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Sums of smoothed functions method for reconstructing binary signals in super Nyquist sampling system

A technology of signal reconstruction and smooth function, applied in electrical components, code conversion and other directions, can solve the problems of precision-complexity, high cost, unsatisfactory computational complexity, etc., to achieve the effect of reducing computational complexity

Inactive Publication Date: 2016-06-01
TSINGHUA UNIV
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  • Application Information

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Problems solved by technology

The accuracy of the semidefinite programming algorithm is very high, but its computational complexity is still unsatisfactory
[0010] Taken together, the accuracy and complexity of the above algorithms are both high

Method used

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  • Sums of smoothed functions method for reconstructing binary signals in super Nyquist sampling system
  • Sums of smoothed functions method for reconstructing binary signals in super Nyquist sampling system
  • Sums of smoothed functions method for reconstructing binary signals in super Nyquist sampling system

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Embodiment Construction

[0066] The present invention will be further described below in conjunction with the accompanying drawings.

[0067] In the present invention, for P O and A new cost function is proposed to solve the problem; and based on this, a novel solution method: SS (Smooth Function Sum) method is proposed.

[0068] noticed for Have

[0069] ||x+1|| 0 +||x-1|| 0

[0070] =n-card(x i , 1≤i≤n|x i =1}+n-card{x i , 1≤i≤n|x i =-1}

[0071] =2n-card{x i , 1≤i≤n|x i ∈ {-1, 1}}

[0072] ≥n

[0073] Where||·|| 0 Indicates the 0 norm, It is easy to verify, the condition for the establishment of the equal sign in the above formula: if and only if x∈{-1, 1} n , that is, the set {-1, 1} n The elements in such that ||x+1|| 0 +||x-1|| 0 reach the minimum. Thus P O becomes

[0074] min||x+1|| 0 +||x-1|| 0

[0075] s.t.y=Ax(L 0 S)

[0076] Accordingly, there is a noisy situation, becomes

[0077] min||x+1|| 0 +||x-1|| 0

[0078] s.t.||y-Ax|| 2 ≤∈(L 0 S ∈ )

[0079...

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Abstract

The invention discloses a sums of smoothed functions method for reconstructing binary signals in a super Nyquist sampling system. The sums of smoothed functions method is called an SS method for short. In adoption of the SS method, firstly, a l0 sum form is taken as an objective function; and further the l0 is approximated by smoothed functions; according to the method, the precision is ensured to be the same to that of a l infinity minimization method; the calculation complexity is reduced to 2-3 levels; the precision--complexity of a current mainstream algorithm is further improved; the value of an initial sigma 0 is determined according to the specific characteristic of the adopted smoothed functions format; the optimum combination of the precision--complexity is realized; finally, the value of a termination sigma min is determined; particularly under a noise condition, the actual noise distribution condition can be effectively reduced; and the solving performance can greatly improved.

Description

technical field [0001] The present invention provides a smoothing function and method for binary signal reconstruction in a super-Nyquist sampling system. Background technique [0002] A new research direction in signal processing in recent years is called compressed sensing, or compressed sampling. Compressed sensing was first used in signal sampling and compression, and was later widely used in various fields of signal processing. The traditional signal processing method is a method based on Nyquist (Nyquist) sampling law. Assuming that the signal bandwidth is f, according to the Nyquist sampling law, the sampling frequency is at least 2f. For some signals with very high bandwidth, such as image signals, extremely high sampling rates are required. This not only puts extremely high requirements on sampling equipment, but also puts great pressure on subsequent storage, transmission, and processing, so new technologies emerge as the times require. In compression technolog...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M7/30
CPCH03M7/30
Inventor 刘彦良韩芳明
Owner TSINGHUA UNIV
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