after hard thresholding

USAGE SUMMARY

The phrase "after hard thresholding" is correct and usable in written English.
It can be used in contexts related to image processing, data analysis, or signal processing where a thresholding technique is applied to separate data points. Example: "The results were analyzed after hard thresholding to determine the significant features in the dataset."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

After hard thresholding, BM3D tries to generate a basic estimate.

EURASIP Journal on Image and Video Processing

To this estimator, one assigns a weight ( {w}_x={N}_{theta}^{-1} ), where N θ is the number of retained non-zero transform coefficients after hard thresholding.

Advanced Structural and Chemical Imaging

The weights ( {w}_x^P={N}_{theta}^{-1} ) are again equal to the number of non-zero transform coefficients after hard thresholding the Anscombe transformed block stack in the 3D transform domain.

Advanced Structural and Chemical Imaging

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

Adjusting the weights in this step is not like the first step, which depends on the number of non-zero coefficients reached after the hard thresholding.

EURASIP Journal on Image and Video Processing

In step 1, the total variance is computed by (sigma ^{2}times N_{mathrm {non-zero}}^{text {hard}}), where (N_{mathrm {non-zero}}^{text {hard}}) is the number of non-zero coefficients after the hard thresholding.

EURASIP Journal on Image and Video Processing

Soft thresholding and hard thresholding have some limitations in denoising of signal[29, 30].

EURASIP Journal on Image and Video Processing

The sparsity constraint given by the ℓ 0-regularization norm is included in the solution by computing the hard thresholding operator after computing the weighted median estimate.

EURASIP Journal on Advances in Signal Processing

Second, the hard thresholding is not used any more after the 3D transform.

EURASIP Journal on Image and Video Processing

BM3D requires the hard thresholding to be performed in a transform domain, after the 3D transform is performed on the similar image blocks.

EURASIP Journal on Image and Video Processing

Hard thresholding.

EURASIP Journal on Image and Video Processing

Iterative hard thresholding.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When describing processes, clearly indicate the stage at which "after hard thresholding" effects are observed to avoid ambiguity. For instance, specify whether an analysis is performed on coefficients or reconstructed signals.

Common error

Avoid assuming that "after hard thresholding" implies only the remaining values are significant. Remember to analyze the discarded values, as they can still provide crucial information about noise or irrelevant data components.

Linguistic Context

The phrase "after hard thresholding" functions as a prepositional phrase, indicating the temporal relationship of an event occurring subsequent to the application of hard thresholding. As Ludwig indicates, it's grammatically correct and used to set a sequence.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "after hard thresholding" is a grammatically correct prepositional phrase predominantly used within scientific and technical contexts. According to Ludwig, its purpose is to denote the timing or sequence of events in relation to the application of a hard threshold. Although the phrase is relatively rare, its usage is precise and crucial for clarity in academic writing. Best practices involve clearly specifying the post-thresholding analysis, and avoiding assumptions about the discarded values, since they can provide insights to the discarded data. While alternatives like "following hard thresholding" or "subsequent to hard thresholding" exist, the core meaning remains consistent: an action takes place once the hard thresholding process is complete.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

post hard thresholding

Replaces "after" with "post", indicating a time or sequence that directly follows the hard thresholding process.

subsequent to hard thresholding

Uses a more formal phrasing to denote the event that immediately follows the hard thresholding.

following hard thresholding

Employs "following" as a synonym for "after", maintaining the temporal relationship of the event.

upon hard thresholding

Indicates that something occurs immediately or very shortly after hard thresholding.

in the wake of hard thresholding

Suggests that something occurs as a direct consequence or result of hard thresholding.

resulting from hard thresholding

Shifts the focus to the outcome or result of hard thresholding, emphasizing causation.

as a consequence of hard thresholding

Highlights the consequential relationship between the hard thresholding and subsequent actions.

hard thresholding outcomes

Focuses solely on the results of hard thresholding, rather than the timing of events.

hard thresholding effects

Concentrates on the effects or impacts that hard thresholding has on the data or process.

hard thresholding completion

Emphasizes the finished status of hard thresholding and what happens after that point.

FAQs

How is "after hard thresholding" typically used in a sentence?

In technical writing, "after hard thresholding" is commonly used to indicate the next step or analysis performed on a dataset once a hard threshold has been applied. For example, "After hard thresholding, the remaining coefficients were analyzed for significant features".

What phrases are similar in meaning to "after hard thresholding"?

Similar phrases include "following hard thresholding", "subsequent to hard thresholding", or "post hard thresholding". These phrases all denote actions or states that occur once the hard thresholding process is complete.

In what contexts is "after hard thresholding" most appropriately used?

"After hard thresholding" is best suited for technical and scientific contexts where data filtering or noise reduction techniques are discussed. It precisely indicates the sequence of operations in signal or image processing.

What are the differences between hard and soft thresholding, and how does this affect the steps "after hard thresholding"?

Hard thresholding either keeps or eliminates coefficients based on a set threshold, while soft thresholding shrinks coefficients towards zero. After hard thresholding, analyses may focus on the retained, unaltered coefficients. In contrast, actions following soft thresholding might need to account for the altered values.