Method and apparatus for quantum-limited data acquisition
First Claim
1. A method for forming a representation of a flux of discrete particles emitted by a plurality of particle emitters, particle emission by each said particle emitter being a random process substantially unaffected by particle emission by any other of said particle emitters, the random process imparting a random noise variation to the particle flux, the particle flux having an information-carrying variation having a bandwidth of interest, the method comprising the steps of:
- detecting particles of the particle flux, and for each detected particle producing a quantized representation datum of said detection, said quantized representation being determined by a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux; and
filtering said quantized representation data through a band-limiting filter of bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest.
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Abstract
The invention relates to forming an image from a random particle flux. Particles of the flux are detected by a discrete-cell detector having a cell size finer than conventionally used. Preferably, the cell size is sufficiently small that almost all cells of the detector count at most one particle during the image acquisition time. The count data are filtered through a band-limiting filter whose bandwidth lies between a bandwidth corresponding to the detector cell size and the flux bandwidth of interest. Outliers may be flattened before filtering. Neighborhoods around each cell are evaluated to differentiate stationary regions (where neighboring data are relatively similar) from edge regions (where neighboring data are relatively dissimilar). In stationary regions, a revised estimate for a cell is computed as an average over a relatively large neighborhood around the cell. In edge regions, a revised estimate is computed as an average over a relatively small neighborhood. For cells lying in an edge region but near a stationary/edge boundary, a revised estimate is computed by extrapolating from data in the nearby stationary region.
118 Citations
45 Claims
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1. A method for forming a representation of a flux of discrete particles emitted by a plurality of particle emitters, particle emission by each said particle emitter being a random process substantially unaffected by particle emission by any other of said particle emitters, the random process imparting a random noise variation to the particle flux, the particle flux having an information-carrying variation having a bandwidth of interest, the method comprising the steps of:
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detecting particles of the particle flux, and for each detected particle producing a quantized representation datum of said detection, said quantized representation being determined by a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux; and filtering said quantized representation data through a band-limiting filter of bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest. - View Dependent Claims (4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
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2. A method for forming a representation of a flux of discrete particles emitted by a plurality of particle emitters, the particle flux having an information-carrying variation having a bandwidth of interest and a random noise variation, said noise variation being such that particle flux values measured by any two non-overlapping particle detectors of any cell size will be statistically independent, and an aggregate variance of fluctuations of the particle flux being non-increasing as a particle detector of fixed total detection area is subdivided into smaller cells, the method comprising the steps of:
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detecting particles of the particle flux, and for each detected particle producing a quantized representation datum of said detection, said quantized representation being determined by a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux; and filtering said quantized representation data through a band-limiting filter of bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest.
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3. A method for forming a representation of a flux of discrete particles emitted by a plurality of independent particle emitters, particle arrival at a cell of a detector of the particles being a Poisson process, the particle flux having an information-carrying variation having a bandwidth of interest, the method comprising the steps of:
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detecting particles of the particle flux, and for each detected particle producing a quantized representation datum of said detection, said quantized representation being determined by a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux; and filtering said quantized representation data through a band-limiting filter of bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest.
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27. A method of processing a numerical image of data acquired by a location-quantizing detector, the data each having a first value and a quantized location, comprising the steps:
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at each datum, evaluating values of data at neighboring locations to differentiate stationary regions and edge regions of said data, said stationary regions being regions of said data in which the first values of neighboring data are relatively similar, said edge regions being regions of said data in which the first values of neighboring data are relatively dissimilar; for data within said stationary regions, determining an estimated value for each said quantized location as a weighted average of said first values over a relatively large neighborhood of data neighboring a said quantized location in said stationary region; and for data within said edge regions, determining an estimated value for each said quantized location as a weighted average of said first values over a relatively small neighborhood of data neighboring a said quantized location in said edge region. - View Dependent Claims (29, 30, 31, 32, 33)
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28. A method of processing a numerical image of data acquired by a location-quantizing detector, the data each having a first value and a quantized location, comprising the steps of:
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at each datum, evaluating values of data at neighboring locations to differentiate stationary regions and edge regions of said data, said stationary regions being regions of said data in which the first values of neighboring data are relatively similar, said edge regions being regions of said data in which the first values of neighboring data are relatively dissimilar; and for quantized vector locations within said edge regions and lying near one of said stationary regions, determining an estimated value by extrapolating from values of data in said near stationary region. - View Dependent Claims (34)
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35. A method of producing a perceptible image on a display device, the display device configured to display pixels of said image, each pixel corresponding to a region of an object to be imaged and having a color value, the method comprising the steps of:
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acquiring average and uncertainty color values corresponding to each pixel of a portion of the image, said average value estimating a value of a property in said corresponding region and said uncertainty value corresponding to an uncertainty in said average value; and adding a random number to the average value for each pixel of said image portion, a standard deviation of each random number being related to said uncertainty value for the pixel; and displaying said randomized pixel values on the display device. - View Dependent Claims (36, 37, 38)
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39. A method for improving the images produced by a device for forming an image of detected particles of a particle flux, the particle flux having an information-carrying variation having a bandwidth of interest and a random noise variation, the device having a particle detector that, for each detected particle, produces a quantized representation datum of said detection, the method comprising the steps of:
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replacing the particle detector with a particle detector having a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux, for sampling said information-carrying variation of the particle flux; and adding to the image device a filter for band-limiting said quantized representation data, said filter having a bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest.
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40. A method for forming a continuous representation of a discrete process, comprising the steps of:
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detecting events of said discrete process with a detector cell size sufficiently small that almost all cells of said detector count at most one said event; constructing from said detected events a count density function; estimating from said count density function an ensemble average count density function.
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41. A method for reducing aliasing noise from sampled data, comprising the steps of:
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sampling a phenomenon in a detector with a relatively large quantization cell size to produce a value for each cell of said detector; defining an array of cells, each said detector cell corresponding to a contiguous group of cells of said defined array; and randomly partitioning the value of each said detector cell among corresponding cells of said defined array. - View Dependent Claims (42)
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43. Apparatus for forming a representation of a flux of discrete particles emitted by a plurality of particle emitters, particle emission by each said particle emitter being random and substantially unaffected by particle emission by any other of said particle emitters and thus imposing a random noise variation on the particle flux, the particle flux having an information-carrying variation having a bandwidth of interest, the apparatus comprising:
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a particle detector for detecting particles of the particle flux, and for each detected particle producing a quantized representation datum of said detection, said particle detector having a quantization cell size that is smaller than a contrast cell size sufficiently small to preserve contrast for the smallest feature of interest of said information-carrying variation of the particle flux; and a band-limiting filter for filtering said quantized representation data, said filter having a bandwidth less than a bandwidth corresponding to said quantization cell size but greater than said bandwidth of interest.
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44. A method for deconvolution filtering for processing a numerical image of data acquired by a location-quantizing detector, the data each having a first value and a quantized location, comprising the steps:
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at each datum, evaluating said first values of data at neighboring locations to differentiate stationary regions and edge regions of said data, said stationary regions being regions of said data in which the first values of neighboring data are relatively similar, said edge regions being regions of said data in which the first values of neighboring data are relatively dissimilar; for each datum not near a boundary between said stationary regions and said edge regions, filtering using an integration area centered on said datum and with a radius not exceeding a distance to said boundary; and for each datum near a stationary edge/boundary, filtering using an integration area asymmetric about said datum.
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45. A method for forming a representation of a flux of discrete particles emitted by a plurality of particle emitters, particle emission by each said particle emitter being random and substantially unaffected by particle emission by any other of said particle emitters, thereby imparting a random variation to the particle flux, the particle flux having an information-carrying variation having a bandwidth of interest, said method comprising the steps of:
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oversampling the particle flux for producing a quantized representation of the particle flux; filtering said oversampled representation through a band-limiting filter for substantially removing all of said random noise variation energy outside said bandwidth of interest; and storing said filtered signal for further image processing or display.
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Specification