Category Archives: Deconvolution

Deconvolution, Sharpening, unsharp mask, USM

The Richardson-Lucy Algorithm

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Deconvolution by the Richardson-Lucy algorithm is achieved by minimizing the convex loss function derived in the last article

(1)   \begin{equation*} J(O) = \sum \bigg (O**PSF - I\cdot ln(O**PSF) \bigg) \end{equation*}

with

  • J, the scalar quantity to minimize, function of ideal image O(x,y)
  • I(x,y), linear captured image intensity laid out in M rows and N columns, corrupted by Poisson noise and blurred by the PSF
  • PSF(x,y), the known two-dimensional Point Spread Function that should be deconvolved out of I
  • O(x,y), the output image resulting from deconvolution, ideally without shot noise and blurring introduced by the PSF
  • **   two-dimensional convolution
  • \cdot   element-wise product
  • ln, element-wise natural logarithm

In what follows indices x and y, from zero to M-1 and N-1 respectively, are dropped for readability.  Articles about algorithms are by definition dry so continue at your own peril.

So, given captured raw image I blurred by known function PSF, how do we find the minimum value of J yielding the deconvolved image O that we are after?

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Deconvolution, Processing, Sharpening

Elements of Richardson-Lucy Deconvolution

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We have seen that deconvolution by naive division in the frequency domain only works in ideal conditions not typically found in normal photographic settings, in part because of shot noise inherent in light from the scene. Half a century ago William Richardson (1972)[1] and Leon Lucy (1974)[2] independently came up with a better way to deconvolve blurring introduced by an imaging system in the presence of shot noise. Continue reading Elements of Richardson-Lucy Deconvolution →

Deconvolution, IQ, Optics, Sharpening, Sharpness, Spatial Resolution

Capture Sharpening: Estimating Lens PSF

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The next few articles will outline the first tiny few steps towards achieving perfect capture sharpening, that is deconvolution of an image by the Point Spread Function (PSF) of the lens used to capture it.  This is admittedly  a complex subject, fraught with a myriad ever changing variables even in a lab, let alone in the field.  But studying it can give a glimpse of the possibilities and insights into the processes involved.

I will explain the steps I followed and show the resulting images and measurements.  Jumping the gun, the blue line below represents the starting system Spatial Frequency Response (SFR)[1], the black one unattainable/undesirable perfection and the orange one the result of part of the process outlined in this series.

Figure 1. Spatial Frequency Response of the imaging system before and after Richardson-Lucy deconvolution by the PSF of the lens that captured the original image.

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Deconvolution, IQ, Sharpening, Spatial Resolution

Downsizing Algorithms: Effects on Resolution

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Most of the photographs captured these days end up being viewed on a display of some sort, with at best 4K (4096×2160) but often no better than HD resolution (1920×1080).  Since the cameras that capture them have typically several times that number of pixels, 6000×4000 being fairly normal today, most images need to be substantially downsized for viewing, even allowing for some cropping.  Resizing algorithms built into browsers or generic image viewers tend to favor expediency over quality, so it behooves the IQ conscious photographer to manage the process, choosing the best image size and downsampling algorithm for the intended file and display medium.

When downsizing the objective is to maximize the original spatial resolution retained while minimizing the possibility of aliasing and moirè.  In this article we will take a closer look at some common downsizing algorithms and their effect on spatial resolution information in the frequency domain.

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Deconvolution, Processing, Sharpening, Spatial Resolution

Raw Converter Sharpening with Sliders at Zero?

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I’ve mentioned in the past that I prefer to take spatial resolution measurements directly off the raw information in order to minimize often unknown subjective variables introduced by demosaicing and rendering algorithms unbeknownst to the operator, even when all relevant sliders are zeroed.  In this post we discover that that is indeed the case for ACR/LR process 2010/2012 and for Capture NX-D – while DCRAW appears to be transparent and perform straight out demosaicing with no additional processing without the operator’s knowledge.

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Deconvolution, Sharpening, Spatial Resolution

What is the Best Single Deconvolution PSF to Use for Capture Sharpening 1?

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Deconvolution is one of the  processes by which we can attempt to undo blurring introduced by our hardware while capturing an image.  It can be performed in the spatial domain via a kernel or in the frequency domain by dividing image data by one or more  Point Spread Functions.  The best single deconvolution PSF to use when Capture Sharpening is the one that resulted in the blurring in the first place: the System PSF.   It is often not easy or practical to determine it. Continue reading What is the Best Single Deconvolution PSF to Use for Capture Sharpening 1? →

Deconvolution, Sharpening, Spatial Resolution

Point Spread Function and Capture Sharpening

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A Point Spread Function is the image projected on the sensing plane when our cameras are pointed at a single, bright, infinitesimally small Point of light, like a distant star on a perfectly dark and clear night.   Ideally, that’s also how it would appear on the sensing material (silicon) of our camera sensors: a singularly small yet bright point of light surrounded by pitch black.  However a PSF can never look like a perfect point because in order to reach silicon it has to travel at least through an imperfect lens (1) of finite aperture (2), various filters (3) and only then finally land typically via a microlens on a squarish photosite of finite dimensions (4).

Each time it passes through one of these elements the Point of light is affected and spreads out a little more in slightly different ways, so that by the time it reaches silicon it is no longer a perfect Point but it is a slightly blurry Point instead: the image that this spread out Point makes on the sensing material is called the System’s Point Spread Function.  It is what we try to undo through Capture Sharpening. Continue reading Point Spread Function and Capture Sharpening →

Deconvolution, IQ, Sharpening, Spatial Resolution

What Radius to Use for Deconvolution Capture Sharpening

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The following approach will work if you know the spatial frequency at which a certain MTF relative energy level (e.g. MTF50) is achieved by your camera/lens combination as set up at the time that the capture was taken.

The process by which our hardware captures images and stores them  in the raw data inevitably blurs detail information from the scene. Continue reading What Radius to Use for Deconvolution Capture Sharpening →

Deconvolution, IQ, Perceptual, Sharpening, Spatial Resolution

Deconvolution vs USM Capture Sharpening

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UnSharp Masking (USM) capture sharpening is somewhat equivalent to taking a black/white marker and drawing along every transition in the picture to make it stand out more – automatically.  Line thickness and darkness is chosen arbitrarily to achieve the desired effect, much like painters do. Continue reading Deconvolution vs USM Capture Sharpening →