A "recent" paradigm to represent digital images has been used in signals previously and promises be the holy grail in computer vision by striking results. Then, the question is Why not study it?.
The first motivation is that a possible relation with my master's thesis exists.
In bag of features, we split the images in blocks, commonly called visual words, and then a feature description is done to represent these visual words. The process is performed in all images in a specific image collection. Then a visual codebook is built with more representative visual words in collection, an approach commonly used is by clustering, i.e. k-means. The visual codebook, or dictionary, is built and each image is represented by the occurrence of visual words according to codebook in image, the asignation is made by the most similar measure between visual word in image and a visual word of codebook.
In sparse representation, we choose a random blocks in an image, called dictionary D. Then, we want obtain a vector x that help to reconstruct the original image how a linear combination between them. The optimization problem is defined by sparse measure of zero norm and the best solution is given by the x vector most sparse. However, the D is not a square matrix and is indetermined problem with number of observations (cols) is greater than basis dimension (rows), so have many infinite solutions. The best solution is given by the x vector most sparse in norm zero, but it is a NP-hard problem. The sparse measure in norm one is a good aproximation and is the same solution in some cases of original optimization problem with advantage that is possible solve with a LP method (basis pursuit, matching pursuit, orthogonal matching pursuit, among others). With sparse solutions the dictionary is the best set of basis that represents the image content and more compact representation of image than fourier, wavelets, curvelets, etc.
I am working in this moment in this approach and how can help me in my master thesis... I hope :)
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