Nonconvex Compressed Sampling of Natural Images and Applications to Compressed MR Imaging

Compressed sensing – with applications to medical imaging

Compressed sensing is a new approach for acquiring signals. It captures and represents signals and images at a rate significantly below Nyquist rate. In certain areas like magnetic resonance imaging (MRI), it is urgent to reduce the time of the patients’ exposure in the electromagnetic radiation. Compressed sensing breaks the canonical rules and effectively reduces the sampling rate without los...

A fast nonconvex Compressed Sensing algorithm for highly low-sampled MR images reconstruction

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained minimization problem with a family of non-convex regularizing objective functions depending on a parameter and a least squares data fit constraint. We propos...

Natural Steganography in JPEG Compressed Images

In natural steganography, the secret message is hidden by adding to the cover image a noise signal that mimics the heteroscedastic noise introduced naturally during acquisition. The method requires the cover image to be available in its RAW form (the sensor capture). To bring this idea closer to a practical embedding method, in this paper we embed the message in quantized DCT coefficients of a ...

A Block-Wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...

Compressed domain indexing of losslessly compressed images