Deep Regularized Compound Gaussian Network

An image estimation system, comprising:

• a source configured to transmit a first waveform towards an object;
• a receiver configured to receive a second waveform that interacted with the object;
• and
• a processor configured to:
• represent c in an equation image x=Φc, wherein Φ is a dictionary to represent the image x, via Compound Gaussian (CG) prior c=z⊙u, where u is a Gaussian random vector, and z is a positive non-Gaussian random vector,
• determine initial estimates for z and u,
• iteratively update z based on an update function g,
• iteratively update u based on a Tikhonov least squares solution,
• determine an optimization landscape for z using intermediate scale variable mapping based on updated values for z and u,
• determine a prior distribution for z using a convolutional neural network, and
• estimate the image x based on the determined optimization landscape for z and prior distribution for z, wherein the image x is an image of the object.

A method, comprising:

• receiving, from a receiver, a waveform that interacted with an object;
• representing c in an equation image x=Φc, wherein Φ is a dictionary to represent the image x, via Compound Gaussian (CG) prior c=z⊙u, where u is a Gaussian random vector, and z is a positive non-Gaussian random vector;
• determining initial estimates for z and u;
• iteratively updating z based on an update function g;
• iteratively updating u based on a Tikhonov least squares solution;
• determining an optimization landscape for z using intermediate scale variable mapping based on updated values for z and u;
• determining a prior distribution for z using a convolutional neural network;
• and
• estimating the image x based on the determined optimization landscape for z and prior distribution for z, wherein the image x is an image of the object.