Method and system for denoising a noisy signal generated by an impulse channel
AssigneeHewlett-Packard Development Company, L.P.
InventorsErik Ordentlich, Ignaclo Ramirez, Gadiel Seroussi, Marcelo Weinberger
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Abstract
In various embodiments of the present invention, a binary mask corresponding to a noisy symbol sequence is produced to indicate which of the symbols in the noisy symbol sequence has potentially been modified, or altered, by a noisy channel. DUDE, DUDE-CTI, and other denoising methods are modified to employ the bit mask in order to avoid the computational overhead and potential errors incurred in attempting to denoise symbols that are not likely to have been altered by the noisy channel.
Claims28
A method for classifying symbols, zi, of a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, as each having one of two or more classification values, the method comprising:
- for each context in the noisy symbol sequence, determining an estimated context dependent clean symbol-occurrence probability distribution;
- and
- for each context-embedded symbol zi embedded within a context ci within the noisy symbol sequence,
- determining an estimated clean symbol-occurrence probability distribution conditioned on the selected context ci=c and context-embedded symbol zi=ak, {circumflex over (P)}(x|c,ak), and
- based on {circumflex over (P)}(x|c,ak) and a three input variable dependent loss function L(x,z,d) depending on a clean symbol value x, a noisy symbol value z, and a class value d, classifying the context-embedded symbol zi as having a particular one of the two or more classification values.
A method for classifying symbols of a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, as being either likely altered by the channel, or “noisy,” or as being likely not altered by the channel, or “clean,” the method comprising:
- constructing a final binary mask Me for each extreme symbol value e corresponding to a potentially “noisy” symbol within the noisy symbol sequence, each -binary-mask element representing whether or not each symbol in the noisy symbol sequence represents a noisy symbol with a particular one of possible extreme grayscale values;
- and
- combining the final binary masks by successive logical OR operations to produce a final binary mask that indicates whether each symbol in the noisy symbol sequence is “noisy” or “clean.”
Computer instructions that implement the method of claim 111 encoded in a computer-readable medium.
A method for denoising a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, the method comprising:
- using a DUDE-based classifier to classify extreme-valued pixels as being either legitimate, extreme-valued pixels or noisy symbols;
- sorting contexts generated from the noisy signal into a first group of extreme-valued contexts and a second group of grayscale contexts;
- employing a modified DUDE to denoise pixels embedded within extreme-value contexts;
- and
- employing a DUDE-CTI to denoise pixels embedded within grayscale contexts.
A method for classifying symbols, zi, of a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, as each having one of two or more classification values, the method comprising:
- roughly cleaning the noisy symbol sequence to produce a next context-generating symbol sequence;
- and
- iteratively
- determining, for each context generated from the next context-generating sequence, an estimated context-dependent clean-symbol-sequence symbol-occurrence probability distribution, and
- for each noisy-symbol-sequence symbol zi embedded within a context ci generated from the next context-generating symbol sequence,
- determining an estimated clean-symbol-sequence symbol-occurrence probability distribution conditioned on the selected context ci=c and context-embedded symbol zi=ak, {circumflex over (P)}(x|c,ak),
- based on {circumflex over (P)}(x|c,ak) and a three input variable dependent loss function L(x,z,d) depending on a clean-symbol-sequence symbol value x, a noisy-symbol-sequence symbol value z, and a class value d, classifying the context-embedded symbol zi as having a particular one of the two or more classification values within a current symbol classification, and
- denoising the noisy symbol sequence according to the current symbol classification to produce a next context-generating symbol sequence.
A method for classifying symbols, zi, of a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, as each having one of two or more classification values, the method comprising:
- determining a first set of merged contexts based on non-extreme-valued symbols of the noisy symbol sequence;
- determining, for each merged context of the first set of contexts, an estimated context dependent clean-symbol-sequence symbol-occurrence probability distribution;
- generating a next symbol classification by,
- for each context-embedded symbol zi embedded within a merged context ci of the first set of merged contexts within the noisy symbol sequence, generating a next symbol classification by classifying the context-embedded symbol zi as having a particular one of the two or more classification values;
- and
- in one or more iterations,
- using the next symbol classification, determining a next set of merged contexts for the noisy symbol sequence;
- determining, for each merged context of the next set of merged contexts, an estimated clean-symbol-sequence symbol-occurrence probability distribution;
- generating a next symbol classification by,
- for each context-embedded symbol zi embedded within a merged context ci of the next set of merged contexts within the noisy symbol sequence,
- determining an estimated clean-symbol-sequence symbol-occurrence probability distribution conditioned on the selected merged context ci=c and context-embedded symbol zi=ak, {circumflex over (P)}(x|c,ak), and
- based on {circumflex over (P)}(x|c,ak) and a three input variable dependent loss function L(x,z,d) depending on a clean-symbol-sequence symbol value x, a noisy-symbol-sequence symbol value z, and a class value d, classifying the context-embedded symbol zi as having a particular one of the two or more classification values within a current symbol classification.
The method of claim 23 further including using a final symbol classification produced in a final iteration to denoise the noisy symbol sequence.
A method for associating metrics with symbols, zi, of a noisy symbol sequence, generated by passing a corresponding clean symbol sequence through a noise-inducing channel, the method comprising:
- for each context in the noisy symbol sequence, determining an estimated context dependent clean symbol-occurrence probability distribution;
- and
- for each context-embedded symbol zi embedded within a context ci within the noisy symbol sequence,
- determining an estimated clean symbol-occurrence probability distribution conditioned on the selected context ci=c and context-embedded symbol zi=ak, {circumflex over (P)}(x|c,ak),
- computing a metric for the context-embedded symbol zi, and
- transmitting the computed metric to a receiving entity.
Dependencies are inferred from the claim text.