Both wavelet denoising and denosing methods using the concept of sparsity are
based on soft-thresholding. In sparsity based denoising methods, it is assumed
that the original signal is sparse in some transform domains such as the
wavelet domain and the wavelet subsignals of the noisy signal are projected
onto L1-balls to reduce noise. In this lecture note, it is shown that the size
of the L1-ball or equivalently the soft threshold value can be determined using
linear algebra. The key step is an orthogonal projection onto the epigraph set
of the L1-norm cost function.Comment: Submitted to Signal Processing Magazin
