Processing of performance sensitive transforms
First Claim
1. A computer implemented method of reducing an error in an output of a digital image processed using a discrete cosine transform equation, the method comprising:
- receiving the digital image for processing using the discrete cosine transform equation;
determining integer numerators and floating point denominators to approximate floating point coefficients of sub-transforms of the discrete cosine transform equation;
determining truncation errors generated from performing multiplication operations using the integer numerators, wherein the multiplication operations are implemented as shift right bit operations;
approximating a cumulative error in an output of the discrete cosine transform equation based on the truncation errors generated from performing the multiplication operations in the sub-transforms;
modifying at least one of the sub-transforms in the discrete cosine transform equation by changing at least one of an addition operation to a subtraction operation and a subtraction operation to an addition operation performed within the at least one of the sub-transforms to reduce the cumulative error in the output of the discrete cosine transform equation;
generating a modified discrete cosine transform equation including the modified at least one sub-transform; and
processing the digital image using the modified discrete cosine transform equation to generate the output.
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Accused Products
Abstract
The present invention provides a method, apparatus, and article of manufacture for controlling truncation error which is introduced when performing a transform equation as a result of lowering the precision of elements of the equation using shift right operations. This is achieved by associating a predetermined truncation amount with a plurality of operations of the transform equation and defining an ordered set of the operations to perform the transform which control the truncation error in the result if each operation introduced the predetermined truncation amount associated with it. Accordingly the transform is performed using the defined ordered set. For example the pre-determined truncation error could be an average truncation error.
11 Citations
18 Claims
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1. A computer implemented method of reducing an error in an output of a digital image processed using a discrete cosine transform equation, the method comprising:
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receiving the digital image for processing using the discrete cosine transform equation; determining integer numerators and floating point denominators to approximate floating point coefficients of sub-transforms of the discrete cosine transform equation; determining truncation errors generated from performing multiplication operations using the integer numerators, wherein the multiplication operations are implemented as shift right bit operations; approximating a cumulative error in an output of the discrete cosine transform equation based on the truncation errors generated from performing the multiplication operations in the sub-transforms; modifying at least one of the sub-transforms in the discrete cosine transform equation by changing at least one of an addition operation to a subtraction operation and a subtraction operation to an addition operation performed within the at least one of the sub-transforms to reduce the cumulative error in the output of the discrete cosine transform equation; generating a modified discrete cosine transform equation including the modified at least one sub-transform; and processing the digital image using the modified discrete cosine transform equation to generate the output. - View Dependent Claims (2, 3, 4, 5, 6)
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7. An apparatus for reducing an error in an output of a digital image processed using a discrete cosine transform equation, the apparatus comprising:
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a processor configured to receive the digital image for processing using the discrete cosine transform equation to determine integer numerators and floating point denominators to approximate floating point coefficients of sub-transforms of the discrete cosine transform equation, and to determine truncation errors generated from performing multiplication operations using the integer numerators, wherein the multiplication operations are implemented as shift right bit operations; and a transformer configured to approximate a cumulative error in an output of the discrete cosine transform equation based on the truncation errors generated from performing the multiplication operations in the sub-transforms, to modify at least one of the sub-transforms in the discrete cosine transform equation by changing at least one of an addition operation to a subtraction operation and a subtraction operation to an addition operation performed within the at least one of the sub-transforms to reduce the cumulative error in the output of the discrete cosine transform equation, to generate a modified discrete cosine transform equation including the modified at least one sub-transform, and to process the digital image using the modified discrete cosine transform equation to generate the output. - View Dependent Claims (8, 9, 10, 11, 12)
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13. A computer readable storage medium tangibly embodying programmed instructions which, when executed by a computer system, are operable for performing a method of reducing an error in an output of a digital image processed using a discrete cosine transform, the method comprising:
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receiving the digital image for processing using the discrete cosine transform equation; determining integer numerators and floating point denominators to approximate floating point coefficients of sub-transforms of the discrete cosine transform equation; determining truncation errors generated from performing multiplication operations using the integer numerators, wherein the multiplication operations are implemented as shift right bit operations; approximating a cumulative error in an output of the discrete cosine transform equation based on the truncation errors generated from performing the multiplication operations in the sub-transforms; modifying at least one of the sub-transforms in the discrete cosine transform equation by changing at least one of an addition operation to a subtraction operation and a subtraction operation to an addition operation performed within the at least one of the sub-transforms to reduce the cumulative error in the output of the discrete cosine transform equation; generating a modified discrete cosine transform equation including the modified at least one sub-transform; and processing the digital image using the modified discrete cosine transform equation to generate the output. - View Dependent Claims (14, 15, 16, 17, 18)
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Specification