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With MIS

Without MIS

Note the images might look a whole lot different but that's cause I implemented Tonemapping + Gamma Correction in the meantime :) With MIS 700spp

Without MIS 700spp

--Found a mistake. I was using the direct lighting equation when calculating the brdf sample. (multiplying by $\cos(\theta^{\prime})$ and dividing by $r^2$). Removed it since we initially sampled through BSDF which is integral over solid angle not area. The image got a little brighter. Still don't know if MIS is working as intended.

After that I come to BRDF sampling. I again sample through either Phong/Cosine based on what I did earlier during light sample calculation. If the sampled ray doesn't hit any light source or not the same one. I set the $brdf\_sample$ to zero. If it hits, I set the $light\_pdf$ to same value as before. Calculate the weights like mentioned above and calculate brdf sample using the original equation (integral over solid angle).

--Found a mistake. I was using the direct lighting equation when calculating the brdf sample. (multiplying by $\cos(\theta^{\prime})$ and dividing by $r^2$). Removed it since we initially sampled through BSDF which is integral over solid angle not area. The image got a little brighter. Still don't know if MIS is working as intended. See answer.

After that I come to BRDF sampling. I again sample through either Phong/Cosine based on what I did earlier during light sample calculation. If the sampled ray doesn't hit any light source or not the same one. I set the $brdf\_sample$ to zero. If it hits, I set the $light\_pdf$ to same value as before. Calculate the weights like mentioned above and calculate brdf sample using the original equation (integral over solid angle).

EDIT5:- After lightxbulb suggestions, I think the problem has resolved.

With MIS

Without MIS

EDIT4:- Here's an overview of what I'm doing now.

First I choose a single light source out of multiple using simple heuristic scheme like the distance, intensity, area and the cosine falloff angles. I appropriately set the weights for the light like this

$light\_pdf = weight/area$

where weight is in range 0-1.

Next I trace the ray to see if light source is visible. If it is I calculate the $light\_sample$ using the direct lighting equation (integral over Area).

Then I calculate the BRDF PDF for this given ray. However I use Lafortune's algorithm for it. If a random number falls under the specular color I sample through the modfied Phong PDF else through Cosine.

The weights are computed using power heuristic, $ weight = light\_pdf^2/(light\_pdf^2+brdf\_pdf^2)$

The MIS estimator is then calculated as

$light\_sample = light\_sample * weight/light\_pdf$

After that I come to BRDF sampling. I again sample through either Phong/Cosine based on what I did earlier during light sample calculation. If the sampled ray doesn't hit any light source or not the same one. I set the $brdf\_sample$ to zero. If it hits, I set the $light\_pdf$ to same value as before. Calculate the weights like mentioned above and calculate brdf sample using the original equation (integral over solid angle).