# AipyTutDeconv

## 1 Module: aipy.deconv

A module implementing various techniques for deconvolving an image by a kernel. Currently implemented are Clean, Least-Squares, and Maximum Entropy.

### 1.1 Function: clean

This is an implementation of the standard Högbom clean deconvolution algorithm [, which operates on the assumption that the image is composed of point sources. This makes it a poor choice for images with distributed flux. The algorithm works by iteratively constructing a model. Each iteration, a point is added to this model at the location of the maximum residual, with a fraction (specified by ’gain’) of the magnitude. The convolution of that point is removed from the residual, and the process repeats. Termination happens after ’maxiter’ iterations, or when the clean loops starts increasing the magnitude of the residual.

### 1.2 Function: lsq

Implements a simple least-square fitting procedure for deconvolving an image. However, to save computing, the gradient of the fit at each pixel with respect pixels in the image is approximated as being diagonal. In essence, this assumes that the convolution kernel is a delta-function. This assumption works for small kernels, but not so well for large ones [. This deconvolution algorithm, unlike maximum entropy, makes no promises about maximizing smoothness while fitting to the expected noise and flux levels. That is, it can introduce structure for which there is no evidence in the original image. Termination happens after ’maxiter’ iterations, or when the score is changing by a fraction less than ’tol’ between iterations. This makes the assumption that the true optimum has a smooth approach.

### 1.3 Function: maxent

The maximum entropy deconvolution (MEM) [ is similar to least-squares deconvolution, but instead of simply minimizing the fit, maximum entropy seeks to do so only to within the specified variance var0, and then attempts to maximize the "smoothness" of the model. This has several desirable effects, including uniqueness of solution, independence from flux distribution (all image scales are equally weighted in the model), and absence of spurious structure in the model. Similar approximations are made in this implementation as in the least-squares implementation.