Abstract: An image processing method includes selecting an image in fixed storage of a computer and loading the selected image into memory of the computer. The method further includes representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values. Thereafter, the initial two-dimensional array of pixel values may be transformed into a hierarchy of progressively axially decremented two-dimensional arrays of signs and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs. Finally, each of the two-dimensional arrays of signs and each pair of one-dimensional values may be stored in the fixed storage as a compressed form of the selected image.

Abstract: An image processing method includes selecting an image in fixed storage of a computer and loading the selected image into memory of the computer. The method further includes representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values. Thereafter, the initial two-dimensional array of pixel values may be transformed into a hierarchy of progressively axially decremented two-dimensional arrays of signs and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs. Finally, each of the two-dimensional arrays of signs and each pair of one-dimensional values may be stored in the fixed storage as a compressed form of the selected image.

Abstract: An image processing method includes selecting an image in fixed storage of a computer and loading the selected image into memory of the computer. The method further includes representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values. Thereafter, the initial two-dimensional array of pixel values may be transformed into a hierarchy of progressively axially decremented two-dimensional arrays of signs and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs. Finally, each of the two-dimensional arrays of signs and each pair of one-dimensional values may be stored in the fixed storage as a compressed form of the selected image.

Abstract: An image processing method includes selecting an image in fixed storage of a computer and loading the selected image into memory of the computer. The method further includes representing the loaded image by a processor of the computer in the memory as an initial two-dimensional array of pixel values. Thereafter, the initial two-dimensional array of pixel values may be transformed into a hierarchy of progressively axially decremented two-dimensional arrays of signs and a pair of one-dimensional values for each 2×2 array of signs amongst the decremented two-dimensional arrays of signs. Finally, each of the two-dimensional arrays of signs and each pair of one-dimensional values may be stored in the fixed storage as a compressed form of the selected image.

Abstract: An invention based on learning a discrete recurrent neural network for a given signal domain is described. In one implementation to the domain of visual images, the method can be used to efficiently compress digital photographs and to devise a new perceptual distortion measure between images that well-matches data collected from a human psychophysics experiment. Other applications of the invention include unsupervised detection of recurrent patterns in high-dimensional data and Shannon-optimal error-correcting coding from few training examples.

Abstract: An invention based on learning a discrete recurrent neural network for a given signal domain is described. In one implementation to the domain of visual images, the method can be used to efficiently compress digital photographs and to devise a new perceptual distortion measure between images that well-matches data collected from a human psychophysics experiment. Other applications of the invention include unsupervised detection of recurrent patterns in high-dimensional data and Shannon-optimal error-correcting coding from few training examples.

Abstract: Methods and supporting systems for administering a loyalty card program include an application residing on a plurality of heterogeneous point-of-sale devices that captures consumer transaction data, wherein the consumer transaction data include the identification of a loyalty card, While the loyalty card is uniquely attributed to an individual consumer, the card may be used to conduct transactions unrelated retail entities, each having its own respective loyalty program, such that values for the individual loyalty programs may be maintained.