PTtools

These are codes for analytical predictions of compressed sensing Phase Transitions and various function for the analysis of PT datasets. Not everything is currently made available. I will make more functions available over time.

To install the R package of PT from github:

> install.packages("devtools")
> library(devtools)
> install_github("monajemi/CompressedSensing", subdir="PTtools/R/PT")
> library(PT)

> predictPT(1/2,'R')
[1] 0.1928448

There is also a MATLAB version of this prediction.

>> predictPT(1/2,'R')

Frames

These are codes for construction of various frames that I have used in my publications

Main function

function  A = buildFrame(n, N, ensembleCode,fieldCode,qOperator,varargin);
% Function: buildFrame.m
% builds desired frame according to information given as input.
%
% input:
% n: # rows
% N: # columns
% ensembleCode: the code for the desired ensemble e.g., 'DG'
% fieldCode: 'R','C','R+'
% qOperator: if set to 1, then an operator A is built for fast calculation of Ax and A'x.
%            if set to 0 (default), frame is explicitly built
% varargin:
% PEG-LDPC and devore/array_pc: 
%   varargin{1}:column degree
%   varargin{2}:sglConcent (0: strict regularity, 1:best-effort)

Examples:

% build a real USE matrix
A = buildFrame(16,64,'USE','R');

% build a Complex DG frame of size 32x128
A = buildFrame(32,32*4,'DG','C');


% build 'non-strictly' regular (best effort) LDPC matrices of degree 3
A = buildFrame(504,1008, 'LDPC','R',[],3,1);
A = buildFrame(504,1008, 'LDPC','R',[],3);


% build 'strictly' regular LDPC matrices of degree 3
A = buildFrame(504,1008, 'LDPC','R',[],3,0);

% build a Devore matrix of size (q^2)x20 with coulmn degree q=3 
A = buildFrame(9,20,'devore',[],[],3)

% build an array parity check matrix of size (j*q)xq^2 for j=3 and q=5;
A = buildFrame(5*3,5^2,'array-pc',[],[],3)

References:

"Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices", Monajemi et al. 2013. Download

"Compressed Sensing Using Binary Matrices of Nearly Optimal Dimensions", Mahsa Lotfi and Mathukumalli Vidyasagar, arXiv: 1808.03001