You need to pay attention that unless properly padded the Multiplication in the Frequency Domain (DFT) applies Circular Convolution while you're after Linear Convolution. For practical examples and ...

In Compressed Sensing the real problem is the ${\left\| \cdot \right\|}_{0}$ norm (Well, Pseudo Norm). One of the great discoveries are conditions under which using ${\left\| \cdot \right\|}_{1} ... View answer Accepted answer 1 votes If the histogram you're displaying is representative than you could methods which are used for binarization in Image Processing. For instance, using Otsu's Method will probably be a robust way to set ... View answer 1 votes For LASSO Case you probably can estimate$ L $pretty good and the best would be using FISTA for acceleration of the Proximal Gradient Method. In general you can use the Line Search as above (Neal ... View answer 0 votes I would use the Bilateral Filter or the Non Local Means Filter. Both are straight forward to implement and their results are surprisingly good. They retain much more details than the Spatially ... View answer 0 votes We're basically after: $$\arg \min_{m} \sum_{i = 1}^{N} \left| m - {x}_{i} \right|$$ One should notice that$ \frac{\mathrm{d} \left | x \right | }{\mathrm{d} x} = \operatorname{sign} \left( x \...
Using few tricks the equation can be transformed into classic Quadratic Programming problem:  E = \arg \max_{E} \sum_{\mathbf{r}} \left( E(\mathbf{r}) - \sum_{\mathbf{s} \in N(\mathbf{r})} {w}_{\...