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Patent Issued for Method and Apparatus for Compressive Sensing with Reduced Compression Complexity

July 22, 2014



By a News Reporter-Staff News Editor at Information Technology Newsweekly -- According to news reporting originating from Alexandria, Virginia, by VerticalNews journalists, a patent by the inventor Ashikhmin, Alexei (Morristown, NJ), filed on February 4, 2011, was published online on July 8, 2014.

The assignee for this patent, patent number 8775490, is Alcatel Lucent (Paris, FR).

Reporters obtained the following quote from the background information supplied by the inventors: "This section introduces aspects that may help facilitate a better understanding of the inventions. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is prior art or what is not prior art.

"A compressive sensing scheme allows compression of a sparse vector x of real or complex numbers (that is, a vector whose entries are primarily zeros, only few being non-zero) into a short vector y. The vector x can then be reconstructed from y with high accuracy. Such compressive sensing schemes have numerous applications.

"Typically the number of entries of y (say M) is much smaller than the number of entries of x (say N). The number N/M is the compression ratio. Thus, instead of keeping in memory (or instead of transmitting, working with, etc.) N real (complex) numbers we have to keep only M real (complex) numbers.

"Below is a list of references that are referred to throughout the present specification:

"[1] A. R. Calderbank, S. Howard, S. Jafarpour, 'Sparse reconstruction via the Reed-Muller Sieve,' IEEE International Symposium on Information Theory, pp. 1973-1977, 2010.

"[2] A. R. Calderbank, S. Howard, S. Jafarpour, 'Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property,' IEEE Journal of Selected Topics in Signal Processing, pp. 358-374, Vol. 4., no. 2, 2010.

"[3] A. R. Calderbank, E. Rains, P. W. Shor, N. J. A. Sloane, 'Quantum Error Correction Via Codes Over GF(4),' IEEE Trans. on Information Theory, vol. 44, pp. 1369-1387, 1998.

"The compressive sensing scheme proposed in [1,2] has good performance. In particular, it has a good compression ratio N/M, it affords a low-complexity decompression algorithm (i.e., reconstruction of x from y), and it has a good accuracy of decompression. However, it does have a high compression complexity, that is, the complexity of computing y from x.

"Thus, new techniques that are able to reduce compression complexity would meet a need and advance compression technology in general."

In addition to obtaining background information on this patent, VerticalNews editors also obtained the inventor's summary information for this patent: "Various methods and devices are provided to address the need for reduced compression complexity in the area of compressive sensing. In one method, a vector x is compressed to obtain a vector y according to y=.PHI..sub.RDx, where .PHI..sub.RD=U.PHI..sub.RM.PHI..sub.RM is a compressive sensing matrix constructed using a second-order Reed-Muller code or a subcode of a second-order Reed-Muller code and U is a unitary matrix from the real or complex Clifford group G. In another method, vector y is decompressed to obtain vector x also according to y=.PHI..sub.RDx. In some embodiments, decompression may involve computing y', U.sup.-1y and then determining the vector x using the computed y'. An article of manufacture is also provided, the article comprising a processor-readable storage medium storing one or more software programs which when executed by one or more processors performs the steps of any of these methods.

"A first and a second apparatus is also provided. Both apparatuses include interface circuitry and a processing device, coupled to the interface circuitry. In the first apparatus, the processing device is adapted to compress a vector x to obtain a vector y according to y=.PHI..sub.RDx, wherein .PHI..sub.RD=U.PHI..sub.RD, .PHI..sub.RM being a compressive sensing matrix constructed using a second-order Reed-Muller code or a subcode of a second-order Reed-Muller code and U being a unitary matrix from the real or complex Clifford group G. In the second apparatus, the processing device is adapted to decompress a vector y to obtain a vector x according to y=.PHI..sub.RDx, wherein .PHI..sub.RD=U.PHI..sub.RM, .PHI..sub.RM being a compressive sensing matrix constructed using a second-order Reed-Muller code or a subcode of a second-order Reed-Muller code and U being a unitary matrix from the real or complex Clifford group G."

For more information, see this patent: Ashikhmin, Alexei. Method and Apparatus for Compressive Sensing with Reduced Compression Complexity. U.S. Patent Number 8775490, filed February 4, 2011, and published online on July 8, 2014. Patent URL: http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=8775490.PN.&OS=PN/8775490RS=PN/8775490

Keywords for this news article include: Alcatel Lucent, Information Technology, Information and Data Theories.

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Source: Information Technology Newsweekly


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