Claims
- 1. A method for processing an original image, comprising:
selecting a known marker value related to predetermined data in the original image; placing the marker value at a known location with respect to the original image so as to modify certain of the image data; if the original image is in a base domain, transforming it to a multiple complementary components in a transform domain; communicating only one of the components as a modified image; receiving the one component for restoration; generating in a closed form, without iteration a plurality of sequences from the one component; removing the predetermined marker data from the marker location(s); combining the sequences to produce an entire restored image.
- 2. The method of claim 1 where the marker value is sufficient to ensure that the component is minimum-phase.
- 3. The method of claim 2 where the marker value is complex.
- 4. The method of claim 1 where elements of the original image are complex in the base domain.
- 5. The method of claim 4 where the original image is a composite of two independent images.
- 6. A machine-readable medium for storing program instructions for carrying out the method of claim 1.
- 7. A system for processing an original image, comprising:
a first digital processor for
selecting a known marker value related to predetermined data in the original image, placing the marker value at a known location with respect to the original image so as to modify certain of the image data, if the original image is in a base domain, transforming it to multiple complementary components in a transform domain; a first storage associated with the first processor for storing at least one of the components; a channel for communicating only one of the components; a second digital processor for
receiving the one component for restoration, generating in a closed form, without iteration a plurality of sequences from the one component, removing the predetermined marker data from the marker location(s); combining the sequences to produce an entire restored image. a second storage associated with the second processor for storing the received one component
- 8. The system of claim 7 where the channel transmits the one component from the first processor to the second processor.
- 9. The system of claim 7 where the channel comprises a storage medium for storing the one component.
- 10. The system of claim 7 further comprising an input device for producing the original image.
- 11. The system of claim 7 further comprising an output device coupled to the second storage for receiving the restored image.
- 12. A method for processing image data representing an original image in a base domain for subsequent restoration, comprising:
selecting a known marker value related to predetermined data in the original image, where the marker value is not strictly real; placing the marker value at a known location with respect to the original image so as to modify certain of the image data in the base domain; transforming the original image including the modified image data to a transform domain having multiple complementary components; communicating less than all of the components as a modified image.
- 13. The method of claim 12 where the marker is placed in the image directly in the base domain.
- 14. The method of claim 12 where the marker is placed directly in at least one of the complementary components.
- 15. The method of claim 12 where the phase of the marker is at least 1° away from 0°, 90°, 180°, and 270°.
- 16. The method of claim 15 where the marker phase is about 45°.
- 17. The method of claim 15 where the marker phase is strictly imaginary.
- 18. A machine-readable medium for storing program instructions for carrying out the method of claim 12
- 19. A system for processing image data representing an original image in a base domain for subsequent restoration, comprising:
a processor for
selecting a known marker value related to predetermined data in the original image, where the marker value is not strictly real, placing the marker value at a known location with respect to the original image so as to modify certain of the image data in the base domain, transforming the original image including the modified image data to a transform domain having multiple complementary components; a channel for communicating less than all of the components as a modified image.
- 20. The system of claim 19 further including a source device for producing the original image.
- 21. The system of claim 20 where the source device comprises at least one of a scanner and a storage device.
- 22 The system of claim 19 where the channel transmits the one component from the processor to a network.
- 23. The system of claim 19 where the channel comprises a storage medium for storing the one component.
- 24. A method for processing an original image in a transform domain having multiple components for subsequent restoration, comprising:
selecting a known marker value in a base domain related to predetermined data for the original image in the base domain, where the marker value is not strictly real; manipulating the original image entirely within the transform domain so as to place data therein representing a transform of the known base-domain marker value at a known location in the base domain; communicating less than all of the components of the manipulated image as a modified image.
- 25. The method of claim 24 where the phase of the marker is at least 1° away from 0°, 90°, 180°, and 270°.
- 26. The method of claim 25 where the marker phase is about 45°.
- 27. The method of claim 25 where the marker phase is strictly imaginary.
- 28. A machine-readable medium for storing program instructions for carrying out the method of claim 24.
- 29. A system for processing an original image in a transform domain having multiple components for subsequent restoration, comprising:
a processor for
selecting a known marker value in a base domain related to predetermined data for the original image in the base domain, where the marker value is not strictly real, manipulating the original image entirely within the transform domain so as to place data therein representing a transform of the known base-domain marker value at a known location in the base domain; a channel for communicating less than all of the components of the manipulated image as a modified image.
- 30. The system of claim 29 further including a source device for producing the original image.
- 31. The system of claim 30 where the source device comprises at least one of a scanner and a storage device.
- 32 The system of claim 29 where the channel transmits the one component from the processor to a network.
- 33. The system of claim 29 where the channel comprises a storage medium for storing the one component.
- 34. A method for processing image data representing an original image for subsequent restoration, comprising:
selecting a known marker value related to predetermined data of the original image; placing the marker value at a known location with respect to the original image so as to modify certain of the image data; if the original image is not already represented in a transform domain having multiple complementary components, transforming it to produce such components; deriving a map representing a certain characteristic of one of the complementary components; embedding the map within another of the complementary components; communicating only the other of the components, including the embedded map, as a modified image.
- 35. The method of claim 34 where the certain characteristic comprises signs of the elements of one component.
- 36. The method of claim 35 where embedding the map comprises multiplying elements of the other component by corresponding elements of the map.
- 37. A machine-readable medium for storing program instructions for carrying out the method of claim 34
- 38. A system for processing image data representing an original image for subsequent restoration, comprising:
a processor for
selecting a known marker value related to predetermined data of the original image, placing the marker value at a known location with respect to the original image so as to modify certain of the image data, if the original image is not already represented in a transform domain having multiple complementary components, transforming it to produce such components, deriving a map representing a certain characteristic of one of the complementary components, embedding the map within another of the complementary components; a channel for communicating only the other of the components, including the embedded map, as a modified image.
- 39. The system of claim 38 further including a source device for producing the original image.
- 40. The system of claim 39 where the source device comprises at least one of a scanner and a storage device.
- 41 The system of claim 38 where the channel transmits the one component from the processor to a network.
- 42. The system of claim 38 where the channel comprises a storage medium for storing the one component.
- 43. A method for processing image data representing an original image for subsequent restoration, comprising:
selecting a known marker value related to predetermined data of the original image; placing the marker value at a known location with respect to the original image so as to modify certain of the image data; if the original image is not already represented in a transform domain having multiple complementary components, transforming it to produce such components; deriving a map representing a certain characteristic of one of the complementary components;
communicating the map and the one component as a modified image.
- 44. The method of claim 43 further comprising modifying the magnitudes of elements of the one component before deriving the map therefrom.
- 45. The method of claim 43 where the characteristic concerns the relationship of the element magnitudes of the one component to a predetermined magnitude.
- 46. The method of claim 43 where the characteristic concerns storage amounts required for the magnitudes of individual elements of the one component.
- 47. The method of claim 46 further comprising storing the individual elements of the one component in different amounts of storage, depending upon their magnitudes.
- 48. A machine-readable medium for storing program instructions for carrying out the method of claim 41
- 49. A system for processing image data representing an original image for subsequent restoration, comprising:
a digital processor for
selecting a known marker value related to predetermined data of the original image, placing the marker value at a known location with respect to the original image so as to modify certain of the image data, if the original image is not already represented in a transform domain having multiple complementary components, transforming it to produce such components; deriving a map representing a certain characteristic of one of the complementary components; a channel for communicating the map and the one component as a modified image.
- 50. The system of claim 49 further including a source device for producing the original image.
- 51. The system of claim 50 where the source device comprises at least one of a scanner and a storage device.
- 52 The system of claim 49 where the channel transmits the one component from the processor to a network.
- 53. The system of claim 49 where the channel comprises a storage medium for storing the one component.
- 54. A method for restoring an image to an original image, comprising:
receiving one component of multiple complementary components of the original image, the one component containing predetermined known marker data corresponding to one or more marker locations; generating in a closed form, without iteration, a plurality of sequences from the one component; removing the predetermined marker data from the marker location(s); combining the sequences to produce an entire restored image.
- 55. The method of claim 54 where the value of the marker data is sufficient to ensure that the original data is minimum-phase in a transform domain.
- 56. The method of claim 54 where the sequences represent even and odd parts of the original image.
- 57. The method of claim 54 where the sequences represent real and imaginary parts of the original image.
- 58. The method of claim 54 where the sequences represent real and imaginary parts of the original image.
- 59. The method of claim 54 where the marker is restricted to a complex value.
- 60. The method of claim 54 where the marker has a strictly real or strictly imaginary value.
- 61. The method of claim 54 where the sequences are approximate parts of the original image.
- 62. The method of claim 61 further comprising converting the sequences from approximate forms to exact forms.
- 63. The method of claim 51 where the received one component includes a map having an element for every element of the one component, and further comprising modifying the elements of the one component in accordance with the elements of the map.
- 64. The method of claim 63 where the map elements represent signs of elements in a component complementary to the one component.
- 65. The method of claim 63 where the map elements represent signs of elements in the one component.
- 66. The method of claim 63 where the map elements represent different lengths of individual elements in the one component.
- 67. The method of claim 66 further comprising expanding the different element lengths to the same length.
- 68. A machine-readable medium for storing program instructions for carrying out the method of claim 54.
- 69. A system for restoring an image to an original image, comprising:
a channel for receiving one component of multiple complementary components of the original image, the one component containing predetermined known marker data corresponding to one or more marker locations; a digital processor for
generating in a closed form, without iteration, a plurality of sequences from the one component, removing the predetermined marker data from the marker location(s), combining the sequences to produce an entire restored image.
- 70. The system of claim 69 where the channel comprises an external storage device holding the one component.
- 71. The system of claim 69 where the channel is coupled to a network for receiving the one component.
- 72. The system of claim 69 further comprising at least one output device coupled to the processor for receiving the restored image.
- 73. The system of claim 72 where the output device comprises at least one of a display, a printer, and a data analyzer.
- 74. A computer-implemented method comprising:
receiving only one component of a transform-domain original image; converting the one component to a base-domain approximate restored image; separating the approximate restored image into even and odd parts; removing the known marker from one of the parts to form a corrected part; producing exact parts from the corrected part and at least one of the other parts; combining the exact parts to produce a final restored image; outputting the final restored image.
- 75. The method of claim 74 where the marker value is sufficiently large to guarantee that the original image is minimum-phase in the transform domain.
- 76. The method of claim 74 where the one component is a magnitude component of a Fourier transform.
- 77. The method of claim 76 where the marker has a complex value.
- 78. The method of claim 74 where the transform-domain original image represents a transform of a base-domain original image having rational elements of a predetermined precision.
- 79. The method of claim 78 where the final restored image has rational elements equal to the elements of the base-domain original image, within the predetermined precision.
- 80. The method of claim 74 further comprising transforming the exact parts to produce a transform-domain final restored image.
- 81. A machine-readable medium for storing program instructions for carrying out the method of claim 74
- 82. A system comprising:
a channel for receiving only one component of a transform-domain original image; a digital processor for
converting the one component to a base-domain approximate restored image, separating the approximate restored image into even and odd parts, removing the known marker from one of the parts to form a corrected part, producing exact parts from the corrected part and at least one of the other parts, combining the exact parts to produce a final restored image, outputting the final restored image.
- 83. The system of claim 82 where the channel comprises an external storage device for holding the one component.
- 84. The system of claim 82 where the channel is coupled to a network for receiving the one component.
- 85. The system of claim 82 further comprising at least one output device coupled to the processor for receiving the restored image.
- 86. The system of claim 85 where the output device comprises at least one of a display, a printer, and a data analyzer.
- 87. A computer-implemented method comprising:
receiving only one component of a transform-domain original image; forming a complex transform from the one component; removing a predetermined marker value to produce a corrected restored image; calculating a real part of the corrected restored image.
- 88. The method of claim 87 where the one component is a phase component of a Fourier transform
- 89. The method of claim 87 where the marker value is sufficiently large to guarantee that the original image is minimum-phase in the transform domain.
- 90. The method of claim 89 where the marker has a complex value.
- 91. The method of claim 87 where removing the marker includes
inverse-transforming the complex transform to a base-domain restored image; removing a marker value from the base-domain restored image so as to change at least one element of the base-domain restored image.
- 92. The method of claim 91 where the marker is removed by subtracting it from a predetermined element of the base-domain restored image.
- 93. The method of claim 87 further comprising producing an exact restored image from the corrected restored image.
- 94. The method of claim 93 where the exact restored image is produced by rounding a function of the corrected restored image.
- 95. A machine-readable medium for storing program instructions for carrying out the method of claim 87.
- 96. A system comprising:
a channel for receiving only one component of a transform-domain original image; a digital processor for
forming a complex transform from the one component, removing a predetermined marker value to produce a corrected restored image, calculating a real part of the corrected restored image.
- 97. The system of claim 93 where the channel comprises an external storage device for holding the one component.
- 98. The system of claim 93 where the channel is coupled to a network for receiving the one component.
- 99. The system of claim 93 further comprising at least one output device coupled to the processor for receiving the restored image.
- 100. The system of claim 93 where the output device comprises at least one of a display, a printer, and a data analyzer.
- 101. A computer-implemented method comprising:
receiving only one component of a transform-domain original image, the one component including a sign map; extracting the sign map from the one component; calculating a magnitude of the one component; restoring another component of the transform-domain image in response to the sign map; inverse-transforming the components to produce a base-domain restored image; removing a predetermined marker value from the restored image.
- 102. The method of claim 101 further comprising:
expanding the resolution of the one component; producing a final image from the restored image.
- 103. The method of claim 101 where the transform-domain original image represents a transform of a base-domain original image having elements of a predetermined precision.
- 104. The method of claim 103 where the final restored image has rational elements equal to the elements of the base-domain original image, within the predetermined precision.
- 105. The method of claim 101 where the marker value ensures that the transform-domain original image is minimum-phase.
- 106. The method of claim 105 where the marker value is real.
- 107. The method of claim 101 where the sign map has elements representing the signs of elements of another transform-domain component of the original image.
- 108. The method of claim 107 further comprising embedding the sign map within the one component.
- 109. The method of claim 108 where the sign map is embedded by multiplying its elements by corresponding elements of the one compionent.
- 110. The method of claim 107 where extracting the sign map includes detecting signs of elements of the one component.
- 111. A machine-readable medium for storing program instructions for carrying out the method of claim 101.
- 112. A system comprising:
a channel for receiving only one component of a transform-domain original image, the one component including a sign map; a digital processor for
extracting the sign map from the one component; calculating a magnitude of the one component; restoring another component of the transform-domain image in response to the sign map; inverse-transforming the components to produce a base-domain restored image; removing a predetermined marker value from the restored image.
- 113. The system of claim 112 where the channel comprises an external storage device for holding the one component.
- 114. The system of claim 112 where the channel is coupled to a network for receiving the one component.
- 115. The system of claim 112 further comprising at least one output device coupled to the processor for receiving the restored image.
- 116. The system of claim 115 where the output device comprises at least one of a display, a printer, and a data analyzer.
- 117. A computer-implemented method comprising:
receiving only one component of a transform-domain original image, the one component comprising multiple elements; receiving a location map having elements designating storage lengths for the elements of the one component; reconstituting the one component in response to the location map; calculating real and imaginary parts of a restored image from the reconstituted component; removing a predetermined marker value from at least one of the parts; combining the parts to produce the restored image.
- 118. The method of claim 117 further comprising receiving a magnitude-sign map having elements indicating the relationships of respective elements of the one component to a threshold magnitude.
- 119. The method of claim 118 where the threshold magnitude is zero.
- 120. The method of claim 118 where the one component is further reconstituted in response to the magnitude-sign map.
- 121. The method of claim 117 further comprising inverse-transforming the restored image to a base-domain final image.
- 122. The method of claim 121 where the final image has multiple elements each having first and second numbers.
- 123. The method of claim 122 where the two numbers of each final-image element comprise a real number and an imaginary number.
- 124. The method of claim 122 further comprising separating the final image into two separated final images.
- 125. The method of claim 124 where each of the separated images compresses a respective one of the numbers of each element of the final image.
- 126. The method of claim 117 where the parts are real and imaginary parts of the restored image in the transform domain.
- 127. The method of claim 126 further comprising inverse transforming the restored image to a base domain.
- 128. The method of claim 117 where the marker value is sufficient to ensure minimum phase of the transform-domain original image.
- 129. The method of claim 128 where the marker value is real.
- 130. The method of claim 128 where the marker value is imaginary.
- 131. A machine-readable medium for storing program instructions for carrying out the method of claim 117
- 132. A system comprising:
a channel for receiving only one component of a transform-domain original image, the one component comprising multiple elements; a digital processor for
receiving a location map having elements designating storage lengths for the elements of the one component, reconstituting the one component in response to the location map, calculating real and imaginary parts of a restored image from the reconstituted component, removing a predetermined marker value from at least one of the parts, combining the parts to produce the restored image.
- 133. The system of claim 132 where the channel comprises an external storage device for holding the one component.
- 134. The system of claim 132 where the channel is coupled to a network for receiving the one component.
- 135. The system of claim 132 further comprising at least one output device coupled to the processor for receiving the restored image.
- 136. The system of claim 135 where the output device comprises at least one of a display, a printer, and a data analyzer.
- 137. A method of processing image data. comprising:
receiving at least first and second original images each comprising multiple elements each having a single value; converting the elements of at least the first original image to different values; combining the first and second images to a composite original image having multiple elements each having a pair of orthogonal values; placing a known marker value related to predetermined data of the composite original image in the composite image so as to modify certain of the composite-image data; transforming the composite image including the modified data to a transform-domain composite original image having multiple complementary components; communicating only one of the components as a modified composite image.
- 138. The method of claim 137 where the marker value is sufficient to ensure that the composite image is minimum-phase in the transform domain.
- 139. The method of claim 137 where the original images are sequences of values in a base domain.
- 140. The method of claim 137 where the orthogonal values represent real and imaginary parts of complex numbers.
- 141. The method of claim 140 where converting the first original image comprises representing its elements as imaginary numbers.
- 142. The method of claim 140 where the elements of the second original image are represented as real numbers.
- 143. A machine-readable medium for storing program instructions for carrying out the method of claim 137.
- 144. A system for processing image data. comprising:
a digital processor for
receiving at least first and second original images each comprising multiple elements each having a single value, converting the elements of at least the first original image to different values, combining the first and second images to a composite original image having multiple elements each having a pair of orthogonal values, placing a known marker value related to predetermined data of the composite original image in the composite image so as to modify certain of the composite-image data, transforming the composite image including the modified data to a transform-domain composite original image having multiple complementary components; a channel for communicating only one of the components as a modified composite image.
- 145. The system of claim 144 further including a source device for producing the original image.
- 146. The system of claim 145 where the source device comprises at least one of a scanner and a storage device.
- 147 The system of claim 144 where the channel transmits the one component from the processor to a network.
- 148. The system of claim 144 where the channel comprises a storage medium for storing the one component.
- 149. A method of processing image data. comprising:
receiving only one component of a transform-domain modified composite image, representing two separate single-valued original images as multiple-valued elements each containing orthogonal values from both of the original images; restoring the composite image from the one component so as to produce a composite restored image having elements each having multiple orthogonal values. removing a predetermined marker value so as to change the data of at least one element of the restored composite image; separating the composite restored image into two individual restored images each having multiple elements having only one value per element, each representing one of the single-valued original images.
- 150. The method of claim 149 where the marker value is sufficient to ensure that the composite image is minimum-phase in the transform domain.
- 151. The method of claim 149 where the orthogonal values represent real and imaginary parts of complex numbers.
- 152. The method of claim 151 further comprising converting one of the individual restored images from imaginary values to real numbers.
- 153. The method of claim 151 where the elements of the second restored image are represented as real numbers.
- 154. The method of claim 149 where the restored images are sequences of values in a base domain.
- 155. A machine-readable medium for storing program instructions for carrying out the method of claim 149.
- 156. A system for processing image data. comprising:
a channel for receiving only one component of a transform-domain modified composite image, representing two separate single-valued original images as multiple-valued elements each containing orthogonal values from both of the original images, a digital processor for
restoring the composite image from the one component so as to produce a composite restored image having elements each having multiple orthogonal values, removing a predetermined marker value so as to change the data of at least one element of the restored composite image, separating the composite restored image into two individual restored images each having multiple elements having only one value per element, each representing one of the single-valued original images.
- 157. The system of claim 156 where the channel comprises an external storage device for holding the one component.
- 158. The system of claim 156 where the channel is coupled to a network for receiving the one component.
- 159. The system of claim 156 further comprising at least one output device coupled to the processor for receiving the restored image.
- 160. The system of claim 159 where the output device comprises at least one of a display, a printer, and a data analyzer.
CLAIM OF PRIORITY
[0001] This application claims priority under 35 USC 119(e) from U.S. Provisional Application Ser. No. 60/467,862, filed May 5, 2003, which application is incorporated herein by reference.
Provisional Applications (1)
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Number |
Date |
Country |
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60467862 |
May 2003 |
US |