Theory and Statistical Description of the Enhanced Multi-Temporal InSAR (E-MTInSAR) Noise-Filtering Algorithm

Round 1

Reviewer 1 Report

[1] Grammar and writing style need to be improved.

[2] Acronym of terms should be used after its first appearance with full name.

[3] After Eqn.(7): I Mk and ISk are not consistent with the symbols appearing in Eqn.(7).

[4] Figure 3: Suggest to add vertical labels to each figure instead of description in the caption.

[5] Eqn.(25): Please elaborate how the derivation is related to eqn.(12).

[6] Eqn.(27): Is the number of independent look (L) the same as N+1 mentioned in the beginning of Section 2?

Please elaborate and make them consistent.

[7] Please elaborate how $\xi_i$ in eqn.(27) is transformed to $\hat{w}_i$ in eqn.(28).

[8] Eqn.(29): Should the subscript h be changed to i in the last term?

[9] Eqn.(32): Please elaborate the two b factors and how this equation is derived.

[10] Please elaborate how eqn.(33) is derived, the definition of $\lambda$, and how the b factors are related to $\lambda$.

[11] Figure 4: Please insert horizontal label and vertical label.

[12] The formulation in Section 3 can be made more compact and understandable.

[13] Please elaborate how eqn.(35) is derived.

[14] Figure 5: Please briefly describe how the horizontal label and vertical label are defined and the meaning of each data point in the figure.

[15] Please fix the above issues and resubmit for further review.

Author Response

Attached is the reply to the reviewer's comments and suggestion

Author Response File: Author Response.pdf

Reviewer 2 Report

The issue dealt with in this paper is of interest to the scientific community working on radar images. In particular, the statistical foundations of the InSAR noise filtering technique are discussed. The paper is generally well structured with a good presentation of the context of the study and the objectives. The analysis of the results is well done with good illustrations. Nevertheless, it would be useful to rework the following points:

- In the introduction, it would be useful to clarify the interest, the motivation and the methodology adopted by placing it better in relation to the works published in the literature.

- It would be useful to specify the limits of the adopted methodology including the different algorithms developed and / or applied. This must be done taking into account the characteristics of the sensor used for the acquisition, the resolution, the polarization, the type of images, the environment, etc.

- It would be useful to check all the equations.

- The conclusion and perspectives should be strengthened to better appreciate the contribution of paper content.

Author Response

see the attached document for the reply to the reviewer's suggestions and observations.

Author Response File: Author Response.pdf

Reviewer 3 Report

Se attached file

Comments for author File: Comments.pdf

Author Response

See the attached file for the reply to the reviewer's suggestions and comments

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Previous comments have been well addressed.

Reviewer 2 Report

Despite some passages that should be strengthened, this version is much better.

Reviewer 3 Report

Well Done!