Package 'R1magic'

Compare L1, L2 and TV on a sparse signal.

Description

Compare L1, L2 and TV on a sparse signal.

Usage

CompareL1_L2_TV1(N, M, per)

Arguments

N	Size of the sparse signal to generate , integer.
M	Number of measurements.
per	Percentage of spikes.

Author(s)

Mehmet Suzen

---

Generate Discrete Fourier Transform Matrix using DFTMatrixPlain.

Description

Generate Discrete Fourier Transform Matrix (NxN).

Usage

DFTMatrix0(N)

Arguments

N	Integer value determines the dimension of the square matrix.

Value

It returns a NxN square matrix.

Author(s)

Mehmet Suzen

See Also

DFTMatrixPlain

Examples

DFTMatrix0(2)

---

Generate Plain Discrete Fourier Transform Matrix without the coefficient

Description

Generate plain Discrete Fourier Transform Matrix (NxN) without a coefficient.

Usage

DFTMatrixPlain(N)

Arguments

N	Integer value defines the dimension of the square plain DFT matrix.

Value

It returns a NxN square matrix.

Author(s)

Mehmet Suzen

Examples

DFTMatrixPlain(2)

---

Generate Gaussian Random Matrix

Description

Generate Gaussian Random Matrix ( zero mean and standard deviation one.)

Usage

GaussianMatrix(N, M)

Arguments

N	Integer value determines number of rows.
M	Integer value determines number of columns.

Value

Returns MxN matrix.

Author(s)

Mehmet Suzen

Examples

GaussianMatrix(3,2)

---

L-p norm of a given complex vector

Description

L-p norm of a given complex vector

Usage

Lnorm(X, p)

Arguments

X	a complex vector, can be real too.
p	norm value

Value

L-p norm of the complex vector

Author(s)

Mehmet Suzen

---

Cumulative mutual coherence

Description

Generate vector of cumulative mutual coherence of a given matrix up to a given order. \ Mutual Cumulative Coherence of a Matrix A at order k is defined as $M(A, k) = max_{p} max_{p \ne q, q \in \Omega } \sum_{q} | <a_{p}, a_{q}> | / ( |a_{p}| |a_{q}|)$

Usage

mutualCoherence(A, k)

Arguments

A	A matrix.
k	Integer value determines number of columns or the order of mutual coherence function to .

Value

Returns k-vector

Author(s)

Mehmet Suzen

References

Compressed sensing in diffuse optical tomography \ M. Suzen, A.Giannoula and T. Durduran, \ Opt. Express 18, 23676-23690 (2010) \ J. A. Tropp \ Greed is good: algorithmic results for sparse approximation, \IEEE Trans. Inf. Theory 50, 2231-2242 (2004)

Examples

set.seed(42)
B <- matrix(rnorm(100), 10, 10) # Gaussian Random Matrix
mutualCoherence(B, 3) # mutual coherence up to order k

---

1-D Total Variation Penalized Objective Function

Description

1-D Total Variation Penalized Objective Function

Usage

objective1TV(x, T, phi, y, lambda)

Arguments

x	Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector
T	sparsity bases ( N x N matrix )
phi	Measurement matrix (M x N).
y	Measurement vector (Mx1).
lambda	Penalty coefficient.

Value

Returns a vector.

Author(s)

Mehmet Suzen

---

Objective function for ridge L1 penalty

Description

Objective function for ridge L1 penalty

Usage

objectiveL1(x, T, phi, y, lambda)

Arguments

x	unknown vector
T	transform bases
phi	measurement matrix
y	measurement vector
lambda	penalty term

Note

Thank you Jason Xu of Washington University for pointing out complex number handling

Author(s)

Mehmet Suzen

---

Objective function for Tikhinov L2 penalty

Description

Objective function for Tikhinov L2 penalty

Usage

objectiveL2(x, T, phi, y, lambda)

Arguments

x	unknown vector
T	transform bases
phi	measurement matrix
y	measurement vector
lambda	penalty term

Note

Thank you Jason Xu of Washington University for pointing out complex number handling

Author(s)

Mehmet Suzen

---

Frequency expression for DFT

Description

Frequency expression for DFT

Usage

oo(p, omega)

Arguments

p	Exponent
omega	Omega expression for DFT

Author(s)

Mehmet Suzen

---

Transform back multiple regression coefficients to unscaled regression coefficients Original question posed by Mark Seeto on the R mailing list.

Description

Transform back multiple regression coefficients to unscaled regression coefficients Original question posed by Mark Seeto on the R mailing list.

Usage

scaleBack.lm(X, Y, betas.scaled)

Arguments

X	unscaled design matrix without the intercept, m by n matrix
Y	unscaled response, m by 1 matrix
betas.scaled	coefficients vector of multiple regression, first term is the intercept

Note

2015-04-10

Author(s)

M.Suzen

Examples

set.seed(4242)
 X            <- matrix(rnorm(12), 4, 3)
 Y            <- matrix(rnorm(4), 4, 1)
 betas.scaled <- matrix(rnorm(3), 3, 1)
 betas        <- scaleBack.lm(X, Y, betas.scaled)

---

1-D Total Variation Penalized Nonlinear Minimization

Description

1-D Total Variation Penalized Nonlinear Minimization

Usage

solve1TV(phi,y,T,x0,lambda=0.1)

Arguments

x0	Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector
T	sparsity bases ( N x N matrix )
phi	Measurement matrix (M x N).
y	Measurement vector (Mx1).
lambda	Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

---

l1 Penalized Nonlinear Minimization

Description

l1 Penalized Nonlinear Minimization

Usage

solveL1(phi,y,T,x0,lambda=0.1)

Arguments

x0	Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector
T	sparsity bases ( N x N matrix )
phi	Measurement matrix (M x N).
y	Measurement vector (Mx1).
lambda	Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

---

l2 Penalized Nonlinear Minimization

Description

l2 Penalized Nonlinear Minimization

Usage

solveL2(phi,y,T,x0,lambda=0.1)

Arguments

x0	Initial value of the vector to be recovered. Sparse representation of the vector ( N x 1 matrix ) X=Tx, where X is the original vector
T	sparsity bases ( N x N matrix )
phi	Measurement matrix (M x N).
y	Measurement vector (Mx1).
lambda	Penalty coefficient. Defaults 0.1

Value

Returns nlm object.

Author(s)

Mehmet Suzen

---

Sparse digital signal Generator.

Description

Sparse digital signal Generator with given thresholds.

Usage

sparseSignal(N, s, b = 1, delta = 1e-07, nlev = 0.05, slev = 0.9)

Arguments

N	Number of signal components, vector size.
s	Number of spikes, significatn components
b	Signal bandwidth, defaults 1.
delta	Length of discrete distances among components, defaults 1e-7.
nlev	Maximum value of insignificant component, relative to b, defaults to 0.05
slev	Maximum value of significant component, relative to b, defaults to 0.9

Author(s)

Mehmet Suzen

---

1-D total variation of a vector.

Description

1-D total variation of a vector.

Usage

TV1(x)

Arguments

x

A vector.

Author(s)

Mehmet Suzen

---