Abstract: The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) generated by projection of a point x-ray source (or other radiation source), positioned at a distinct focus, through the volume to a plane at which the respective projection image is acquired (“detector plane”). In one aspect, the improvements are with respect to back-projecting a two-dimensional representation lying in the detector plane (representing, for example, a difference between an originally-acquired measured projection image and a subsequently-generated estimate thereof) to generate three-dimensional representation (which can be used, for example, to update an estimate of the volume).

Abstract: Improved methods of operating a digital data processor to perform binary division include estimating reciprocals of at least selected divisors based on value accessed from a look-up table. For divisors in a first numerical range, the estimation can be based on a value stored in a first look-up table at an index defined by the divisor. For divisors in a second numerical range, the estimation can be based on an index that is a bitwise-shifted function of the divisor. The methods can be applied to scalar and vector binary division.

Abstract: The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) generated by projection of a point x-ray source (or other radiation source), positioned at a distinct focus, through the volume to a plane at which the respective projection image is acquired (“detector plane”). In one aspect, the improvements are with respect to back-projecting a two-dimensional representation lying in the detector plane (representing, for example, a difference between an originally-acquired measured projection image and a subsequently-generated estimate thereof) to generate three-dimensional representation (which can be used, for example, to update an estimate of the volume).

Abstract: The invention provides improved methods and systems for rapidly performing a median filter calculation for a value at a predetermined position in a matrix of values representing a neighborhood about the predetermined position. The method includes ordering the values in each column of the matrix to create an ordered matrix having rows; determining a maximum value for a row of the ordered matrix having the lowest values; determining a median value for a row of the ordered matrix having middle values; and determining a minimum value for a row of the ordered matrix having the highest values. Based on these determinations, the median filter value for the neighborhood can be calculated as a second median value of the maximum value for a row of the ordered matrix having the lowest values, median value for a row of the ordered matrix having middle values, and minimum value for a row of the ordered matrix having the highest values. The calculated median filter value can then be output as necessary.

Abstract: The invention provides improved methods and systems for generation of square roots of vector and administrative operands. The methods utilize bit-manipulation operations to halve intermediate values, generated by a processor reciprocal square root operation, during a multistep process square root determination. Such methods can also multiply an original operand (whose square root is being determined) with such an intermediate value, e.g., or a halved or other value thereon. The invention also provides methods and apparatus for determination of square roots square roots of large groups of numbers by interleaving vector and administrative instructions to take advantage of necessary delays in the vector processing pipeline architecture to speed overall processing.