# Transform matrix creation in compressed sensing

In Compressed sensing ECG reconstruction I would like to use biorthogonal wavelet basis as transform/sparsifying domain. I found out that wfilters command in MATLAB will give 4 type of filters, but which filter I would use to make the transform matrix?

Either decomposition lowpass/highpass or reconstruction low pass/high pass or is there any other better ways to make the transform matrix??

I recommend not forming the transform matrix directly. That will cost more memory and take longer to compute the transform. Instead, use the idwt/dwt or waverec/wavedec functions in place of multiplying by A/A.T. Many reconstruction solvers and convex optimisation toolboxes support supplying function handles for this instead of a matrix. If you are implementing your own solver it should also be easy enough to integrate these functions instead of the matrix-vector products.

• Can please elaborate a little more in detail,I didnt get the point multiplying by A/A.T – Abhishek Sadasivan Feb 5 '16 at 15:29

To clarify Thomas Arildsen's answer, you generally have to specify multiplication by the sensing matrix and the sensing matrix transpose. Without a transform matrix, this would be:

multA(z) = A*z;
multAtranspose(z) = A'*z


When you use a transform, the data x becomes x=IT(u), where T is the transform, IT is the inverse transform, and u is the sparse signal in the transform basis. The multiply operation with A becomes:

multA(z) = A*IT(z);
multAtranspose(z) = T(A'*x)