Many inverse problems are solved by optimization methods. Mathematically, gradient-search optimization methods work well when the objective function is convex (e.g., a ``basin'') in the searching range; and the wider the basin of attraction leading to the bottom, the more likely that the optimizations converge to the optimum point. Optimizations have difficulties when there exists more than one point with zero gradient (e.g. local minima, flat area) in the searching range. Unfortunately, this is usually the case in many realistic inverse problems. The complexity of objective functions can be affected by many factors, such as noise, frequency bandwidth, and features of the information in the observed data.
As studied in the above section, an MRA can decompose signals into various resolution levels. The data with coarse resolutions contain less detailed information and lower frequencies, while keeping major features of the original signal consistent with the low frequency information. These less-information data can serve as a relaxation to optimizations. Therefore, by using data at coarser resolution levels, complexity of objective functions may be reduced, which increases the performance of optimizations.