CN107403628A - A kind of voice signal reconstructing method based on compressed sensing - Google Patents

A kind of voice signal reconstructing method based on compressed sensing Download PDF

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CN107403628A
CN107403628A CN201710520775.5A CN201710520775A CN107403628A CN 107403628 A CN107403628 A CN 107403628A CN 201710520775 A CN201710520775 A CN 201710520775A CN 107403628 A CN107403628 A CN 107403628A
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calculation matrix
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CN107403628B (en
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刘昱
王映雪
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Tianjin University
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
    • G10L21/00—Speech or voice signal processing techniques to produce another audible or non-audible signal, e.g. visual or tactile, in order to modify its quality or its intelligibility
    • G10L21/04—Time compression or expansion
    • G10L21/043—Time compression or expansion by changing speed
    • G10L21/045—Time compression or expansion by changing speed using thinning out or insertion of a waveform
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
    • H03M7/3062—Compressive sampling or sensing

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  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Linguistics (AREA)
  • Quality & Reliability (AREA)
  • Signal Processing (AREA)
  • Health & Medical Sciences (AREA)
  • Audiology, Speech & Language Pathology (AREA)
  • Human Computer Interaction (AREA)
  • Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Multimedia (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a kind of voice signal reconstructing method based on compressed sensing, gathers primary speech signal；The maximum matching degree numerical value of calculation matrix and measured value is obtained, calculates current residue riWith the inner product value of column vector in calculation matrix, maximum inner product value now in iterative process each time is obtained, selects best match item；Search out the maximum coherence item with reconstructed residual in calculation matrix；Augment index collection Λ and Increment Matrix Ω：The row number of selected maximum coherence item is added in indexed set Λ successively, selected maximum coherence leu is added in Increment Matrix；The new approximation of signal is obtained, least square problem is solved and obtains new approximation xi：Obtain and measured value y and current delta matrix ΩiMost suitable reconstruct vector xi；Update residual error ri；According to iterations i≤K and uj>=U/ μ, complete reconstruct.Present invention, avoiding the increase of the data volume in OMP recovery algorithms and amount of storage, and signal reconstruction speed is improved on signal reconstruction accuracy is ensured.

Description

A kind of voice signal reconstructing method based on compressed sensing
Technical field
The present invention relates to the multiple fields such as voice processing technology, compressed sensing technology, particularly one kind to be based on compressed sensing Voice signal reconstructing method.
Background technology
Voice is the most direct most convenient of the mankind most efficiently communication mode, however, traditional audio signal processing method is Establish on nyquist sampling theorem, not only cause larger sampled signal data amount and waste big quantity space when encoding Redundant data is stored, causes data volume, amount of calculation and amount of storage all bigger.In the compressed sensing that 2006 formally propose (Compressed Sensing, CS) technology has openness feature using natural sign under some bases, it is carried out non- The adaptive overall situation samples and just can recover original letter from less measured value with high probability by suitable restructing algorithm Number, so as to avoid the drawbacks of traditional signal processing method is brought.Therefore the Speech processing mode based on compressed sensing The defects of traditional approach can be effectively prevented from, so as to substantially reduce data volume and place on the premise of reconstruction signal precision is ensured Manage the time.The design of restructing algorithm is one of key problem of Speech Signal Compression sensing.
The compressed sensing recovery algorithms algorithm of main flow mainly has convex optimized algorithm, greedy algorithm and combinational algorithm at present.Its In, the measured value required for convex optimized algorithm is less, but the complexity calculated is higher.Although the and arithmetic speed of combinational algorithm Comparatively fast, but substantial amounts of measured value is needed.Greedy algorithm has then taken compromise between both the above algorithm.Most passed through in greedy algorithm Orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm of allusion quotation is using relatively broad, but without excellent The OMP algorithms of change are using the decision condition that is terminated as algorithm iteration of degree of rarefication of signal, and in fact the degree of rarefication of signal is not It is an accurate numerical value, therefore the iterations of OMP algorithms can not be determined sufficiently accurately.Changed if degree of rarefication value is excessive Generation number is excessive, cause amount of calculation it is excessive calculate the time it is longer, iterations is very few if degree of rarefication value is too small, causes signal Quality reconstruction is not good enough.Therefore the reconstruct end condition of OMP algorithms still needs further to be optimized.
The content of the invention
For overcome the deficiencies in the prior art, the present invention proposes a kind of voice signal reconstruct side based on compressed sensing Method, this method in addition to degree of rarefication, recycle measured value to be used as with the correlation arranged in calculation matrix except degree of rarefication in the algorithm Outside another loop termination condition, realize the optimization of OMP recovery algorithms, suitable for voice signal compressed sensing recover.
A kind of voice signal reconstructing method based on compressed sensing of the present invention, this method comprise the following steps：
Step 1, collection primary speech signal, obtain calculation matrixMeasured value y and signal degree of rarefication K；
Step 2, initialization indexed set Λ, residual error r, Increment Matrix Ω and iterations i, and suitable threshold value ratio is set Example μ：r0=y,I=1, μ=1.2；
Column vector in step 3, calculating and calculation matrixWith the maximum inner product value of measured valueJ represents column vector in calculation matrixSequence number；Calculation matrix herein and residual error it is interior Standard of the product as measurement matching degree, that is, the maximum matching degree numerical value of calculation matrix and measured value is obtained,
Step (4), calculate current residue riWith the inner product value of column vector in calculation matrix Maximum inner product value now in iterative process each time is obtained, selects best match item；
Step 5, search out index λiSo thatWherein λiRepresent calculation matrix In select column vectorSequence number, that is, search out the row number arranged in calculation matrix with the maximum coherence of current reconstructed residual；
Step 6, augment index collection Λ and Increment Matrix Ω：Λi=Λi-1∪{λi,It will select most The row number of big coherent term is added in indexed set Λ successively, and selected maximum coherence leu is added in Increment Matrix；
Step 7, the new approximation for obtaining signal, solve least square problem and obtain new approximation xi：xi=argminx|| y-Ωix||；Least square is to draw the best match of signal by minimizing square error to weigh, therefore obtains and measure Value y and current delta matrix ΩiMost suitable reconstruct vector, as above-mentioned new approximation xi；
Step 8, renewal residual error ri=y- Ωixi, so that next iteration carries out the selection of maximum coherence item；
If step 9, iterations i≤K and uj>=U/ μ, then return to step 4, otherwise export the reconstruction value x of now signaliWith Index set Λi, complete the reconstruct of this signal.
The present invention has simple, easy-operating feature, avoids in OMP recovery algorithms because degree of rarefication chooses improper cause Data volume and amount of storage increase, the speed of signal reconstruction is improved on the basis of signal reconstruction accuracy is ensured；Can be with Compressed sensing for voice signal is recovered.
Brief description of the drawings
Fig. 1 is a kind of voice signal reconstructing method overall flow figure based on compressed sensing of the present invention.
Embodiment
Embodiments of the present invention are described in further detail below in conjunction with accompanying drawing.The framework of the present invention is realized can It is divided into following steps：
One of principle due to OMP recovery algorithms is the correlation by the use of residual error and calculation matrix as from calculation matrix Selecting Index row foundation, and this index column be added in Increment Matrix be used for primary signal reconstruct, therefore the present invention Unitary construction thinking is made again with residual values and the correlation that is arranged in calculation matrix in addition to degree of rarefication for the end condition of algorithm For criterion.
As shown in figure 1, a kind of voice signal reconstructing method based on compressed sensing of the present invention specifically includes following steps：
Step 1, collection primary speech signal, obtain calculation matrixMeasured value y and signal degree of rarefication K；
Step 2, initialization indexed set Λ, residual error r, Increment Matrix Ω and iterations i, and suitable threshold value ratio is set Example μ：r0=y,I=1, μ=1.2；
Step 3, the maximum matching degree numerical value for obtaining calculation matrix and measured value, that is, calculate and column vector in calculation matrix With the maximum inner product value of measured valueThe basic thought of OMP algorithms be in each iteration, from Over-complete dictionary of atoms (i.e. calculation matrix) in the atom that is most matched with the residual error of signal of selection carry out sparse bayesian learning, and weigh and match The standard of degree is the inner product of calculation matrix and residual error, and j represents column vector in calculation matrixSequence number；
Step 4, calculate current residue riInner product value with column vector in calculation matrix is The maximum inner product value in iterative process each time now is obtained to select best match item；
Step 5, search out index λ so thatWherein λiRepresent to select in calculation matrix Determine column vectorSequence number, that is, search out in calculation matrix with current reconstructed residual ri-1Maximum coherence row row number；
Step 6：Augment index collection Λ and Increment Matrix Ω：Λi=Λi-1∪{λi,By selected maximum The row number of coherent term (is added in indexed set, selected maximum coherence leu is added in Increment Matrix successively；
Step 7：The new approximation of signal is obtained, least square problem is solved and obtains new approximation xi：xi=argminx|| y-Ωix||；Least square is to draw the best match of signal by minimizing square error to weigh, therefore obtains and measure Value y and current delta matrix ΩiMost suitable reconstruct vector xi；
Step 8：Update residual error ri：ri=y- Ωixi, because the approximation of now signal has been updated over, therefore residual error Also carry out being recalculated to the selection that next iteration carries out maximum coherence item；
Step 9：If iterations i≤K and uj>=U/ μ, then return to step 4, otherwise export the reconstruction value x of now signaliWith Index set Λi, complete the reconstruct of this signal.Stopping criterion for iteration is except foundation in original OMP recovery algorithms in this step Outside limitation of the iterations no more than degree of rarefication K, in order to avoid caused by K values are larger computing it is excessive and according to the original of OMP algorithms There is provided the limitation of calculation matrix and the inner product value of residual error again for reason.

Claims (1)

1. a kind of voice signal reconstructing method based on compressed sensing, it is characterised in that this method comprises the following steps：
Step (1), collection primary speech signal, obtain calculation matrixMeasured value y and signal degree of rarefication K；
Step (2), initialization indexed set Λ, residual error r, Increment Matrix Ω and iterations i, and suitable threshold percentage is set μ：r0=y,I=1, μ=1.2；
Column vector in step (3), calculating and calculation matrixWith the maximum inner product value of measured valueJ represents column vector in calculation matrixSequence number；Calculation matrix herein and residual error Standard of the inner product as measurement matching degree, that is, the maximum matching degree numerical value of calculation matrix and measured value is obtained,
Step (4), calculate current residue riWith the inner product value of column vector in calculation matrixObtain Maximum inner product value in iterative process now each time, select best match item；
Step (5), search out index λiSo thatWherein λiRepresent to select in calculation matrix Determine column vectorSequence number, that is, search out the row number arranged in calculation matrix with the maximum coherence of current reconstructed residual；
Step (6), augment index collection Λ and Increment Matrix Ω：Λi=Λi-1∪{λi,By selected maximum The row number of coherent term is added in indexed set Λ successively, and selected maximum coherence leu is added in Increment Matrix；
Step (7), the new approximation for obtaining signal, solve least square problem and obtain new approximation xi：xi=argminx||y- Ωix||；Least square is to draw the best match of signal by minimizing square error to weigh, therefore is obtained and measured value y With current delta matrix ΩiMost suitable reconstruct vector, as above-mentioned new approximation xi；
Step (8), renewal residual error ri=y- Ωixi, so that next iteration carries out the selection of maximum coherence item；
Step (9) if, iterations i≤K and uj>=U/ μ, then return to step (4), otherwise export the reconstruction value x of now signaliWith Index set Λi, complete the reconstruct of this signal.
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CN110717949A (en) * 2018-07-11 2020-01-21 天津工业大学 Interference hyperspectral image sparse reconstruction based on TROMP

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