After converting a 1D signal to 2D using matlab code, can the ridgelet transform be applied? Is this transformation effective compared to wavelet?
Of course you can. But it is unlikely this will be very effective, unless the features of your signal are well aligned in different orientations in 2D, so that the ridgelet can sparsify them. You can observe this from ridgelet shapes:
Since it possesses a long support in one direction, it is not very effective with signals having a lot of discontinuities. Of course, it depends a lot on the nature of the signals you are considering. Changing 1D to 2D, or 2D to 1D affects the structure of data a lot. In the following pictures taken from a presentation of an overview of wavelets in 2D, you can see a speech signal (JFK at Rice university launching the moon program), and an image turned into 1D:
On the next images, you have the speech turned into 2D, and the full 2D image represented in 1D above.
Most of the structure is lost in both cases.