Main content:
- The algorithm flow of FPC
- The MATLAB realization of FPC
- 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:
- Iterative Error Convergence curve:
- 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