# How we can encode/decode sparse signals?

I have question and looking for help. Suppose we have a vector of real values (lat's say 64 length resulting from factorization 8*8 block image). We got a sparse representation of that vector (let's suppose that the sparse vector is 128 length with very few active elements, about 4 coefficients). I want to send this sparse vector through a channel, so I need bit stream of 1,0. Are there any efficient encoding/decoding technique for the sparse signals ?

• Since you have all sample, I think you are better to avoid compressive sampling, it is for efficeint sampling not coding.decoding. For signal compression, there are tones of compression algorithms, like LRZ,Huffman,... Aug 13, 2016 at 13:06

## 1 Answer

Since you have tagged your question compressive-sensing, I would guess that you are interested in a compressive sensing solution to this. In principle, this could work by taking a number (less than 64) of random linear combinations (measurements) of your length 64 vector and transmitting these. At the receiver, the fact that this vector has a sparse representation allows you to reconstruct it again from these measurements. However, compressive sensing does not work that well on low-dimensional vectors (64 is relatively small) and so I do not expect this scheme to work very well.

A more natural solution, since you mention that you know the sparse length 128 representation of the vector, is to use run-length encoding (Wikipedia explanation) of the sparse representation and transmit that. Since the sparse vector is almost all zeros, this should be very efficient.

• Well, if I understood correctly, you are saying that we can take some measurements and transmit them and at the receiver side we get the original signal from the sparse version . Instead why not we send the sparse version and the receiver get the original signal from the sparse version directly? I know the sparse signal is longer but the active elements on it is very limited, does that point make sense? Apr 18, 2016 at 16:19