טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRoy Amel
SubjectAdaptive Method for Online Identification and Recovery
of Jointly Sparse Vectors
DepartmentDepartment of Electrical Engineering
Supervisor Professor Emeritus Feuer Arie
Full Thesis textFull thesis text - English Version


Abstract

The field of Sparse Representation (SR) has evolved during the past decade or so. The main idea behind SR is to find the solution of an underdetermined system of equations using a priori information where the solution has only few inputs other than zero, namely the solution is sparse. Although being relatively a new research subject, there are plenty of areas in the field of signal processing which use SR; a few examples for SR applications are, image compression, image denoising, clustering and coding. In the present study we address the problem of sparse solutions to underdetermined system of equations, where many different sparse solutions are sequentially required, having the same, but unknown, sparsity structure. This type of problem arises in a number of applications such as multiband signals reconstruction and source localization. We present a novel approach which is adaptive in that it solves a sequence of weighted problems where the weights are adaptively updated from one instance of time to the next rather than collecting the measurement vectors and only then solving it as a unified block. This approach avoids delays and large memory requirements (at the cost of increased computational load) with the added capability of tracking changes in joint signal supports.