Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  proposes a new fBm (fractional Brownian motion) interpolation/reconstruction method from partially known samples based on CS (Compressive Sampling). Since 1/ƒ property implies por law decay of the fBm spectrum, the fBm signals should be sparse in frequency domain. This property motivates the adoption of CS in the development of the reconstruction method. Hurst parameter H that occurs in the por law determines the sparsity level, therefore the CS reconstruction quality of an fBm signal for a given number of known subsamples will depend on H. Hover, the proposed method does not require the information of H to reconstruct the fBm signal from its partial samples. The method employs DFT (Discrete Fourier Transform) as the sparsity basis and a random matrix derived from known samples positions as the projection basis. Simulated fBm signals with various values of H are used to show the relationship beten the Hurst parameter and the reconstruction quality. Additionally, US-DJIA (Dow Jones Industrial Average) stock index monthly values time-series are also used to show the applicability of the proposed method to reconstruct a real-world data.
['Andriyan Bayu Suksmono']
I am writing a research paper on a idea Reconstruction of fractional Brownian motion signals from its sparse samples based on Compressive Sampling
[{"from": "human", "value": "I am writing a research paper on a idea Reconstruction of fractional Brownian motion signals from its sparse samples based on Compressive Sampling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  proposes a new fBm (fractional Brownian motion) interpolation/reconstruction method from partially known samples based on CS (Compressive Sampling). Since 1/\u0192 property implies por law decay of the fBm spectrum, the fBm signals should be sparse in frequency domain. This property motivates the adoption of CS in the development of the reconstruction method. Hurst parameter H that occurs in the por law determines the sparsity level, therefore the CS reconstruction quality of an fBm signal for a given number of known subsamples will depend on H. Hover, the proposed method does not require the information of H to reconstruct the fBm signal from its partial samples. The method employs DFT (Discrete Fourier Transform) as the sparsity basis and a random matrix derived from known samples positions as the projection basis. Simulated fBm signals with various values of H are used to show the relationship beten the Hurst parameter and the reconstruction quality. Additionally, US-DJIA (Dow Jones Industrial Average) stock index monthly values time-series are also used to show the applicability of the proposed method to reconstruct a real-world data."}]