Correction to: A novel cost-effective sparsity-aware algorithm with Kalman-based gain for the identification of long acoustic impulse responses

1 Correction to: Signal, Image and Video Processing https://doi.org/10.1007/s11760-020-01715-2

Unfortunately, the above article has been published with some typos in it.

The corrected sentences are given below:

• 1. In n the subsection 4.1 Derivation of the proposed algorithm (IPNLMS), under part (b) Step 2: Simplifcation, the second line in fourth paragraph should read as:

  This replacement is to set a fxed overall adaptation step-size independent on the infuence of the input signal power $\sigma_x^2$, and to have an update equation form comparable to IPNLMS

• 2. In equation (27), the zero symbol ‘0’ in ${\mathbf{0}}_{N_{q}\times1}$should be written in bold because it refers to the vector of the first N_q zero elements in m. In addition, the elements of the vector should be spaced and separated, as shown below:

  $${\mathbf{m}}_{N\times1}=\left[\varvec{{0}}_{N_{q}\times1}, \quad 1, \quad e^{-1/\phi}, \quad e^{-2/\phi}, \ldots, e^{-(N_{m}-1)/\phi} \right] ^{\varvec{T}}$$

  (27)

• 3. In equation (28) the zero symbols ‘0’ should be written in bold because they refer to the zero portions in the matrix w. That is:

  $$ {\mathbf{w}}=\left[\begin{array}{cc} {\mathbf{0}}_{N_{q}\times N_{q}} & {\mathbf{0}}_{N_{q} \times N_{m}} \\ {\mathbf{0}}_{N_{m}\times N_{q}} & {\mathbf{P}}_{N_{m}\times N_{m}} \\ \end{array}\right] {\mathbf{m}}+{\mathbf{q}}$$

  (28)