CS Approach for CV Data Capture and

CS Approach for CV Data Capture and RecoveryIn this section, we discuss the proposed CS approach for CV data capture and recovery. In particular, it illustrates how to select the matrix T to transform the original CV data vector to a sparse one and the matrix º that satisfies the RIP of order 2K to guarantee accurate recovery.Suppose x ∈ RN is a vector of CV data samples, e.g.,speed samples collected at a fixed rate. According toEq. (1), we need a transform α = TT x so that has a sparse representation in the domain of T . Typical trans-forms include discrete Fourier transform (DFT), discrete cosine transform (DCT), and Discrete Wavelet Transform (DWT). DCT is a Fourier-based transform similar to DFT, but uses cosine functions and the transformed coefficients are real numbers. DWT is more suitable for piecewise constant signals (Razzaque and Dobson 2014), which is not applicable to fluctuating speed samples. Therefore, we select DCT to transform the CV speed signal (Batal and Hauskrecht 2009):