Symmetric tight frame wavelets with dilation factor M=4

Abdelnour, A. Farras

doi:10.1016/j.sigpro.2011.05.005

Cited by 7 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…

\int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty

r = italicsup ({}, r : \int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty) .

This is defined for the rank 2 wavelet. A wavelet with large regularity approaches an ideal filter, and therefore, the FB will have better performance .…”

Section: Proposed Waveletmentioning

confidence: 99%

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

View full text Add to dashboard Cite

Summary A new method for computation of discrete wavelet transform is introduced. The impulse response of the finite impulse response (FIR) filter, as the main block in filter bank method, is realized such that orthonormal wavelet transform is achieved without using any multiplier as the most challenging part of the FIR filters. It is proved that the calculated Sobolev regularity of the proposed wavelet is higher than that of Daubechies for the same support width. Compared with most popular known wavelets, simulation results of the newly introduced wavelet for signal denoising prove remarkable advantage of our wavelet especially in terms of complexity and power consumption. The proposed wavelet and well‐known Daubechies wavelet are separately implemented on the Spartan‐6 FPGA (Field Programmable Gate Array) to compare the performance of them. The occupied slices and LUTs (Lookup Table) in realization of the proposed wavelet in comparison with those of Daubechies wavelet are decreased by 50% and 56%, respectively. Its power consumption at 100 MHz is also reduced by 86% in comparison with the Daubechies wavelet, and maximum frequency is increased by 186%. Implementation with standard cells of a 0.18‐μm CMOS (Complementary Metal Oxide Semiconductor Field Effect Transistor) technology shows 75% and 85% reduction in the power and chip area, respectively.

show abstract

“…

\int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty

r = italicsup ({}, r : \int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty) .

This is defined for the rank 2 wavelet. A wavelet with large regularity approaches an ideal filter, and therefore, the FB will have better performance .…”

Section: Proposed Waveletmentioning

confidence: 99%

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…The detailed derivation has been published in an earlier work. 20 For the case k = 1 corresponding to K 0 ∈ 2N, and given K min , we seek a polynomial A(x) obtained from a truncated Taylor series such that…”

Section: Lowpass Filter Designmentioning

confidence: 99%

“…The lowpass filter is first designed separately using either Gröbner bases [22][23][24] or Taylor polynomials. 20 The remaining filters are obtained given the lowpass filter and using Gröbner bases. The resulting filterbanks enjoy a limited redundancy when compared with their dyadic tight frame counterparts, 5/3 for M = 4 versus a redundancy of 3 (for three dyadic wavelets) and 2 (for two dyadic wavelets), while maintaining smooth limit functions.…”

Section: Introductionmentioning

confidence: 99%

Tight frame 6-band symmetric wavelets with limited redundancy

Abdelnour

2011

SPIE Proceedings

Self Cite

View full text Add to dashboard Cite

We consider the design of 6-channel tight frame symmetric wavelet with scaling factor M = 4. The lowpass filter is designed using either Gröbner bases or truncated Taylor series methods. The bandpass and highpass filters are then designed using Gröbner bases. The resulting filters have linear phase, smooth limit functions, and reduced redundancy. It was possible to obtain filterbanks with K 0 (zeros at z = 1 and z = ±j for the lowpass filter) up to 5 and K min (zeros at z = 1 for bandpass/highpass filters) of 1 or greater. The proposed filterbanks generate five wavelets and a scaling function with the underlying filters related as follows: H 5−i (z) = H i (−z), i = 0 . . . 5.

show abstract

“…In this paper, we presented a novel denoising method for CE signal based on the construction of a tight frame [16] learning from the input signal. Since the decomposition of CE signal under the learned tight frame filter is sparse, an adaptive threshold incorporating the spatial correlation between adjacent coefficients was computed to remove the noise.…”

Section: Introductionmentioning

confidence: 99%

Denoising method for capillary electrophoresis signal via learned tight frame

Wang

Gao

et al. 2020

IET signal process.

View full text Add to dashboard Cite

Since capillary electrophoresis (CE) signals are always contaminated by random noise, which has negative influence on the accuracy of detection and analysis, it is necessary to remove noise before further applications of the CE signals. In this study, a tight frame learned from the data itself is applied to the removal of noise for CE signals. To achieve an effective decomposition of the CE signal, a one-dimensional discrete tight frame tailored to the input signal is first constructed by introducing tight frame constraint into the popular dictionary learning model. Then, due to each subband containing different information of the noise, an adaptive threshold is computed to shrink the detail coefficients instead of using a global threshold. Finally, the denoised CE signal is reconstructed from the thresholded coefficients by using the inverse transform of the tight frame. To evaluate the denoising efficiency, the proposed method is applied to the simulated CE signals and real CE signals. Experimental results indicate that compared with other denoising methods, the proposed method obtains a better shape preservation of the peaks as well as a higher signal-to-noise ratio.

show abstract

Symmetric tight frame wavelets with dilation factor M=4

Cited by 7 publications

References 41 publications

A new discrete wavelet transform appropriate for hardware implementation

A new discrete wavelet transform appropriate for hardware implementation

Tight frame 6-band symmetric wavelets with limited redundancy

Denoising method for capillary electrophoresis signal via learned tight frame

Contact Info

Product

Resources

About