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This paper proposes a new fBm (fractional Brownian motion)interpolation/reconstruction method from partially known samples based on CS(Compressive Sampling). Since 1/f property implies power law decay of the fBmspectrum, the fBm signals should be sparse in frequency domain. This propertymotivates the adoption of CS in the development of the reconstruction method.Hurst parameter H that occurs in the power law determines the sparsity level,therefore the CS reconstruction quality of an fBm signal for a given number ofknown subsamples will depend on H. However, the proposed method does notrequire the information of H to reconstruct the fBm signal from its partialsamples. The method employs DFT (Discrete Fourier Transform) as the sparsitybasis and a random matrix derived from known samples positions as theprojection basis. Simulated fBm signals with various values of H are used toshow the relationship between the Hurst parameter and the reconstructionquality. Additionally, US-DJIA (Dow Jones Industrial Average) stock indexmonthly values time-series are also used to show the applicability of theproposed method to reconstruct a real-world data.

Reconstruction of Fractional Brownian Motion Signals From Its Sparse Samples Based on Compressive Sampling