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How would one go about importance sampling the sphere with respect to projected solid angle instead of just the solid angle,
in order to importance sample the product of both the lambertian brdf and a spherical light source?

The main purpose of using Metropolis Light Transport is for improving efficiency on the paths that are unlikely to be found by chance, such as sharp caustics or light coming in through a crack in a almost closed door. However it is inferior to ordinary path tracing techniques when the path is highly...

Here is a paper on improving bidirectional path tracing by reusing light sub-paths across eye sub-paths: Probabilistic Connections for Bidirectional Path Tracing abstract: Bidirectional path tracing (BDPT) with Multiple Importance Sampling is one of the most versatile unbiased ren- dering algorithms...

I came across two papers on the website for Johannes Hanika, that are promising Improved half vector space light transport Abstract : "In this paper, we present improvements to half vector space light transport (HSLT) [KHD14], which make this approach more practical, robust for difficult input geome...

What I have figured out that I could do is take the Golden point set as described in the original paper and and then assume that a total of, for instance 2^64 will be generated, and then choose the index within the period with the van der corput sequence. The problem is however is given the how seco...

A way to get around the MLT limitation of your architecture is to use a multiple proposal metropolis sampler such as described in the first paper of my Useful Markov Chain Monte Carlo Papers to apply to Graphics post.

The idea is, as opposed to combining the Half Vector Space perturbation with Veach's original perturbations, instead using the Multiplexed Metropolis Light Transport(MMLT) mutations in order to more robustly handle glossy corners and the like, while reserving the costly Half Vector Space perturbatio...

Here are some papers for addressing limitations of the Metropolis Light Transport algorithm. Flickering in animations The remedy to this limitation is to mutate paths through both space and time, not just space. Physically-based Animation Rendering with Markov Chain Monte Carlo Poor SIMD efficiency ...

The idea i am presenting is to use some form of vertex merging to provide an initial guess which is then iteratively corrected into an unbiased path using manifold( Manifold Exploration ) or half vector space perturbations( The Natural-Constraint Representation of the Path Space for Efficient Light ...

The idea of optimizing for the ideal acceptance ratio is the fundamental principle of Adaptive Markov Chain Monte Carlo methods.