Method and apparatus for quantum-limited data acquisition

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:

• 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.

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:

• 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.

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:

• 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.

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:

• 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.

A method for forming a continuous representation of a discrete process, comprising the steps of:

• 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.

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:

• 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.