Wavelet footprints based signal recovery technique for signal coding

In the real-world the majority of the signals are observed as piecewise smooth functions but their representations in a raw data format consume a huge amount of storage and processing power. In spite of the wavelets provide a good representation for the piecewise polynomial signals and its discontinuities, there is still a fair amount of correlation between wavelet coefficients produced by the discontinuities in the signal. Consequently Dragotti et al [4]. Introduced a new concept called wavelet footprints with a new robuts Algorithm called ADFP to sparse the representation of the piecewise smooth signals in 1D. However this paper proposes a new idea to achieve a better compression performance than wavelet footprints with ADFP algorithm. The introduced idea based observation which is the wavelet footprints dictionary obeys the restricted isometry property (RIP) which produces a solution equal to L1 minimization. The results showed that proposed technique outperforms the wavelet footprints based on adaptive depth footprints pursuit (ADFP) in the compression ratio with high accuracy.