基于压缩感知理论的MRI快速算法测试软件包是在附后的一系列压缩感知理论相关原始算法软件包的基础上整理成适合于MRI快速算法需要的集成软件包。根据处理的图像大小将各种算法列表分类，并给出各种算法的相对重建时间、重建精度对比数据及相应的重构图像。
大尺度图像（256 x 256）测试结果对比表
| Algorithms |
Sub-Algorithms |
Reconstruction Time (s) |
MSE |
PSNR |
Reconstruction Images (256 x 256) |
| BPDN |
IT |
1.984763e+000 |
4.907349e+000 |
4.125633e+001 |
|
| PCD |
4.464305e+001 |
3.971649e+000 |
4.217509e+001 |
|
| PPPA |
2.958087e+000 |
5.903447e+002 |
2.045374e+001 |
|
| FBMP |
FBMPC |
1.094662e+003 |
2.863306e+002 |
2.359612e+001 |
|
| FBMPR |
4.197287e+002 |
3.008671e+002 |
2.338105e+001 |
|
| IST |
IST |
4.572562e+000 |
3.744394e+001 |
3.243098e+001 |
|
| GPSR |
GPSR-Basic |
2.916670e+000 |
3.825282e+001 |
3.233816e+001 |
|
| GPSR-BB |
1.389199e+000 |
3.826416e+001 |
3.233688e+001 |
|
| L1_LS |
L1_LS |
1.443935e+002 |
8.892715e+000 |
3.867446e+001 |
|
| L1magic |
Tvdantzig |
2.206536e+003 |
9.271381e+001 |
2.849336e+001 |
|
| Tvqc |
4.447328e+002 |
9.734653e+001 |
2.828159e+001 |
|
| Tveq |
1.676582e+003 |
9.675391e+001 |
2.830811e+001 |
|
| L1dantzig |
8.750181e+001 |
2.865390e+001 |
3.359296e+001 |
|
| L1qc |
4.957916e+002 |
3.175873e+001 |
3.314617e+001 |
|
| L1eq |
8.057766e+001 |
5.270093e+001 |
3.094662e+001 |
|
| L1decode |
6.380241e+000 |
8.967947e+001 |
2.863787e+001 |
|
| RecPF |
RecPF |
3.362514e+000 |
1.530939e+003 |
1.631522e+001 |
|
| SMP |
SMP |
1.530959e+000 |
4.472975e+001 |
3.165883e+001 |
|
| SSMP |
2.874842e+000 |
3.425566e+001 |
3.281748e+001 |
|
| SpaRSA |
SpaRSA |
2.706987e+000 |
3.747763e+001 |
3.242708e+001 |
|
| SparseMRI |
SparseMRI |
7.417183e+000 |
1.551814e+001 |
3.625640e+001 |
|
| TVAL3 |
TVAL3 |
4.306348e+000 |
7.728485e+001 |
2.928386e+001 |
|
| TwIST |
TwIST |
1.336680e+001 |
5.376707e+002 |
2.085964e+001 |
|
| YALL1 |
PDCT |
3.174095e+000 |
2.568893e+001 |
3.406734e+001 |
|
| PDWHT |
1.562219e+000 |
2.585704e+001 |
3.403901e+001 |
|
| PDFT |
1.859088e+000 |
9.250793e-001 |
4.850301e+001 |
|
| mcLeastR |
mcLeastR |
5.191548e-001 |
1.114050e+003 |
1.769575e+001 |
|
| mc_sgLeastR |
mc_sgLeastR |
1.274801e+000 |
5.123681e+002 |
2.106898e+001 |
|
MSE : Mean Square Error
PSNR : Peak Signal to Noise Ratio
BPDN : Basis Pursuit Denoising
IT : Iterative Thresholding
PCD : Parallel Coordinate Descent
PPPA : Predual Proximal Point Algorithm
FBMP : Fast Bayesian Matching Pursuit
FBMPC : Fast Bayesian Matching Pursuit Complex Gaussian.
FBMPR : Fast Bayesian Matching Pursuit Real-valued Gaussian
IST : Iterative Shrinkage/Thresholding Algorithms
GPSR : Gradient Projection for Sparse Reconstruction
GPSR-Basic : Basic Gradient Projection for Sparse Reconstruction
GPSR-BB : Barzilai-Borwein Gradient Projection for Sparse Reconstruction
L1_LS : L1-Regularized Least Squares Problem Solver
L1magic : Recovery of Sparse Signals via Convex Programming
Tvdantzig : the total variation dantzig program
Tvqc : minimum total variation with quadratic constraints
Tveq : minimum total variation with equality constraints.
L1dantzig : minimum L1 dantzig program
L1qc : minimum L1 with quadratic constraints
L1eq : minimum L1 with equality constraints
L1decode : minimum L1 decoding via linear programming
RecPF : Reconstruction from Partial Fourier data
SMP : Sparse Matching Pursuit algorithm
SpaRSA : Sparse Reconstruction by Separable Approximation
Sparse MRI : The Application of Compressed Sensing for Rapid MR Imaging
TVAL3 : Total Variation Minimization by Augmented Lagrangian and Alternating Direction Algorithms
TwIST : Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
YALL1 : Your ALgorithms for L1 Optimization
PDCT : Partial discrete-cosine transform
PDWHT : Partial discrete-Walsh-Hadamard transform
PDFT : Partial discrete-Fourier transform
mcLeastR : Least Squares Loss for Multi-class (task) Learning via the (group) L1/Lq-norm Regularization
mc_sgLeastR : Least Squares Loss for Multi-class (task) Learning via the sparse group Lasso penalty
Large Scale Images（256 x 256）
Original Image
BPDN-IT BPDN-PCD BPDN-PPPA FBMPC
FBMPR IST GPSR-Basic GPSR-BB
L1-LS Tvdantzig Tvqc Tveq
L1dantzig L1qc L1eq L1decode
RecPF SMP SSMP SpaRSA
SpareMRI TVAL3 TwIST YALL1-PDCT
YALL1-PDWHT YALL1-PDFT mcLeastR mc_sgLeastR
小尺度图像（64 x64）测试结果对比表
| Algorithms |
Sub-Algorithms |
Reconstruction Time (s) |
MSE |
PSNR |
Reconstruction Images (64 x 64) |
| Fast-Laplace |
Fast-Laplace |
4.787138e+001 |
1.214812e+002 |
2.731971e+001 |
 |
| FPC |
FPC |
7.391355e+000 |
5.218587e+003 |
1.098927e+001 |
|
| ISD |
ISD |
1.755763e+003 |
5.369287e+001 |
3.086563e+001 |
|
| SL0 |
SL0 |
7.257664e+000 |
1.058698e+003 |
1.791708e+001 |
|
| Greed |
Nomp |
5.248659e-001 |
5.239353e+002 |
2.097202e+001 |
|
| SPGL1 |
SPGL1 |
1.935836e+002 |
7.241748e+001 |
2.956637e+001 |
|
| L1 |
LeastR |
5.324849e+000 |
1.789664e+003 |
1.563708e+001 |
|
| NNLeastR |
5.386454e+000 |
1.223279e+004 |
7.289542e+000 |
|
FastLaplace : the fast Laplace algorithm
FPC : Fixed Point Continuation (FPC) for l1-Regularized Least Squares
ISD : Iterative Support Detection
SL0 : Smoothed L0 (SL0) algorithm
Greed : Greedy algorithms
Nomp : Nearly Orthogonal Matching Pursuit
SPGL1: Solver for large-scale L1
LeastR : Least Squares Loss with the L1-norm Regularization
NNLeastR : Least Squares Loss with the L1-norm Regularization subject to non-negative constraint
Small Scale Images（64 x 64）x500%
Original Image
FastLaplace FPC
ISD SL0
Greed-Nomp SPGL1
leastR nnleastR
基于压缩感知理论的MRI快速算法测试软件包下载链接
压缩感知理论相关原始算法软件包下载链接：
BPDN (package bpdn_web.zip)：http://www.math.univ-paris13.fr/~malgouy/software/index.html
FBMP (package fbmp_v1_2.zip)：http://www2.ece.ohio-state.edu/~zinielj/fbmp/download.html
GPSR (package GPSR_6.0.zip)：http://www.lx.it.pt/~mtf/GPSR/
L1_LS (package l1_ls_matlab.zip)：http://www.stanford.edu/~boyd/l1_ls/
L1magic (package l1magic-1.1.tar.gz)：http://www.l1-magic.org/
RecPF (package RecPF_v2.2_pub)：http://www.caam.rice.edu/~optimization/L1/RecPF/
SMP (package cs-code.zip)：http://groups.csail.mit.edu/toc/sparse/wiki/index.php?title=Sparse_Recovery_Experiments
SpaRSA (package SpaRSA_2.0.zip)：http://www.lx.it.pt/~mtf/SpaRSA/
SparseMRI (package sparseMRI_v0.2.tar.gz)：http://www.stanford.edu/~mlustig/SparseMRI.html
TVAL3 (package TVAL3_beta2.4.zip)：http://www.caam.rice.edu/~optimization/L1/TVAL3/
TwIST (package _v2.zip): http://www.lx.it.pt/~bioucas/TwIST/TwIST.htm
YALL1 (package YALL1-b6.zip):http://yall1.blogs.rice.edu/
FastLaplace (package FastLaplace.zip)：http://ivpl.eecs.northwestern.edu/system/files/FastLaplace.zip
fpc_v2.zip (package fpc_v2.zip)：http://www.caam.rice.edu/~optimization/L1/fpc/
Greed (package sparsify_0_4.zip)：http://www.personal.soton.ac.uk/tb1m08/sparsify/sparsify.html
ISD (package ISD_v1.1.zip)：http://www.caam.rice.edu/~optimization/L1/ISD/
SL0 (package SL0MatlabCodeV2.zip)：http://ee.sharif.edu/~SLzero/
SPGL1 (package spgl1-1.7.zip)：http://www.cs.ubc.ca/labs/scl/index.php/Main/Spgl1
SLEP (package SLEP_4.0.zip)：http://www.public.asu.edu/~jye02/Software/SLEP/index.htm
