Daniel Otero - SSIM-based Optimization

The SSIM-based Optimization framework is a set of algorithms that help you to solve a wide variety of optimization problems that employ the Structural Similarity Index Measure (SSIM) as a fidelity term. Since the SSIM was conceived for quantifying the similarity of images based on how our Human Visual System (HSV) works, these algorithms were developed to carry out imaging tasks, so do not expect good results if you want to use them in other applications in which images are not involved.

Here you will find MATLAB implementations of the algorithms that are described in this paper. Click on any of the buttons to download the MATLAB code of the desired algorithm. Please cite the article in case you employ these methods in your research.

CONSTRAINED SSIM-BASED OPTIMIZATION

Algorithm I can be employed to carry out a wide variety of imaging tasks that are stated as constrained SSIM-based optimization problems - it is a type of "Lord of the Rings" method: "one algorithm to solve them all." It is robust and, in general, depending on the specified accuracy, will get as close as possible to the global optimal solution, nevertheless, it is slow.

Algorithm I

It is worthwhile to mention that you need to install CVX if you want to use this algorithm. CVX can be downloaded here.

UNCONSTRAINED SSIM-BASED OPTIMIZATION

These set of algorithms are implementations of Algorithms III and IV for several imaging applications. They are much faster than Algorithm I but do not necessarily converge to the global optimal solution but to a minimizer. If you can not find your desired SSIM-based imaging task, you can use the algorithms as guidelines to create your own implementations.

SSIM and L2

Both Algorithm III and Algorithm IV rely on Algorithm II to work, which solves an unconstrained SSIM-based optimization problem that possess a quadratic term as a regularizer. This algorithm is presented in two flavours: Algorithm II-A and Algorithm II-B. Algorithm II-A is, say, a general purpose algorithm for SSIM-L2 applications, whereas Algorithm II-B is a "special case" that can be used in some circumstances to speed up computations. It is very recommended to use it with implementations of Algorithm IV.

Algorithm II-A

Algorithm II-B

SSIM and L1

The following algorithm solves a SSIM-based optimization problem in which the L1 norm is employed as a regularizer. In particular, we use Algorithm III for this purpose. This implementation is a good example of how to combine the concepts of "similarity" and "sparsity" in imaging.

Algorithm III and L1

SSIM and Total Variation (TV)

In this case, you can see how a SSIM-TV denoising application can be implemented by using either Algorithm III or Algorithm IV. From a Maximum a Posteriori point of view, the SSIM approach is not ideal, however, it might be convenient in some cases according to the experimental results that can be found in the paper.

Algorithm III and TV

Algorithm IV and TV

By the way, in these implementations you might want to use your favourite method for computing the proximal operator of the TV norm. In our case, we employed this code:

This is an implementation of Chambolle's algorithm, which was introduced in this paper.