function [MW,theta,L] = compute_best_direction(M,T,s)

% compute_best_direction - optimize the lagrangian over a single square
%
%   [MW,theta] = compute_best_direction(M,T,s);
%
%   M is a 2D image, s is a super-resolution factor
%       (the # of tested direction is 2*n*s)
%   T is the threshold (the higher, the most you want to compress)
%   theta is the optimal direction, ie. the one that gives minimizes the
%   Lagrangian
%       L(theta) = | M - F_theta(M) |^2 + m * T^2
%   where :
%       F_theta(M) = perform_warped_haar(M,theta,1)
%       m = #{ coefficients of |F_theta(M)| above T }
%
%   Copyright (c) 2005 Gabriel Peyr