How does the audio example square with nyquist limit? Basically you can get it back, mostly, with some clever tricks, but Iām not crazy thinking that the original was decimated beyond lossless recovery right?
I think the glitchy colors arise because the image overflows the 0..255 range of uint8 which is usually used for digital images. The values should be clamped when converting from float to int.
JPEG compression works in a similar way: the image is segmented in blocks, each of them is transformed to frequency domain via DCT and then the frequency coefficients are quantized, or discarded if small. The rules for the last step are optimized to minimize human perception of discrepancy between original and compressed image.
What compressed sensing shows is that even a very rough optimization step, completion unaware of contents and human perception, can give worse but comparable results.
Supposedly Helm.ai is using compressed sensing in some way for self-driving car vision. According to an article/interview I saw.
The way it was mentioned made it sound like the compression could be very smart somehow in terms of useful feature extraction. Although I was probably just reading too much into a fluff-piece. Maybe they are just using it to make it easier to get real-time processing (via normal deep learning techniques).
Finally, a hands-on guide to implementing the "enhance this image" command from SF movies! Sort of.
Also, an important observation about approximation, outliers, and deviation measures.
This is incredible, though I'm a little confused as to why the psi matrix is IDCT and not something of a Fourier flavor...
This is a Big Deal in MRI image reconstruction. As the MR scanner samples in the frequency domain (or k-space, in the nomenclature) one can significantly accelarete MR exams by using C/S reconstruction. The only restriction is that the sampling mask is random. This causes incoherent artifacts in image space, which can be removed by denoising the image in a sparse domain, e.g. wavelets. See also the work by Lustig et al. https://onlinelibrary.wiley.com/doi/full/10.1002/mrm.21391