1. A method for transforming a seismic trace f(t) in response to a seismic source wavelet I(t) into a compressed domain comprising the steps of transforming said seismic source wavelet I(t) into a zero-degree phase wavelet Φ p (t) and a shifted 90 degree phase wavelet Ψ p (t), where the wavelets Φ p (t) and Ψ p (t) span a two dimensional sub-space, creating a sub-space dictionary as 
 D s ={(Φ p , Ψ p )} p∈Γ where Γ is a set of wavelets which are derived using Φ p (t) wavelet and Ψ p (t) wavelet, projecting said seismic trace f(t) onto said dictionary D s to find the best matching projection, with a residual determined after each projection matching, wherein the sum of said residuals determines the fidelity in data compression.