Kernel estimation for time-frequency distributions using epigraph set of L1-NORM

In this article, a new kernel estimation method is introduced using the epigraph set of the l₁-norm. The new method produces a high-resolution and cross-term free estimates for Cohen´s Class of Time-frequency (TF) distributions. The kernel estimation process starts with an initial rough TF distribution. This initial estimate is orthogonally projected onto the epigraph set of the l₁ norm in TF domain. Epigraph set of the l₁ norm produces a sparse time-frequency distribution. Sparsity in TF domain leads to cross-term free TF distributions. Experimental results are presented and the TF distributions obtained with the estimated kernel are compared to those obtained with an optimized kernel.