Compressibility analysis of asymptotically mean stationary processes

This work provides new results for the analysis of random sequences in terms ? p -compressibility. The characterize degree which a sequence can be approximated by its best k -sparse version under different rates significant coefficients (compressibility analysis). In particular, notion strong -characterization is introduced to denote that has well-defined asymptotic limit (sample-wise) -term approximation error when fixed rate considered (fixed-rate main theorem this shows rich family asymptotically mean stationary (AMS) processes -characterization. Furthermore, we present and analyze -approximation function processes. Adding ergodicity AMS processes, introduce demonstrating constant determined closed-form process. Our analyses contribute theory understanding discrete-time sparse and, on technical side, confirm how instrumental point-wise ergodic determine compressibility expression even stationarity assumptions are relaxed.