CN106485014A - A kind of 1 bit compression Bayes's cognitive method of strong robustness - Google Patents

Abstract

The invention belongs to signal detection and estimation (signal detection and estimation) technical field, more particularly to a kind of using deformation greatest hope (variational expectation maximization, V EM) algorithm while distinguished symbol reversion error and the robust Bayes's compression sensing method for estimating sparse signal.The present invention provides a kind of 1 bit compression Bayes's cognitive method of strong robustness.The present invention is by sign-inverted error modeling to be become the non-quantized observation of the disturbance of a sparse noise vector, and it is sparse to promote to apply inverse Gauss Gamma layering priori on the sparse noise vector, by using bayesian theory, you can complete the Combined estimator to sign-inverted error and sparse signal.Number and the position of sign-inverted error can be accurately determined by Combined estimator.

Description

A kind of 1 bit compression Bayes's cognitive method of strong robustness

Technical field

The invention belongs to signal detection and estimation (signal detection and estimation) technical field, special Algorithm is simultaneously using deformation greatest hope (variational expectation-maximization, V-EM) not to be related to one kind Distinguished symbol reversion error and robust Bayes's compression sensing method of estimation sparse signal.

Background technology

1 traditional bit compression perception algorithm all think 1 bit measurement be errorless, but due to signals collecting with transmission During can all introduce noise, therefore some bits can be inverted to and state contrary before, and this can cause these Traditional algorithm has sizable performance loss.

Some algorithms have been had to take into account sign-inverted problem, such as self adaptation exceptional value tracing algorithm, self adaptation at present Noise normalization fixed-point iteration algorithm etc., these algorithms can be automatically found sign-inverted error.But these algorithms are required for Know the number of reversion error, this can not possibly know in advance, and therefore the practicality of these algorithms is not high.In the present invention, By sign-inverted error modeling to be become the non-quantized observation of the disturbance of a sparse noise vector, so as to be managed using Bayes Error and sparse signal are inverted by accurately to determine.

Content of the invention

It is an object of the invention to provide a kind of 1 bit compression Bayes's cognitive method of strong robustness.The present invention passes through will Sign-inverted error modeling becomes the non-quantized observation of the disturbance of a sparse noise vector, and applies on the sparse noise vector Plus inverse Gauss-Gamma layering priori is sparse to promote, by using bayesian theory, you can complete to sign-inverted error and The Combined estimator of sparse signal.Number and the position of sign-inverted error can be accurately determined by Combined estimator.

Describe for convenience, first the present invention is introduced using system model and term：

If in 1 bit quantization problem, t=sign (y)=sign (Ax+w), wherein,See for binary system Measured value,For non-quantized original measurement value,For a sparse noise vector, i.e., only There is little nonzero coefficient, sign represents and sign function taken to vector element, if the element is more than 0, return 1, otherwise return 0.

K- sparse signal is randomly generated, and the supported collection of K- sparse signal is to be uniformly distributed to randomly select according to one 's.Calculation matrixIn each value be to randomly generate from the Gaussian Profile of a zero mean unit variance, and And its each row are all normalized.Sign-inverted error is also to be uniformly distributed to randomly generate according to one, wherein, m =200, n=100, K=10, L=10.

Perceive matrix：In order to line sampling is carried out to signal, play a part of dimensionality reduction, n dimensional signal is mapped to m dimension empty Between, usual m<<n.

Openness：Signal can be with some element linear expressions in one group of base or a dictionary.Represent it is essence when this True, it is sparse just to claim this signal.The information included by most high dimensional signal can be wrapped well below its dimension Contain, sparse signal model is that this high dimensional signal provides mathematical explanation.

Rarefaction representation：As soon as signal can be with some element linear expressions in group base, this group base is called sparse base.Sparse Expression of the signal under sparse base is the rarefaction representation of signal.

A kind of 1 bit compression Bayes's cognitive method of strong robustness, comprises the following steps that：

S1, perception matrix A with stochastical sampling property is constructed, sampling is carried out to signal and obtains y, step-up error preset value ε；

S2, the priori of construction parameters, Posterior distrbutionp：

T with regard to the Posterior distrbutionp of y is：Wherein, σ (y_i)=1/ (1+exp (- Y) it is) logical function, and can leads,

The Gauss of x, w against Gamma priori is：

S3, structure object function, specially：

Variable δ between S31, introducing, according to Jaakkola-Jordon inequality

Wherein, z=(2t-1) y,

λ (δ)=(1/4 δ) tanh (δ/2), tanh (δ)=(exp (x)-exp (- x))/(exp (x)+exp (- x))；

S32, structure alternative functions

S33, θ={ x, α, w, β } is made, build object function G (t, θ, δ)=F (t, x, w, δ) p (x | α) p (α) p (w | β) p (β)；

S4, make q (θ)=q_x(x)q_α(α)q_w(w)q_β(β), each parameter is updated using V-EM algorithm：

S41, renewal q_x(x)：

Wherein, Λ_α=diag (α₁,...α_n),

Λ_δ=diag (λ (δ₁),...λ(δ_m)), then the mean variance of x is respectively Φ_x=(Λ_<α>+2A^TΛ_δA)^-1, Λ_<α>=diag (<α₁>,…<α_n>),<α_i>For α_iWith regard to being distributed q_α(α) expectation；

S42, renewal q_w(w)：

Wherein, Λ_<β>=diag (<β₁>,...<β_n>),< β_i>For β_iWith regard to being distributed q_β(β) expectation, therefore the mean variance of w be respectivelyΦ_w= (Λ_<β>+2Λ_δ)^-1；

S43, renewal q_α(α)：

Wherein,ForWith regard to being distributed q_xThe expectation of (x), Therefore α obeys following Gamma distribution：Wherein,Then α_i's It is desired for

S44, renewal q_β(β)：

Wherein,ForWith regard to being distributed q_wThe expectation of (w), Therefore β obeys following Gamma distribution：WhereinThen α_i's It is desired for

S45、RightDerivation, can obtainMake above formula obtain for 0

Wherein,<xx^T>=μ_xμ_x ^T+Φ_x；

If the above-mentioned iterative process of S6 meets end conditionStop iteration, otherwise returning S4 is carried out Next iteration.

The invention has the beneficial effects as follows：

The present invention requires no knowledge about the sparse degree of the prior information of sign-inverted number and sparse signal, while also without Other design parameters, in the case that bit reversal error numbers are more, the present invention compares other algorithms bigger performance Advantage.

Description of the drawings

Fig. 1 is each algorithm bit reversal error numbers L and NMSE, the relation of Hamming error.

Fig. 2 is each algorithm measurement number of times m and NMSE, the relation of Hamming error.

Specific embodiment

With reference to specific embodiment, the present invention is described in further detail.

S1, perception matrix A with stochastical sampling property is constructed, sampling is carried out to signal and obtains y, step-up error preset value ε；

S2, the priori of construction parameters, Posterior distrbutionp：

T with regard to the Posterior distrbutionp of y is：Wherein, σ (y_i)=1/ (1+exp (- Y) it is) logical function, and can leads,

The Gauss of x, w against Gamma priori is：

S3, structure object function, specially：

Variable δ between S31, introducing, according to Jaakkola-Jordon inequality

Wherein, z=(2t-1) y,

λ (δ)=(1/4 δ) tanh (δ/2), tanh (δ)=(exp (x)-exp (- x))/(exp (x)+exp (- x))；

S32, structure alternative functions

S33, θ={ x, α, w, β } is made, build object function G (t, θ, δ)=F (t, x, w, δ) p (x | α) p (α) p (w | β) p (β)；

S4, make q (θ)=q_x(x)q_α(α)q_w(w)q_β(β), each parameter is updated using V-EM algorithm：

S41, renewal q_x(x)：

Wherein, Λ_α=diag (α₁,...α_n),

Λ_δ=diag (λ (δ₁),...λ(δ_m)), then the mean variance of x is respectively Φ_x=(Λ_<α>+2A^TΛ_δA)^-1, Λ_<α>=diag (<α₁>,...<α_n>),<α_i>For α_iWith regard to being distributed q_α(α) expectation；

S42, renewal q_w(w)：

Wherein, Λ_<β>=diag (<β₁>,...<β_n>),< β_i>For β_iWith regard to being distributed q_β(β) expectation, therefore the mean variance of w be respectivelyΦ_w= (Λ_<β>+2Λ_δ)^-1；

S43, renewal q_α(α)：

Wherein,ForWith regard to being distributed q_xThe phase of (x) Hope, therefore α obeys following Gamma distribution：Wherein,Then α_iBe desired for

S44, renewal q_β(β)：

Wherein,ForWith regard to being distributed q_wThe expectation of (w), Therefore β obeys following Gamma distribution：WhereinThen α_i's It is desired for

S45、RightDerivation, can obtainMake above formula obtain for 0 Wherein,<xx^T>=μ_xμ_x ^T+Φ_x；

If the above-mentioned iterative process of S6 meets end conditionStop iteration, otherwise returning S4 is carried out Next iteration.

Through aforesaid operations, the dual estimation to sparse signal and bit reversal error is just completed.

Below by other correlation techniques with the inventive method algorithm performance comparative analysis, to verify the present invention's further Performance.

Using two kinds of measurement indexs come the performance of metric algorithm.

One recovery accuracy for being used to weigh sparse signal, is called normalized mean squared error (Normalized Mean Squared Error, abbreviation NMSE)；

One is used to weigh bit reversal error size, is called the definition of Hamming error (Hamming error) .NMSE ForThe definition of Hamming error is

M=200, n=100, K=10 in Fig. 1, compare those calculations for ignoring bit reversal error as can be seen from this figure Method (BIHT, 1-BCS), the present invention have bigger performance advantage；And those algorithms for considering bit reversal errors are compared, with The increase of bit reversal error, the robustness of this algorithm are higher.N=100, K=10, L=10 in Fig. 2, that is, have 10 bits anti- Turn error, from this figure, it can be seen that increase of the present invention with measurement number m, the performance of algorithm compare other algorithms have bigger Lifting.

To sum up, the inventive method is the 1 bit quantization error estimation based on compressed sensing, and which is by bit reversal error A sparse signal is modeled as, by well-designed iterative algorithm, each relevant parameter of more new algorithm, is requiring no knowledge about ratio On the premise of special reversion error numbers and position, Combined estimator is carried out to sparse signal and bit reversal error.In bit reversal In the case that error numbers are more, the present invention compares other algorithms and has higher robustness, with bigger performance advantage.

Claims (1)

1. 1 bit compression Bayes's cognitive method of a kind of strong robustness, it is characterised in that comprise the following steps that：

S1, perception matrix A with stochastical sampling property is constructed, sampling is carried out to signal and obtains y, step-up error preset value ε；

S2, the priori of construction parameters, Posterior distrbutionp：

T with regard to the Posterior distrbutionp of y is：Wherein, σ (y_i(1+exp (- y)) is for)=1/ Logical function, and can lead,

The Gauss of x, w against Gamma priori is：

S3, structure object function, specially：

Variable δ between S31, introducing, according to Jaakkola-Jordon inequality

Wherein, z=(2t-1) y,

λ (δ)=(1/4 δ) tanh (δ/2), tanh (δ)=(exp (x)-exp (- x))/(exp (x)+exp (- x))；

S32, structure alternative functions

S33, θ={ x, α, w, β } is made, build object function G (t, θ, δ)=F (t, x, w, δ) p (x | α) p (α) p (w | β) p (β)；

S4, make q (θ)=q_x(x)q_α(α)q_w(w)q_β(β), each parameter is updated using V-EM algorithm：

S41, renewal q_x(x)：

Wherein, Λ_α=diag (α₁,...α_n),

Λ_δ=diag (λ (δ₁),...λ(δ_m)), then the mean variance of x is respectivelyΦ_x= (Λ_<α>+2A^TΛ_δA)^-1, Λ_<α>=diag (<α₁>,...<α_n>),<α_i>For α_iWith regard to being distributed q_α(α) expectation；

S42, renewal q_w(w)：

Wherein, Λ_<β>=diag (<β₁>,...<β_n>),<β_i>For β_iWith regard to being distributed q_β(β) expectation, therefore the mean variance of w be respectivelyΦ_w=(Λ_<β>+2 Λ_δ)^-1；

S43, renewal q_α(α)：

Wherein,ForWith regard to being distributed q_xThe expectation of (x), therefore α obeys following Gamma distribution：Wherein,Then α_iExpectation For

S44, renewal q_β(β)：

Wherein,ForWith regard to being distributed q_wThe expectation of (w), therefore β obeys following Gamma distribution：WhereinThen α_iExpectation For

S45、RightDerivation, can obtainMake above formula obtain for 0 Wherein,<xx^T>=μ_xμ_x ^T+Φ_x；

If the above-mentioned iterative process of S6 meets end conditionStop iteration, otherwise return S4 carries out next Secondary iteration.