Create custom convolution layer and compare two keras layers

Question

I am currently creating a network in keras to perform harmonic/percussive source separation on an audio spectrogram using a median filtering technique (http://dafx10.iem.at/papers/DerryFitzGerald_DAFx10_P15.pdf).

Given an input magnitude spectrogram S, and denoting the ith time frame as S_i, and the hth frequency slice as S_h, a percussion-enhanced spectrogram frame P_i can be generated by performing median filtering on S_i : P_i = M{S_i, l_perc} where M denotes the median filtering and l_perc is the filter length. The individual percussion-enhanced frames P_i are then combined to yield a percussion-enhanced spectrogram P. Similarly, a harmonic-enhanced spectrogram frequency slice H_h can be obtained by median filtering frequency slice S_h : H_i = M{S_h, l_harm}.

Once you have P and H, you can see whether each frequency bin S_h,i belongs either to the harmonic or the percussive source : if H_h,i > P_h,i, S_h,i goes to the harmonic spectrogram and takes the value 0 in the percussive spectrogram, and vice versa.

In my network, given the input spectrogram and for a specific time frame S_i, I need to compute the medians horizontally for each frequency h. This can be easily done with a lambda layer and tensorflow :

layer_H = Lambda(lambda x:tf.contrib.distributions.percentile(x[0], 50, axis=0))(layer)

Here, the length of the harmonic median filter l_harm is the horizontal length of the input spectrogram. The output is a vector whose size is equal to the number of frequencies (in my case, 88).

The next step is where I am stuck right now : I need to compute the medians vertically for the current time frame S_i, given the length of the percussive median filter l_perc, and knowing that I want the resulting vector to be the same size as the input, so I have to be careful on each end of the the input (the size of the filter will be between l_harm and l_harm/2 depending on where we're at). This looks like some sort of convolution, for lack of a better word.

Once I have the two resulting vectors H_i and P_i, I want to compare them and assign each value of the original frame S_i to either a percussive layer (L_p) or a harmonic layer (L_h). So, I have three different inputs, H_i, P_i and S_i, and I want to end up with L_p and L_h by comparing H_i and P_i, and continue building my network from there. If H_i,j > P_i,j, then Lp_i,j = 0 and Lh_i,j = S_i,j.

To sum up, I am stuck on two different problems :

1. How to compute the horizontal medians ?

2. How to implement in the network the operations that will allow me to go from H_i, P_i and S_i to L_p and L_h ?

Thank you very much in advance !