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Nathanael Perraudin
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version 1.7.1
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demos/demo_dequantization.m

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%DEMO_DEQUANTIZATION
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%DEMO_DEQUANTIZATION Dequantization demo
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% This demo shows how a quantized signal, sparse in the DCT domain, can be dequantized
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% solving a convex problem using Douglas-Rachford algorithm
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%
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% .. C = { x | ||Dx - y_Q||_infty <= alpha/2 }
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%
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% .. math:: C = \{ x | \|Dx - y_Q\|_\infty <= \frac{\alpha}{2} \}
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%d
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%
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% Its prox is the orthogonal projection onto that set, which is realized
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% by entry-wise 1D projections onto the quantization stripes. This is
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% realized for all the entries at once by function proj_box.

prox/Contents.m

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% PROX_TV1D - Proximal operator of the 1D TV norm
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% PROX_TV4D - Proximal operator of the 4D TV norm
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% PROX_SUM_LOG - Proximal operor for the sum of logarithms.
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% PROX_SUM_LOG_NORM2 - Proximal operator of log-barrier - sum(log(x))
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%
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% Projection operators
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% PROJ_B1 - Projection on a B1-Ball

prox/prox_sum_log.m

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% sol : Solution.
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% info : Structure summarizing informations at convergence
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%
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% `prox_l1(x, gamma, param)` solves:
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% `prox_sum_log(x, gamma, param)` solves:
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%
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% .. sol = argmin_{z} 0.5*||x - z||_2^2 - gamma * sum(log(z))
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%
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% * *info.crit* : Stopping critterion used
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%
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%
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% See also: prox_l1 prox_l2 prox_tv
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% See also: prox_l1 prox_l2 prox_tv prox_sum_log_norm2
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%
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% Author: Vassilis Kalofolias

prox/prox_sum_log_norm2.m

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function [sol,info] = prox_sum_log_norm2(x, alpha, beta, gamma, param)
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%PROX_SUM_LOG_NORM2 Proximal operator of log-barrier - sum(log(x))
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% Usage: sol = prox_sum_log(x, alpha, beta, gamma)
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% sol = prox_sum_log(x, alpha, beta, gamma, param)
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% Usage: sol = prox_sum_log_norm2(x, alpha, beta, gamma)
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% sol = prox_sum_log_norm2(x, alpha, beta, gamma, param)
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% [sol, info] = prox_sum_log_norm2(x, alpha, beta, gamma, param)
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%
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% Input parameters:
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%
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% `prox_l1(x, gamma, param)` solves:
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%
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% .. sol = argmin_{z} 0.5*||x - z||_2^2 - gamma * (alpha*sum(log(z)) +
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% beta/2 ||z||^2)
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% .. sol = argmin_{z} 0.5*||x - z||_2^2 - gamma * (alpha*sum(log(z)) + beta/2 ||z||^2)
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%
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% .. math:: sol = \arg\min_{z} \frac{1}{2} \|x - z\|_2^2 - \gamma (\alpha \sum_i(log(z_i)) + \beta/2 \|z\|_2^2)
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%

solver/fbf_primal_dual.m

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% Warning! This stopping criterion is different from other solvers!
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%
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% * *param.mu* : parameter mu of paper [1]
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% * *param.epsilon: parameter epsilon of paper [1]
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% * *param.normalized_timestep: from 0 to 1, mapping to [epsilon,
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% (1-epsilon)/mu]
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% * *param.epsilon*: parameter epsilon of paper [1]
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% * *param.normalized_timestep*: from 0 to 1, mapping to [epsilon,
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% (1-epsilon)/mu]
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%
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% See also: solvep fb_based_primal_dual
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%

solver/solvep.m

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%
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% For the 'rel_norm' stopping criterion, the algorithm end if
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%
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% .. || n(t) - n(t-1) ||_2 / || n(t) ||_2 < tol,
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% .. ' || n(t) - n(t-1) ||_2 / || n(t) ||_2 < tol,
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%
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% .. math:: \frac{ \| n(t) - n(t-1) \|_2 }{\| n(t)\|_2} < tol,
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%

unlocbox_version

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1.6.3
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1.7.1

utils/Contents.m

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% Other
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% snr - Signal to noise ratio
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% soft_threshold - Soft thresholding operation
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% seet_seed - Set a new seed
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% set_seed - Set a new seed
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% vec - Vectorize
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% svdecon - Acceleleration of svd
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% svdsecon - Acceleleration of svds

utils/set_seed.m

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function set_seed(my_seed)
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%SET_SEED sets the seed of the default random random generator
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% Usage: set_seed(new_seed)
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% set_seed
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% Usage: set_seed(my_seed)
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% set_seed()
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%
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% Input parameters:
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% new_seed
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%
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% Output parameters:
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% none
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%
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% my_seed : new_seed
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%
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% Set the seed of the default random random generator
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% code author: Vassilis Kalofolias
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% date: August 2013
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%rng('default');
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end
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end
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