Reconstruction Filter - Image Processing

Image Processing

In image processing, digital reconstruction filters are used both to recreate images from samples as in medical imaging and for resampling. A number of comparisons have been made, by various criteria; one observation is that reconstruction can be improved if the derivative of the signal is also known, in addition to the amplitude, and conversely that also performing derivative reconstruction can improve signal reconstruction methods.

Resampling may be referred to as decimation or interpolation, accordingly as the sampling rate decreases or increases – as in sampling and reconstruction generally, the same criteria generally apply in both cases, and thus the same filter can be used.

For resampling, in principle the analog image is reconstructed, then sampled, and this is necessary for general changes in resolution. For integer ratios of sampling rate, one may simplify by sampling the impulse response of the continuous reconstruction filter to produce a discrete resampling filter, then using the discrete resampling filter to directly resample the image. For decimation by an integer amount, only a single sampled filter is necessary; for interpolation by an integer amount, different samplings are needed for different phases – for instance, if one is upsampling by a factor of 4, then one sampled filter is used for the half-way point, while a different sampled filter is used for the point 1/4 of the way from one point to another.

A subtlety in image processing is that (linear) signal processing assumes linear luminance – that doubling a pixel value doubles the luminance of the output. However, images are frequently gamma encoded, notably in the sRGB color space, so luminance is not linear. Thus to apply a linear filter, one must first gamma decode the values – and if resampling, one must gamma decode, resample, then gamma encode.