Recently in learning, DCT dictionary to find a lot of materials, can find through the following procedure to construct a complete DCT dictionary,
% Create an initial dictionary from the DCT frame
Pn=ceil (SQRT (K)); % % % Pn=16 bb=8 produce 64 * 256 dictionary
DCT=zeros (bb, Pn);
For k=1-0: Pn 1,
V=cos ([1-0: bb - 1] '* k * PI/Pn);
If k> 0,
V=V - scheme (V);
end;
DCT (:, k + 1)=V/norm (V); % norm (V) represents the Euclidean distance
end;
% to produce 64 * 256 dictionary
DCT=kron (DCT, DCT);

But I still can't find what is the theory basis of this program,
First, V=cos ([1-0: bb - 1] '* k * PI/Pn); What is the mathematical support?
Second, minus the mean, divided by the norm (V) and the role of the normalized?
Third, DCT=kron (DCT, DCT); Don't understand the

Hope you to solve!

CodePudding user response:

DCT dictionary is what, to introduce the original poster can not

CodePudding user response:

First, V=cos ([1-0: bb - 1] '* k * PI/Pn); This part of the code, in fact, the original DCT on a finer frequency sampling, the original just calculate an odd number of points (2 x + 1) of the numerical, here also the even odd between numerical calculation,
Second, minus the mean, and divided by the norm (V) is the function of normalization, but this one turns into the early, after treated with kron is no longer the matrix column normalized (zero mean and variance), so I think this step is redundant,
Third, DCT=kron (DCT, DCT); Kron rent is to be in the kron product, kron specific role can be baidu; Why do kron product? This step is equal to the DCT is multiplied by the two elements in the dictionary, in fact is the multiplication of two items of cosine, cosine multiplication of modulation, and modulation is will complete dictionary to expand to complete one of the methods which dictionary
In addition, this program has a mistake, they have to calculate the coefficient of DCT transform nuclear before
In conclusion, the application of DCT is actually the first dictionary in finer frequency sampling, again through the kron to modulation of dictionary, eventually won the complete dictionary,

Ideas about the above all that in my blog "build DCT over complete dictionary" (http://blog.csdn.net/dugudaibo/article/details/78418318) are instructions, in addition in my blog and implementation of simple method,

Welcome, welcome comments in my blog,