Math_563_Project

Solver Parameter struct i

i[struct]: Input Parameter

• i.maxiter [int]: Iteration Limit

• i.gammal1 [double]: Amount of De-noising in l1

• i.gammal2 [double]: Amount of De-noising in l2

• i.rhoprimaldr [double]: Relaxation Parameter rho in douglasrachfordprimal

• i.tprimaldr [double]: Stepsize t in douglasrachfordprimal

• i.rhoprimaldualdr [double]: Relaxation Parameter rho in douglasrachfordprimaldual

• i.tprimaldualdr [double]: Stepsize t in douglasrachfordprimaldual

• i.rhoadmm [double]: Relaxation Parameter pho in ADMM

• i.tadmm [double]: Stepsize t in ADMM

• i.tcp [double]: stepsize for chambollepock

• i.scp [double]: stepsize for chambollepock

• For Extra Optional Parameters refer to end of Usage

Ex) Specify your own values (empty field will be replaced by default values)

% Set common input parameters for all algorithms
i.maxiter = 500;
i.gammal1 = 0.049;

% Set default input parameters for primal douglas-rachford algorithm
i.tprimaldr = 2.0;
i.rhoprimaldr = 0.1;

Ex) Use all default values provided at +salsa/+defaults/get_input_param_def.m by initializing with an empty struct

i = struct();

Initial Starting point struct x

In addition to the starting point values of each algorithm, you can pass the original image, I, using this struct. This enable error calculations using the true data.

Ex) Specify your own values (empty field will be replaced by default values)

% case "douglasrachfordprimal"
[m, n] = size(Image);
x.z1 = zeros(m, n);
x.z2 = zeros(m,n,3);

Ex) Use all default values provided at "+salsa/+defaults/get_starting_point_def.m" by initializing an empty struct

x = struct();

Provide Full File Path to Image : img_path

Ex) Give your own file path:

img_path  = "./somedir/somesubdir/file.png";

Ex) Pick a default image [cameraman, mcgill, manwithhat, salsa_default]:

img_path = salsa.defaults.get_img_def("salsa_default");

Apply Blur + Noise to Image

Ex) Provide your own blur, noise types using:

[I, kernel, b] = salsa.img.corrupt(img_path, ...
                                   blur_type, blur_arg, ...
                                   noise_type, noise_arg, ...
                                   pad_type)

Where:

• blur_type = {'average', 'disk', 'gaussian', log', 'laplacian', 'motion'}
• blur_arg = corresponding vals in cell format = or pass {} to use defaults
• noise_type = {'gaussian', 'poisson', 'salt & pepper', 'speckle'}
• noise_arg = corresponding vals in cell format = or pass {} to use defaults
• pad_type = {'symmetric', 'replicate', 'circular'}

Ex) Use defualt values:

[I, kernel, b] = salsa.img.corrupt(img_path);

Where,

• Default Blur : Motion {len = 15, theta = 0}
• Default Noise : Salt & Pepper {d = 0.1}

Extra i struct options: Parameters for ploting and printing:

• i.sample_rate [int]: Output to screen frequency

• i.verbos [logical]: Prints progress to terminal

• i.plt_final [logical]: Plot final result

• i.plt_progress [logical]: Plots deblurred image while iterating

• i.plt_rel_err [logical]: Plot Error vs iterations

• i.plt_diff [logical]: Plot difference Image between x_original and x_final

NOTE: In addition to setting i.plt_rel_err = true, you can pass the original image, I, in the initial starting point struct, x, to calculate the error of:

|I - x_{k}|/|I| 

Otherwise, the error would be:

|x_{k} - x_{k-1}|/|x_{k}|

Ex)

x.I = I;
i.plt_rel_err = true;

NOTE: For using plt_diff, you need to pass the original image, I, in the initial starting point struct, x, similar to above.

Extra i struct options: Easter egg options

• i.spicy [logical]: Activates a Subpackage of easter eggs

The spicy subpackage consists of:

1. disp_salsa_bottle.m Used to display our welcome message!

2. disp_salsa_error.m Used to output a special error message incase an algorithm diverges!

3. spill_the_beans.m Fun creative food related receipes generated by ChatGPT

4. stewchastic.m Highly sophisticated Stochastic Solver

Ex)

salsa.spicy.spill_the_beans()

To use the stewchastic solver, choose it as a solver like below:

x_final = salsa.solver("l1","stewchastic", x, kernel, b, i);

Call Solver

• problem : Choice of Norm in the Optimization Function ['l1' | 'l2']
• algorithm : Optimization Algorithm ['douglasrachfordprimal' | 'douglasrachfordprimaldual' | 'admm' | 'chambollepock' | 'stewchastic'] Ex)

x_final = salsa.solver("l1","stewchastic", x, kernel, b, i);