Systolic radon transform processor

Claim 2

A line-scan-to-Radon-transform converter adapted for receiving words representing the x- and y-axis Cartesian coordinate location of each pixel and words representing the amplitude of said pixel, comprising: first memory means preprogrammed with information relating to a particular value of θ, the angle relative to said x-axis at which the Radon transform is to be calculated; first multiplying means coupled to said first memory means and to sequentially receive, for each pixel in its turn, said x-axis word representing the x-position of said pixel for producing a first product signal representative of said x-axis word multiplied by a trigonometric function of θ; second multiplying means coupled to said first memory means and to receive said y-axis word representing the y-position of said pixel for producing a second product signal representative of said y-axis word multiplied by another trigonometric function of θ; adder means coupled to said first and second multiplying means for combining said first and second product signals relating to the same pixel for generating a sum signal indicative of the value of ρ at which said pixel contributes to the Radon transform for said value of θ; second memory means including individual storage locations addressed by each of a plurality of values of ρ, said second memory means being addressed by said sum signal for producing for each addressed storage location a cumulated signal representing the current value of a line integral at the value of ρ corresponding to said pixel for said value of θ; summing means coupled to said second memory means for receiving said cumulated signal from said storage location addressed by said sum signal for updating said cumulated signal at said storage location addressed by said sum signal by adding to said cumulated signal said word representing the amplitude of said pixel; and means coupled to said second memory means and adapted for being enabled for reading from said storage locations the value of said line integral for each value of ρ at said value of θ.

Claim 3

A converter according to claim 1 wherein at least one of said first and second multiplying means comprises a memory including addressable storage locations, each of which is preprogrammed with a word representing the address of said storage location multiplied by a trigonometric function of said value of θ.

Claim 4

A converter according to claim 2 wherein said one of said multiplying means is said first multiplying means, and said trigonometric function is the cosine.

Claim 5

A converter according to claim 2 wherein said one of said multiplying means is said second multiplying means, and said trigonometric function is the sine.

Claim 6

A converter array for generating the Radon transformation from a stream of x- and y-axis Cartesian coordinate words representing in turn the location of each pixel and a corresponding stream of amplitude words representing the amplitude of the corresponding pixel, comprising a plurality of Radon transform converters, each of said converters being coupled to receive said x- and y-axis words and amplitude words, each of said converters including first memory means preprogrammed with information relating to a particular value of θ individual to the converter, where θ is the angle in said Cartesian coordinate system at which the transform is to be taken, each of said converters further comprising: first multiplying means coupled to said first memory means and to sequentially receive, for each pixel in its turn, said x-axis word representing the x-position of said pixel for producing a first product signal representative of said x-axis word multiplied by the cosine of θ; second multiplying means coupled to said first memory means and to receive said y-axis word representing the y-position of said pixel for producing a second product signal representative of said y-axis word multiplied by the sine of θ; adder means coupled to said first and second multiplying means for adding together said first and second product signals relating to the same pixel for generating a sum signal indicative of the value of ρ at which said pixel contributes to the Radon transform for said value of θ; second memory means including individual storage locations addressed by each of a plurality of values of ρ, said second memory means being addressed by said sum signal for producing for each addressed storage location a cumulated signal representing the current value of a line integral at the value of ρ corresponding to said pixel for said value of θ; summing means coupled to said second memory means for receiving said cumulated signal from said storage location addressed by said sum signal for updating said cumulated signal at said storage location addressed by said sum signal by adding to said cumulated signal said word representing the amplitude of said pixel; and means coupled to said second memory means and adapted for being enabled for reading from said storage locations the value of said line integral for each value of ρ at said value of θ.

Claim 7

A converter array for generating the Radon transformation from a stream of x- and y-axis Cartesian coordinate words representing in turn the location of each pixel and a corresponding stream of amplitude words representing the amplitude of the corresponding pixel, comprising a plurality of Radon transform converters, each of said converters being coupled to receive said x- and y-axis words and amplitude words, each of said converters including first memory means preprogrammed with information relating to a particular value of θ individual to the converter, where θ is the angle in said Cartesian coordinate system at which the transform is to be taken, each of said converters further comprising: first multiplying means coupled to said first memory means and to sequentially receive, for each pixel in its turn, said x-axis word representing the x-position of said pixel for producing a first product signal representative of said x-axis word multiplied by the cosine of θ; second multiplying means coupled to said first memory means and to receive said y-axis word representing the y-position of said pixel for producing a second product signal representative of said y-axis word multiplied by the sine of θ; adder means coupled to said first and second multiplying means for adding together said first and second product signals relating to the same pixel for generating a sum signal indicative of the value of ρ at which said pixel contributes to the Radon transform for said value of θ; second memory means including individual storage locations addressed by each of a plurality of values of ρ, said second memory means being addressed by said sum signal for producing for each addressed storage location a cumulated signal representing the current value of a line integral at the value of ρ corresponding to said pixel for said value of θ; summing means coupled to said second memory means for receiving said cumulated signal from said storage location addressed by said sum signal for updating said cumulated signal at said storage location addressed by said sum signal by adding to said cumulated signal said word representing the amplitude of said pixel; and means coupled to said second memory means and adapted for being enabled for reading from said storage locations the value of said line integral for each value of ρ at said value of θ.

Claim 8

A converter according to claim 5 wherein at least one of said first and second multiplying means comprises a memory including addressable storage locations, each of which is preprogrammed with a word representing the address of said storage location multiplied by a trigonometric function of said value of θ.

Claim 11

A method according to claim 7 further comprising the step of: performing said multiplying the x-position signals, multiplying the y-position signals, adding, and summing together and storing steps for each of a plurality of fixed values of said fixed angle.

Claim 12

An inverse Radon transform converter for receiving words representing ρ and θ and the value of the Radon transform for each value of ρ and θ, comprising: first multiplying means coupled to receive words representative of the θ value of each pixel for generating a word representative of x cos θ, where the value of x represents a position in a rectangular x-y coordinate system for which the inverse Radon transform is to be calculated; subtracting means coupled to said first multiplying means and to sequentially receive, for each pixel in its turn, words representative of the ρ value of said pixel for producing a difference signal representing ρ-x cos θ; dividing means coupled to said subtracting means and to receive words representative of said θ value of said pixel for dividing said difference signal by sin θ to produce the quotient signal y=(ρ-x cos θ)/sin θ; summing means including a first input port coupled to receive words representative of the value M of said Radon transform of said pixels for summing said words representative of the value of M with words applied to a second input port; and memory means coupled to said dividing means and to said summing means, and including individual storage locations addressed by each of said plurality of values of y produced by said dividing means for producing for each addressed storage location a cumulated signal representing the current value of the inverse Radon transform at the value of y corresponding to said pixel for said value of x, and for applying said current value of said inverse Radon transform to said second input port of said summing means for generating an updated value of said inverse Radon transform at the output of said summing means, and for substituting said updated value at said addressed storage locations.

Claim 13

An inverse Radon transform converter for receiving words representing ρ and θ and the value of the Radon transform for each value of ρ and θ, comprising: first multiplying means coupled to receive words representative of the θ value of each pixel for generating a word representative of x cos θ, where the value of x represents a position in a rectangular x-y coordinate system for which the inverse Radon transform is to be calculated; subtracting means coupled to said first multiplying means and to sequentially receive, for each pixel in its turn, words representative of the ρ value of said pixel for producing a difference signal representing ρ-x cos θ; dividing means coupled to said subtracting means and to receive words representative of said θ value of said pixel for dividing said difference signal by sin θ to produce the quotient signal y=(ρ-x cos θ)/sin θ; summing means including a first input port coupled to receive words representative of the value M of said Radon transform of said pixels for summing said words representative of the value of M with words applied to a second input port; and memory means coupled to said dividing means and to said summing means, and including individual storage locations addressed by each of said plurality of values of y produced by said dividing means for producing for each addressed storage location a cumulated signal representing the current value of the inverse Radon transform at the value of y corresponding to said pixel for said value of x, and for applying said current value of said inverse Radon transform to said second input port of said summing means for generating an updated value of said inverse Radon transform at the output of said summing means, and for substituting said updated value at said addressed storage locations.