**3. Data-Driven Redundant Transform Model Based on Tight Frame**

In this section, we present our data-driven redundant transform based on Parseval frames (DRTPF, Section 3.1) model along with an efficient redundant transform learning algorithm (Section 3.2) which contains the sparse coding algorithm (Section 3.2.1) and the transform pair update algorithm (Section 3.2.2).
