A brief talk on compression perception (31): Fixed-point continuous method FPC for compression-aware reconstruction algorithm

Main content:

1. The algorithm flow of FPC
2. The MATLAB realization of FPC
3. Experiment and result of one-dimensional signal

A reconstruction algorithm based on convex optimization

A compression-aware reconstruction algorithm based on convex optimization.

Convex optimization problems for constraints:

To constrain the convex optimization problem:

In the compression perception, the J function and the H function are selected:

First, the algorithm of FPC

FPC, full name fixed-point continuation, translated here for fixed-point continuous.

Mathematical model:

Algorithm:

The algorithm uses the contraction formula shrinkage (also called soft threshold value soft thresholding) in the iterative process, and the algorithm is simple and graceful.

Iterative process:

Gradient

Merging, you get the formula for the entire iterative process:

The reason is called continuous continuation, because of the choice of u, we need a continuous path tracking strategy, that is, for the parameter U, select an appropriate continuous ascending sequence to guide the whole iterative process to converge.

Algorithm Flow:

Specific reference: http://www.caam.rice.edu/~optimization/L1/fpc/

Second, the implementation of the MATLAB FPC (FPC.M)

You can download the relevant code from the link above and don't post it here.

Experiment and results of three or one-D signal (BASIC_RUN.M)

1, before and after the reconstruction signal value XS and x contrast:

1. Iterative Error Convergence curve:

1. The FPC compares with the following three algorithms:

A brief talk on compression perception (31): Fixed-point continuous method FPC for compression-aware reconstruction algorithm