simplest model for the covariance matrix is selected so that it fits the data to within a specified level as determined by the selected goodness-of-fit criterion.

Abstract: Input data comprising a video signal is processed using a combination of a known image processing method to deblur, or sharpen, the image and convolution with Pixon™ kernels for smoothing. The smoothing process utilizes a plurality of different size Pixon™ kernels which operate in parallel so that the input data are convolved with each different Pixon™ kernel simultaneously. The smoothed image is convolved with the point response function (PRF) to form data models that are compared against the input data, then the broadest Pixon™ kernel that fits the input data within a predetermined criterion are selected to form a Pixon™ map. The data are smoothed and assembled according to the Pixon™ map, then are deconvolved and output to a video display or other appropriate device, providing a clearer image with less noise.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape size, and/or position) as needed to best fit the data.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.