# US 2021/0333237 A1 · Distortion-free boundary extension method for online wavelet denoising

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- Number: US 2021/0333237 A1
- Document ID: US20210333237A1
- Status: Published application
- Kind: A1
- Application number: 17/202,787
- Filed: 2021-03-16
- Published: 2021-10-28
- Earliest claimed: 2020-04-27
- Assignees: Harbin Engineering University
- Applicants: Harbin Engineering University
- Inventors: Lanyong ZHANG; Menglin WANG; Sheng LIU; Chengyu LI
- Web page: https://patentgrep.com/patent/US20210333237A1

## CPC

- G01N 27/82: for investigating the presence of flaws
- G01R 33/12: Measuring magnetic properties of articles or specimens of solids or fluids (involving magnetic resonance G01R33/20)
- G06F 17/148: {Wavelet transforms}
- G06F 2218/06: by applying a scale-space analysis, e.g. using wavelet analysis
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

The present disclosure provides a distortion-free boundary extension method for online wavelet denoising. The method includes: S1: acquiring a signal segment xn, and performing a distortion-free boundary extension on the signal segment to obtain M+N+L data; S2: decomposing a lifting wavelet of the N data to be denoised into j layers to acquire approximation coefficients and detail coefficients; S3: calculating a threshold of each layer of the lifting wavelet; S4: thresholding the detail coefficients of each layer to obtain estimated values of the detail coefficients; S5: performing wavelet reconstruction by the approximation coefficients and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal after denoising; and S6: outputting data.

## Claims

### Claim 1

A distortion-free boundary extension method for online wavelet denoising, comprising the following steps:
S1: acquiring a signal segment xn, and performing a distortion-free boundary extension on the signal segment to obtain M+N+L data, wherein M represents a number of historical data used for a distortion-free left extension; L represents a number of future data used for a distortion-free right extension; N represents a number of data to be denoised;
S2: decomposing a lifting wavelet of the N data to be denoised into j layers to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1};
S3: calculating a threshold Tj of each layer of the lifting wavelet;
S4: thresholding the detail coefficients {dj, . . . , d2,d2} of each layer to obtain estimated values of the detail coefficients;
S5: performing wavelet reconstruction by the approximation coefficients sj and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal {circumflex over (x)}n after denoising; and
S6: outputting data.

### Claim 2 (depends on 1)

The distortion-free boundary extension method for online wavelet denoising according to claim 1, wherein in S1, the distortion-free boundary extension comprises:
S101: reading, when 0<t≤N+L, N+L sampling points from a sampling start point;
S102: symmetrically extending, when N+L<t<N+L+1, a left boundary of the N+L sampling points read for a length of M, and storing in a buffer A; outputting, if buffer A is full, data in A to a next-level wavelet denoiser, and sliding latter M+L data in buffer A to former M+L spaces in the same order, and clearing a remaining buffer space;
S103: letting k be a cycle counter, k=1;
S104: reading, when kN+L+1≤t≤kN+L+N, P sampling points into A; executing S105 if P=N; executing S107 if P<N;
S105: determining, when kN+L+N<t<kN+L+N+1, that buffer A is full, and performing a sliding window operation in A;
S106: letting k=k+1, and returning to S104; and
S107: ending.

### Claim 3 (depends on 1)

The distortion-free boundary extension method for online wavelet denoising according to claim 1, wherein in S3, the threshold Tj of each layer of the lifting wavelet is calculated as follows:
T
j
=
σ
⁢
2
⁢
ln
⁢
⁢
N
1
+
1
⁢
g
⁢
j
,
j
=
1
,
2
,
3
wherein, σ represents a standard deviation of noise.

### Claim 4 (depends on 2)

The distortion-free boundary extension method for online wavelet denoising according to claim 2, wherein in S3, the threshold Tj of each layer of the lifting wavelet is calculated as follows:
T
j
=
σ
⁢
2
⁢
ln
⁢
⁢
N
1
+
1
⁢
g
⁢
j
,
j
=
1
,
2
,
3
wherein, σ represents a standard deviation of noise.

### Claim 5 (depends on 3)

The distortion-free boundary extension method for online wavelet denoising according to claim 3, wherein in S4, the estimated values of the detail coefficients obtained by thresholding the detail coefficients {dj, . . . , d2,d1} of each layer are:
d
^
j
=
d
j
×
1
⁢
0
-
(
T
j

d
j

+
ɛ
)
γ
wherein, γ=4, ε=10−5.

### Claim 6 (depends on 4)

The distortion-free boundary extension method for online wavelet denoising according to claim 4, wherein in S4, the estimated values of the detail coefficients obtained by thresholding the detail coefficients {dj, . . . , d2,d1} of each layer are:
d
^
j
=
d
j
×
1
⁢
0
-
(
T
j

d
j

+
ɛ
)
γ
wherein, γ=4, ε=10−5.

### Claim 7 (depends on 1)

The distortion-free boundary extension method for online wavelet denoising according to claim 1, wherein a boundary extension in the reconstruction in S5 remains consistent with that in the wavelet decomposition in S2.

### Claim 8 (depends on 1)

The distortion-free boundary extension method for online wavelet denoising according to claim 1, wherein in S2, the wavelet is decomposed into j≤3 layers.

### Claim 9

A distortion-free boundary extension device for online wavelet denoising, comprising a distortion-free boundary extension module and a wavelet denoiser, wherein
the distortion-free boundary extension module is used for performing a distortion-free boundary extension on an acquired signal segment to obtain M+N+L data, wherein M represents a number of historical data used for a distortion-free left extension; L represents a number of future data used for a distortion-free right extension; N represents a number of data to be denoised;
the wavelet denoiser is used for decomposing a lifting wavelet of the N data to be denoised into j layers to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1}, calculating a threshold Tj of each layer of the lifting wavelet, thresholding the detail coefficients {dj, . . . , d2,d1} of each layer to obtain estimated values of the detail coefficients, performing wavelet reconstruction by the approximation coefficients sj and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal {circumflex over (x)}n after denoising, and outputting data.

### Claim 10 (depends on 9)

The distortion-free boundary extension device for online wavelet denoising according to claim 9, wherein the wavelet denoiser calculates the threshold Tj of each layer of the lifting wavelet as follows:
T
j
=
σ
⁢
2
⁢
ln
⁢
⁢
N
1
+
lgj
,
⁢
j
=
1
,
2
,
3
the estimated values of the detail coefficients obtained by thresholding the detail coefficients {dj, . . . , d2,d1} of each layer are:
d
^
j
=
d
j
×
1
⁢
0
-
(
T
j

d
j

+
ɛ
)
γ
wherein, γ=4, ε=10−5.

### Claim 11

An electronic device, comprising a memory, a processor and a computer program, wherein the computer program is stored in the memory, and the processor runs the computer program to execute the following steps:
S1: acquiring a signal segment xn, and performing a distortion-free boundary extension on the signal segment to obtain M+N+L data, wherein M represents a number of historical data used for a distortion-free left extension; L represents a number of future data used for a distortion-free right extension; N represents a number of data to be denoised;
S2: decomposing a lifting wavelet of the N data to be denoised into j layers according to the historical data and the future data to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1};
S3: calculating a threshold Tj of each layer of the lifting wavelet;
S4: thresholding the detail coefficients {dj, . . . , d2,d1} of each layer to obtain estimated values of the detail coefficients;
S5: performing wavelet reconstruction by the approximation coefficients sj and the estimated values of the detail coefficients obtained by thresholding to obtain a reconstructed signal {circumflex over (x)}n after denoising; and
S6: outputting data.

### Claim 12 (depends on 11)

The electronic device according to claim 11, wherein in S1, the distortion-free boundary extension comprises:
S101: reading, when 0<t≤N+M, N+M sampling points from a sampling start point;
S102: symmetrically extending, when N+M<t<N+M+1, a left boundary of the N+M sampling points read for a length of M, and storing in a buffer A; outputting, if buffer A is full, data in A to a next-level wavelet denoiser, and sliding latter M+N data in buffer A to former M+N spaces in the same order, and clearing a remaining buffer space;
S103: letting k be a cycle counter, k=1;
S104: reading, when kN+M+1≤t≤kN+M+N, P sampling points into A; executing S105 if P=N; executing S107 if P<N;
S105: determining, when kN+M+N<t<kN+M+N+1, that buffer A is full, and performing a sliding window operation in A;
S106: letting k=k+1, and returning to S104;
S107: ending; and
S108: acquiring, when performing a distortion-free boundary extension on a k-th signal segment, M historical data in a (k−1)-th signal segment in buffer A, to-be-denoised data in the k-th signal segment and L future data in a (k+1)-th signal segment to generate M+N+L data used for the distortion-free boundary extension on the k-th signal segment.

### Claim 13 (depends on 11)

The electronic device according to claim 11, wherein in S3, the threshold Tj of each layer of the lifting wavelet is calculated as follows:
T
j
=
σ
⁢
2
⁢
ln
⁢
⁢
N
1
+
lgj
,
⁢
j
=
1
,
2
,
3
wherein, σ represents a standard deviation of noise.

### Claim 14 (depends on 12)

The electronic device according to claim 12, wherein in S3, the threshold Tj of each layer of the lifting wavelet is calculated as follows:
T
j
=
σ
⁢
2
⁢
1
⁢
n
⁢
N
1
+
lgj
,
j
=
1
,
2
,
3
wherein, σ represents a standard deviation of noise.

### Claim 15 (depends on 13)

The electronic device according to claim 13, wherein in S4, the estimated values of the detail coefficients obtained by thresholding the detail coefficients {dj, . . . , d2,d1} of each layer are:
d
^
j
=
d
j
×
1
⁢
0
-
(
T
j

d
j

+
ɛ
)
γ
wherein, γ=4, ε=10−5.

### Claim 16 (depends on 14)

The electronic device according to claim 14, wherein in S4, the estimated values of the detail coefficients obtained by thresholding the detail coefficients {dj, . . . , d2,d1} of each layer are:
d
^
j
=
d
j
×
1
⁢
0
-
(
T
j

d
j

+
ɛ
)
γ
wherein, γ=4, ε=10−5.

### Claim 17 (depends on 11)

The electronic device according to claim 11, wherein a boundary extension in the reconstruction in S5 remains consistent with that in the wavelet decomposition in S2.

### Claim 18 (depends on 11)

The electronic device according to claim 11, wherein in S2, the wavelet is decomposed into j≤3 layers.

### Claim 19 (depends on 11)

The electronic device according to claim 11, wherein the S2: decomposing a lifting wavelet of the N data to be denoised into j layers according to the historical data and the future data to acquire approximation coefficients sj and detail coefficients {dj, . . . , d2,d1} specifically comprises:
acquiring, from the historical data, data used for a left boundary of the N data to be denoised during the j-layer decomposition of the lifting wavelet; and
acquiring, from the future data, data used for a right boundary of the N data to be denoised during the j-layer decomposition of the lifting wavelet.