Nonuniform sparse recovery with random convolutions

We discuss the use of random convolutions for Compressed Sensing applications. In particular, we will show that after convolving an N-dimensional, s-sparse signal with a Rademacher or Steinhaus sequence, it can be recovered via l
₁
-minimization using only m ≳ s log(N/ε) arbitrary chosen samples with probability at least 1 - ε.